diff --git a/.DS_Store b/.DS_Store new file mode 100644 index 00000000..89a4c67b Binary files /dev/null and b/.DS_Store differ diff --git a/2020-07-runaway-electron-paper-scripts/runaway_electron_rate_plots.m b/2020-07-runaway-electron-paper-scripts/runaway_electron_rate_plots.m new file mode 100644 index 00000000..6c84b7ac --- /dev/null +++ b/2020-07-runaway-electron-paper-scripts/runaway_electron_rate_plots.m @@ -0,0 +1,557 @@ +% Produce the runaway electron fraction plots + +% Calculate the relativistic and non-relativistic runaway electron rates +% from what is in Franz's thesis (pg 71 - which comes from Connor and Hastie, Nucl. +% Fusion, 15:415, 1975). + +clear all; + +set(groot,'defaultLineLineWidth',2.0) +set(groot,'defaultAxesFontSize',20) +set(groot,'defaultLegendFontSize',20) + +cgs.e = 4.803e-10; +cgs.m_e = 9.109e-28; +cgs.c = 2.997e10; +cgs.amu = 1.66e-24; +cgs.kB = 1.38e-16; + +SI.e = 1.602e-19; +SI.c = 3e8; +SI.m_e = 9.1e-31; +SI.amu = 1.66e-27; +SI.eps0 = 8.854e-12; +SI.kB = 1.38e-23; + +Z_b = 1; +energy_eV = 20e3; +T_e_eV = 2/3*energy_eV; +T_e_K = T_e_eV * 11605; + +% calculate Dreicer E field in cgs + +cgs.n_e = 5e13; +cgs.coulomb_ln = 23.5-log(cgs.n_e^(1/2)*T_e_K^(-5/4))-sqrt(10^-5+((log(T_e_K)-2)^2)/16); % NRL forumulary +coulomb_ln = cgs.coulomb_ln; +cgs.th_e = cgs.m_e * cgs.c^2 / (T_e_eV); +% cgs.v_th = 4.19e7*T_e_eV^(1/2); +cgs.v_th = sqrt(cgs.kB*T_e_K/cgs.m_e); +cgs.E_D = 4*pi * cgs.e^3 * cgs.n_e * cgs.coulomb_ln / (cgs.m_e * cgs.v_th^2); % from Connor Hastie 1975 +cgs.E_R = 4*pi*cgs.n_e*cgs.e^3*cgs.coulomb_ln/(cgs.m_e*cgs.c^2); +cgs.v_c = @(E_cgs) sqrt(4*pi*cgs.e^3 * cgs.n_e * cgs.coulomb_ln / (cgs.m_e * E_cgs)); +disp(['E_D V/m (from cgs): ',num2str(cgs.E_D*300*100)]); +disp(['E_R V/m (from cgs): ',num2str(cgs.E_R*300*100)]); +disp(['E_R V/m (from cgs 2): ',num2str(cgs.E_D*300*100*cgs.kB*T_e_K/(cgs.m_e*cgs.c^2))]); +disp(['E_D / E_R : ', num2str(cgs.E_D/cgs.E_R)]); +disp(['v_th m/s (from cgs): ',num2str(cgs.v_th/100)]); + + +% calculate Dreicer E field in SI + +SI.n_e = cgs.n_e*1e6; +SI.v_th = sqrt(T_e_eV*SI.e/SI.m_e); +SI.coulomb_ln = coulomb_ln; +SI.E_D = SI.n_e*SI.e^3*SI.coulomb_ln/(2*pi*SI.eps0^2*SI.m_e ... + *SI.v_th^2);%1/(4*pi*SI.eps0^2) * SI.n_e * SI.e^3 * SI.coulomb_ln / (SI.m_e * SI.v_th^2); +disp(['E_D V/m (from SI): ', num2str(SI.E_D)]); +disp(['v_th m/s (from SI): ',num2str(SI.v_th)]); + +% calculate the RE production rate + +cgs.nu_ee2 = 4*pi * cgs.n_e * cgs.e^4 * cgs.coulomb_ln / (cgs.th_e^(3/2) * cgs.m_e^3 * cgs.c^3); +cgs.nu_ee = 4*pi * cgs.n_e * cgs.e^4 * cgs.coulomb_ln / (cgs.m_e^2 * cgs.v_th^3); +disp(['nu_ee 1/s (from cgs): ',num2str(cgs.nu_ee)]); +disp(['nu_ee 1/s (from cgs 2): ',num2str(cgs.nu_ee2)]); + +% normalized (norm) parameters for use in mirror2_velocity_div +% here we have 3 types of variables ... +% 1) T,n,v_th - absolute values in SI +% 2) T_ref, n_ref, v_th_ref - these are the "reference values" (or the "tilde" values in the manuscript) +% 3) T_norm, n_norm, v_th_norm - these are T_norm = T / T_ref + + +ref.energy_eV = 20e3; +ref.T_eV = 2/3*ref.energy_eV; +ref.T_K = ref.T_eV * 11605; +ref.n_e_m3 = 5e19; +ref.v_th = sqrt (2*ref.T_eV*SI.e / SI.m_e); +ref.coulomb_ln = 23.5-log((ref.n_e_m3*1e-6)^(1/2)*ref.T_K^(-5/4))-sqrt(10^-5+((log(ref.T_K)-2)^2)/16); +ref.E_D = SI.e^3 * ref.n_e_m3 * ref.coulomb_ln / (4*pi*SI.eps0^2 * ref.T_eV * SI.e); + +norm.delta = SI.v_th / SI.c; +norm.v_th = sqrt(T_e_eV / ref.T_eV); +norm.p = SI.m_e * ref.v_th; +norm.n = SI.n_e / ref.n_e_m3; %SI.n_e; +norm.nu_ee = (ref.T_eV/T_e_eV)^(3/2) * coulomb_ln / ref.coulomb_ln; +norm.tau = 10^5; % this is relative to the B field or some other thing not present in these calcs +norm.E = ref.E_D/2; +norm.n = SI.n_e/ref.n_e_m3; + +disp(['delta: ', num2str(norm.delta)]); +disp(['tau: ', num2str(norm.tau)]); % this is relative to the B field or some other thing not present in these calcs +disp(['E: ', num2str(norm.E), ' (this is E_D/2)']); +disp(['v_th: ', num2str(norm.v_th)]); +disp(['nu_ee: ', num2str(norm.nu_ee)]); +disp(['n: ', num2str(norm.n)]); + +% Scan over E/E_D (0 to 0.6) for Zb=1 - compare with Fig 9 (pg 68) of Franz + +ratio_max = 0.3; +N = 15; +ratio = linspace(0.2,ratio_max,N); + +% Franz +Cn = 1/SI.n_e; +T1 = @(E,Z_b) Cn .* cgs.nu_ee .* (E ./ cgs.E_D).^(3/16*Z_b+1); +T2 = @(E,Z_b) exp(-cgs.E_D./(4.*E)-sqrt((1+Z_b).*cgs.E_D./E)); + +% Kruskal & Bernstein +kruskal_bernstein = @(E) 0.35 .* E.^(-3/8) .* exp(-((2./E).^(1/2)+1./(4*E))); + +% Connor & Hastie 1975 eq (67) +C = 1; +T1 = @(E,Z) C .* cgs.n_e * cgs.nu_ee * (E/cgs.E_D).^(-3/16*(Z+1)); +T2 = @(E,Z) exp(-cgs.E_D./(4*E)-sqrt((1+Z).*cgs.E_D./E)); +T3 = @(E,Z) exp( -cgs.kB*T_e_K./(cgs.m_e.*cgs.c^2) * ( 1/8*(cgs.E_D./E).^2 + 2/3*(cgs.E_D./E).^(3/2).*(1+Z).^(1/2) ) ); +% T3 = @(E,Z) exp( -norm.delta.^2 * 0.5 * ( 1/8*(cgs.E_D./E).^2 + 2/3*(cgs.E_D./E).^(3/2).*(1+Z).^(1/2) ) ); % account for the vth^2=2T/m vs vth^2=T/m difference + +connor_hastie_nr = @(E,Z) T1(E,Z) .* T2(E,Z); +connor_hastie_r = @(E,Z) connor_hastie_nr(E,Z) .* T3(E,Z); + +% Kulsrud data + +kulsrud_E1 = [0.04,0.06,0.08,0.1]; +kulsrud_Z1 = [1.914e-6,5.411e-5,3.177e-4,1.004e-3]; + +kulsrud_E2 = [0.06,0.08,0.1]; +kulsrud_Z2 = [2.611e-5,1.735e-4,5.839e-4]; + +kulsrud_E3 = [0.08,0.1]; +kulsrud_Z3 = [1.047e-4,3.757e-4]; + +kulsrud_E10 = [0.08,0.1]; +kulsrud_Z10 = [9.0e-6,4.49e-5]; + +kulsrud_E008 = [1,2,3,10]; +kulsrud_Z008 = [3.177e-4,1.735e-4,1.047e-4,9.0e-6]; + +CH_normfac_nr = 1/(connor_hastie_nr(0.1*cgs.E_D,1)/kulsrud_Z1(end)); +CH_normfac_r = CH_normfac_nr; +KB_normfac = 1/(kruskal_bernstein(0.1)/kulsrud_Z1(end)); + +% Scan over E/E_D ratio +do_E_scan = true; +if do_E_scan + + + N2 = 15; + ratio_max2 = 0.1; + ratio2 = linspace(0.002,ratio_max2,N2); + args.p_max = 10; + args.v_th = ref.v_th; + args.nu_ee = norm.nu_ee; + args.tau = norm.tau; + args.n = ref.n_e_m3; + num_steps = 10; + + m_D = 3.3443*10^-27; %Deuterium mass in kg + m_He = 6.7*10^-27; %helium 4 mass in kg + m_Ne = 3.3509177*10^-26; %neon 20 in kg + + % Non-relativistic + args.delta = 0; + args.Z = 1; + args.m = m_D; + % for Z = [1 2 10] + for i=1:N2 + % args.E = 0.2*ratio2(i) * SI.E_D ; % E into asgard is 2*E/E_D per the normalization + args.E_D = SI.E_D; + args.frac = 0.005*ratio2(i); + %args.Z = Z6 +% if Z == 1 +% args.m = m_D; +% elseif Z == 2 +% args.m = m_He; +% else +% args.m = m_Ne; +% end + dt = 6.125e-04; + if dt > 2000 + dt = 2000; + end + num_steps = 1; + [~,~,~,~,~,outputs(i)] = asgard(@mirror2_velocity_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',4,'lev',4,'case',3,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true,'normalize_by_mass',true); + alpha_nr(i,1) = outputs(i).alpha_t{end}; + dt_nr(i,1) = dt; + end + +% end +% semilogy(dt_nr,alpha_nr(:,1)); +% % Relativistic +% args.delta = norm.delta; +% for Z = [1 2 10] +% for i=1:N2 +% args.E = ratio2(i) * SI.E_D; % E into asgard is 2*E/E_D per the normalization +% args.Z = Z; +% if Z == 1 +% args.m = m_D; +% elseif Z == 2 +% args.m = m_He; +% else +% args.m = m_Ne; +% end +% dt = 1e-4;%2./args.E.^2/num_steps; +% if dt > 2000 +% dt = 2000; +% end +% [~,~,~,~,~,outputs(i)] = asgard(@mirror2_velocity_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',4,'lev',4,'case',3,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true); +% alpha_r(i,Z) = outputs(i).alpha_t{end}; +% end +% end + + end + end + + % Relativistic + args.delta = norm.delta; + + + set(groot,'defaultLineLineWidth',2.0) + set(groot,'defaultAxesFontSize',20) + set(groot,'defaultLegendFontSize',14) + figure('Position',[0 0 600 600]) + semilogy(ratio,kruskal_bernstein(ratio)*KB_normfac,'LineWidth',10,'Color','#E8E7E7','DisplayName','K-B (nr)'); + title('RE production rate benchmark','Interpreter','latex'); + xlabel('$E/E_D$','Interpreter','latex'); + ylabel('RE production rate $\alpha$ [arb. units]','Interpreter','latex'); + ylim([1e-10 1]); + hold on + red = '#E74C3C'; + blue = '#2E86C1'; + green = '#229954'; + semilogy(ratio,connor_hastie_nr(ratio*cgs.E_D,1)*CH_normfac_nr,'LineStyle','--','DisplayName','C-H (nr, Z=1)','color',red); + semilogy(ratio,connor_hastie_r(ratio*cgs.E_D,1)*CH_normfac_r,'LineStyle',':','DisplayName','C-H (r, Z=1)','color',red); + semilogy(ratio,connor_hastie_nr(ratio*cgs.E_D,10)*CH_normfac_nr,'LineStyle','--','DisplayName','C-H (nr, Z=10)','color',blue); + semilogy(ratio,connor_hastie_r(ratio*cgs.E_D,10)*CH_normfac_r,'LineStyle',':','DisplayName','C-H (r, Z=10)','color',blue); + semilogy(kulsrud_E1,kulsrud_Z1,'Marker','s','MarkerSize',26,'MarkerFaceColor','auto','DisplayName','Kulsrud (nr, Z=1)','color',red); + semilogy(kulsrud_E2,kulsrud_Z2,'Marker','s','MarkerSize',26,'MarkerFaceColor','auto','DisplayName','Kulsrud (nr, Z=2)','color',green); + semilogy(kulsrud_E10,kulsrud_Z10,'Marker','s','MarkerSize',26,'MarkerFaceColor','auto','DisplayName','Kulsrud (nr, Z=10)','color',blue); + norm_fac = kulsrud_Z1(end)/alpha_nr(N2,1); + disp(['norm_fac: ',num2str(norm_fac)]); + hold on +<<<<<<< HEAD + semilogy(ratio2,alpha_nr(:,1)*norm_fac,'LineWidth',5,'DisplayName','ASGarD (nr, Z=1)','color','red'); + % semilogy(ratio2,alpha_nr(:,2)*norm_fac,'LineWidth',5,'DisplayName','ASGarD (nr, Z=2)','color','green'); + % semilogy(ratio2,alpha_nr(:,10)*norm_fac,'LineWidth',5,'DisplayName','ASGarD (nr, Z=10)','color','blue'); + + % semilogy(ratio2,alpha_r(:,1)*norm_fac,'LineWidth',5,'DisplayName','ASGarD (r, Z=1)','color','red','LineStyle',':'); + %semilogy(ratio2,alpha_r(:,2)*norm_fac,'LineWidth',5,'DisplayName','ASGarD (r, Z=2)','color','green','LineStyle',':'); + %semilogy(ratio2,alpha_r(:,10)*norm_fac,'LineWidth',5,'DisplayName','ASGarD (r, Z=10)','color','blue','LineStyle',':'); + legend + + hold off +end + +% Compare DoF required for given accuracy in alpha + +do_dof_scan = false; +if do_dof_scan + + args.p_max = 10; + args.v_th = norm.v_th; + args.nu_ee = norm.nu_ee; + args.tau = norm.tau; + args.n = norm.n; + args.delta = 0; + num_steps = 20; + + E = [0.1,0.07,0.055]; + E_string = {'010','007','0055'}; + + for i=1:numel(E) + args.E = E(i); + dt = 2./args.E.^2/num_steps; + deg = 3; + lev = 4; + if E(i)<0.06 + lev=4; + end + lev_str = num2str(lev); + + % Set this to produce the fullgrid (FG) results - these take + % considerable time. + do_FG = false; + if do_FG + [~,~,~,~,~,output_FG_deg4] = asgard(@mirror2_velocity_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',4,'lev',lev,'case',3,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','FG','update_params_each_timestep',true,'output_grid','fixed'); + save(['output_FG_E',E_string{i},'_deg4_lev',lev_str','.mat'],'output_FG_deg4'); + clear output_FG_deg4; + + [~,~,~,~,~,output_FG_deg5] = asgard(@mirror2_velocity_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',5,'lev',lev,'case',3,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','FG','update_params_each_timestep',true,'output_grid','fixed'); + save(['output_FG_E',E_string{i},'_deg5_lev',lev_str','.mat'],'output_FG_deg5'); + clear output_FG_deg5; + + [~,~,~,~,~,output_FG_deg6] = asgard(@mirror2_velocity_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',6,'lev',lev,'case',3,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','FG','update_params_each_timestep',true,'output_grid','fixed'); + save(['output_FG_E',E_string{i},'_deg6_lev',lev_str','.mat'],'output_FG_deg6'); + clear output_FG_deg6; + + [~,~,~,~,~,output_FG_deg7] = asgard(@mirror2_velocity_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',7,'lev',lev,'case',3,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','FG','update_params_each_timestep',true,'output_grid','fixed'); + save(['output_FG_E',E_string{i},'_deg7_lev',lev_str','.mat'],'output_FG_deg7'); + clear output_FG_deg7; + end + + % Set this to produce the sparsegrid (SG) and adaptive (ASG) + % results. + do_SG = true; + if do_SG + [~,~,~,~,~,output_SG] = asgard(@mirror2_velocity_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',deg,'lev',lev,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true,'output_grid','fixed'); + [~,~,~,~,~,output_SG_deg6] = asgard(@mirror2_velocity_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',6,'lev',lev,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true,'output_grid','fixed'); + [~,~,~,~,~,output_1em0] = asgard(@mirror2_velocity_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',deg,'lev',lev,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true,'adapt',true,'adapt_threshold',1e0,'output_grid','fixed','adapt_initial_condition',true); + [~,~,~,~,~,output_1em1] = asgard(@mirror2_velocity_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',deg,'lev',lev,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true,'adapt',true,'adapt_threshold',1e-1,'output_grid','fixed','adapt_initial_condition',true); + [~,~,~,~,~,output_1em2] = asgard(@mirror2_velocity_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',deg,'lev',lev,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true,'adapt',true,'adapt_threshold',1e-2,'output_grid','fixed','adapt_initial_condition',true); + [~,~,~,~,~,output_1em3] = asgard(@mirror2_velocity_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',deg,'lev',lev,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true,'adapt',true,'adapt_threshold',1e-3,'output_grid','fixed','adapt_initial_condition',true); + [~,~,~,~,~,output_1em4] = asgard(@mirror2_velocity_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',deg,'lev',lev,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true,'adapt',true,'adapt_threshold',1e-4,'output_grid','fixed','adapt_initial_condition',true); + [~,~,~,~,~,output_1em5] = asgard(@mirror2_velocity_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',deg,'lev',lev,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true,'adapt',true,'adapt_threshold',1e-5,'output_grid','fixed','adapt_initial_condition',true); + + alpha_SG(i,:) = cell2mat(output_SG.alpha_t); + alpha_SG_deg6(i,:) = cell2mat(output_SG_deg6.alpha_t); + alpha_1em0(i,:) = cell2mat(output_1em0.alpha_t); + alpha_1em1(i,:) = cell2mat(output_1em1.alpha_t); + alpha_1em2(i,:) = cell2mat(output_1em2.alpha_t); + alpha_1em3(i,:) = cell2mat(output_1em3.alpha_t); + alpha_1em4(i,:) = cell2mat(output_1em4.alpha_t); + alpha_1em5(i,:) = cell2mat(output_1em5.alpha_t); + + dof_SG(i) = numel(output_SG.fval_t{end}); + dof_SG_deg6(i) = numel(output_SG_deg6.fval_t{end}); + dof_1em0(i) = numel(output_1em0.fval_t{end}); + dof_1em1(i) = numel(output_1em1.fval_t{end}); + dof_1em2(i) = numel(output_1em2.fval_t{end}); + dof_1em3(i) = numel(output_1em3.fval_t{end}); + dof_1em4(i) = numel(output_1em4.fval_t{end}); + dof_1em5(i) = numel(output_1em5.fval_t{end}); + + end + end + + set(groot,'defaultLineLineWidth',2.0) + set(groot,'defaultAxesFontSize',20) + set(groot,'defaultLegendFontSize',14) + ms = 12; + lw = 2; + + % Plot the convergence of the FG results to set the "correct" answer to + % which the SG and ASG results need to converge to. + plot_FG_convergence = false; + if plot_FG_convergence + load('output_FG_E010_deg4_lev4.mat'); + output_FG_E010_deg4_lev4 = output_FG_deg4_lev4; + load('output_FG_E010_deg5_lev4.mat'); + output_FG_E010_deg5_lev4 = output_FG_deg5_lev4; + load('output_FG_E010_deg6_lev4.mat'); + output_FG_E010_deg6_lev4 = output_FG_deg6_lev4; + + load('output_FG_E007_deg4_lev4.mat'); + output_FG_E007_deg4_lev4 = output_FG_deg4_lev4; + load('output_FG_E007_deg5_lev4.mat'); + output_FG_E007_deg5_lev4 = output_FG_deg5_lev4; + load('output_FG_E007_deg6_lev4.mat'); + output_FG_E007_deg6_lev4 = output_FG_deg6_lev4; + load('output_FG_E007_deg7_lev4.mat'); + output_FG_E007_deg7_lev4 = output_FG_deg7; + + load('output_FG_E0055_deg4_lev5.mat'); + output_FG_E0055_deg4_lev5 = output_FG_deg4; + load('output_FG_E0055_deg5_lev5.mat'); + output_FG_E0055_deg5_lev5 = output_FG_deg5; + + load('output_FG_E0055_deg4_lev4.mat'); + output_FG_E0055_deg4_lev4 = output_FG_deg4; + load('output_FG_E0055_deg5_lev4.mat'); + output_FG_E0055_deg5_lev4 = output_FG_deg5; + load('output_FG_E0055_deg6_lev4.mat'); + output_FG_E0055_deg6_lev4 = output_FG_deg6; + load('output_FG_E0055_deg7_lev4.mat'); + output_FG_E0055_deg7_lev4 = output_FG_deg7; + + + figure('Position',[0 0 600 600]) + dof = numel(output_FG_E010_deg4_lev4.fval_t{end}); + semilogy(cell2mat(output_FG_E010_deg4_lev4.alpha_t),'DisplayName',['FG (E/E_D=0.1,deg=4,lev=4), DoF=',num2str(dof)],'LineWidth',lw,'Color','#3D67F5','LineStyle','-.'); + xlabel('{Normalized Time ($\tilde{t}=t/\tilde{\nu}_{ee}$)}','Interpreter','latex'); + ylabel('{RE Production Rate ($\alpha(\tilde{t}))$ [arb. units]}','Interpreter','latex'); + title('Full Grid (FG) Convergence of $\alpha$','Interpreter','latex'); + hold on + dof = numel(output_FG_E010_deg5_lev4.fval_t{end}); + semilogy(cell2mat(output_FG_E010_deg5_lev4.alpha_t),'DisplayName',['FG (E/E_D=0.1,deg=5,lev=4), DoF=',num2str(dof)],'LineWidth',lw,'Color','#3D67F5','LineStyle','--'); + dof = numel(output_FG_E010_deg6_lev4.fval_t{end}); + semilogy(cell2mat(output_FG_E010_deg6_lev4.alpha_t),'DisplayName',['FG (E/E_D=0.1,deg=6,lev=4), DoF=',num2str(dof)],'LineWidth',lw,'Color','#3D67F5'); + + dof = numel(output_FG_E007_deg4_lev4.fval_t{end}); + semilogy(cell2mat(output_FG_E007_deg4_lev4.alpha_t),'DisplayName',['FG (E/E_D=0.07,deg=4,lev=4), DoF=',num2str(dof)],'LineWidth',lw,'Color','#52A95E','LineStyle','-.'); + dof = numel(output_FG_E007_deg5_lev4.fval_t{end}); + semilogy(cell2mat(output_FG_E007_deg5_lev4.alpha_t),'DisplayName',['FG (E/E_D=0.07,deg=5,lev=4), DoF=',num2str(dof)],'LineWidth',lw,'Color','#52A95E','LineStyle','--'); + dof = numel(output_FG_E007_deg6_lev4.fval_t{end}); + semilogy(cell2mat(output_FG_E007_deg6_lev4.alpha_t),'DisplayName',['FG (E/E_D=0.07,deg=6,lev=4), DoF=',num2str(dof)],'LineWidth',lw,'Color','#52A95E','LineStyle',':'); + dof = numel(output_FG_E007_deg7_lev4.fval_t{end}); + semilogy(cell2mat(output_FG_E007_deg7_lev4.alpha_t),'DisplayName',['FG (E/E_D=0.07,deg=7,lev=4), DoF=',num2str(dof)],'LineWidth',lw,'Color','#52A95E'); + + dof = numel(output_FG_E0055_deg4_lev4.fval_t{end}); + semilogy(cell2mat(output_FG_E0055_deg4_lev4.alpha_t),'DisplayName',['FG (E/E_D=0.055,deg=4,lev=4), DoF=',num2str(dof)],'LineWidth',lw,'Color','#EE1839','LineStyle','-.'); + dof = numel(output_FG_E0055_deg5_lev4.fval_t{end}); + semilogy(cell2mat(output_FG_E0055_deg5_lev4.alpha_t),'DisplayName',['FG (E/E_D=0.055,deg=5,lev=4), DoF=',num2str(dof)],'LineWidth',lw,'Color','#EE1839','LineStyle','--'); + dof = numel(output_FG_E0055_deg6_lev4.fval_t{end}); + semilogy(cell2mat(output_FG_E0055_deg6_lev4.alpha_t),'DisplayName',['FG (E/E_D=0.055,deg=6,lev=4), DoF=',num2str(dof)],'LineWidth',lw,'Color','#EE1839','LineStyle',':'); + dof = numel(output_FG_E0055_deg7_lev4.fval_t{end}); + semilogy(cell2mat(output_FG_E0055_deg7_lev4.alpha_t),'DisplayName',['FG (E/E_D=0.055,deg=7,lev=4), DoF=',num2str(dof)],'LineWidth',lw,'Color','#EE1839'); + +% dof = numel(output_FG_E0055_deg4_lev5.fval_t{end}); +% semilogy(cell2mat(output_FG_E0055_deg4_lev5.alpha_t),'DisplayName',['FG (E/E_D=0.055,deg=4,lev=5), DoF=',num2str(dof)],'LineWidth',4,'Color','#A569BD','LineStyle','-.'); + dof = numel(output_FG_E0055_deg5_lev5.fval_t{end}); + semilogy(cell2mat(output_FG_E0055_deg5_lev5.alpha_t),'DisplayName',['FG (E/E_D=0.055,deg=5,lev=5), DoF=',num2str(dof)],'LineWidth',4,'Color','#A569BD','LineStyle',':'); + + legend('FontSize',10) + ylim([10^-8 10^-1]) + + legend + hold off + + end + + plot_SG = true; + if plot_SG + if ~exist('output_FG_E010_deg4_lev4') + load('output_FG_E010_deg4_lev4.mat'); + output_FG_E010_deg4_lev4 = output_FG_deg4_lev4; + load('output_FG_E007_deg4_lev4.mat'); + output_FG_E007_deg4_lev4 = output_FG_deg4_lev4; + load('output_FG_E007_deg6_lev4.mat'); + output_FG_E007_deg6_lev4 = output_FG_deg6_lev4; + load('output_FG_E0055_deg4_lev4.mat'); + output_FG_E0055_deg4_lev4 = output_FG_deg4; + load('output_FG_E0055_deg6_lev4.mat'); + output_FG_E0055_deg6_lev4 = output_FG_deg6; + end + lw=2; + ms=12; + figure('Position',[0 0 600 600]) + dof = numel(output_FG_E010_deg4_lev4.fval_t{end}); + semilogy(cell2mat(output_FG_E010_deg4_lev4.alpha_t),'DisplayName',['FG (E/E_D=0.1,deg=4,lev=4), DoF=',num2str(dof)],'LineWidth',lw,'Color','#3D67F5'); + xlabel('{Normalized Time ($\tilde{t}=t/\tilde{\nu}_{ee}$)}','Interpreter','latex'); + ylabel('{RE Production Rate ($\alpha(\tilde{t}))$ [arb. units]}','Interpreter','latex'); + title('Sparse Grid (SG) Convergence of $\alpha$','Interpreter','latex'); + hold on + dof = numel(output_FG_E007_deg4_lev4.fval_t{end}); + semilogy(cell2mat(output_FG_E007_deg4_lev4.alpha_t),'DisplayName',['FG (E/E_D=0.07,deg=4,lev=4), DoF=',num2str(dof)],'LineWidth',lw,'Color','#52A95E','LineStyle','--'); + dof = numel(output_FG_E007_deg6_lev4.fval_t{end}); + semilogy(cell2mat(output_FG_E007_deg6_lev4.alpha_t),'DisplayName',['FG (E/E_D=0.07,deg=6,lev=4), DoF=',num2str(dof)],'LineWidth',lw,'Color','#52A95E'); + dof = numel(output_FG_E0055_deg4_lev4.fval_t{end}); + semilogy(cell2mat(output_FG_E0055_deg4_lev4.alpha_t),'DisplayName',['FG (E/E_D=0.055,deg=4,lev=4), DoF=',num2str(dof)],'LineWidth',lw,'Color','#A569BD','LineStyle','--'); + dof = numel(output_FG_E0055_deg6_lev4.fval_t{end}); + semilogy(cell2mat(output_FG_E0055_deg6_lev4.alpha_t),'DisplayName',['FG (E/E_D=0.055,deg=6,lev=4), DoF=',num2str(dof)],'LineWidth',lw,'Color','#A569BD'); + + semilogy(alpha_SG(1,:),'DisplayName',['SG (E/E_D=0.1,deg=4,lev=4), DoF=',num2str(dof_SG(1))],'Color','black','Marker','s','Color','#3D67F5','MarkerSize',ms,'LineStyle','none'); + semilogy(alpha_SG(2,:),'DisplayName',['SG (E/E_D=0.07,deg=4,lev=4), DoF=',num2str(dof_SG(2))],'Color','black','Marker','s','Color','#52A95E','MarkerSize',ms,'LineStyle','none'); + semilogy(alpha_SG(3,:),'DisplayName',['SG (E/E_D=0.055,deg=4,lev=4), DoF=',num2str(dof_SG(3))],'Color','black','Marker','s','Color','#A569BD','MarkerSize',ms,'LineStyle','none'); + semilogy(alpha_SG_deg6(2,:),'DisplayName',['SG (E/E_D=0.07,deg=6,lev=4), DoF=',num2str(dof_SG_deg6(2))],'Color','black','Marker','o','Color','#52A95E','MarkerSize',ms,'LineStyle','none'); + semilogy(alpha_SG_deg6(3,:),'DisplayName',['SG (E/E_D=0.055,deg=6,lev=4), DoF=',num2str(dof_SG_deg6(3))],'Color','black','Marker','o','Color','#A569BD','MarkerSize',ms,'LineStyle','none'); + legend('FontSize',10) + ylim([10^-8 10^-1]) + legend + hold off + end + + plot_ASG = true; + if plot_ASG + if ~exist('output_FG_E010_deg4_lev4') + load('output_FG_E010_deg4_lev4.mat'); + output_FG_E010_deg4_lev4 = output_FG_deg4_lev4; + load('output_FG_E007_deg6_lev4.mat'); + output_FG_E007_deg6_lev4 = output_FG_deg6_lev4; + load('output_FG_E0055_deg6_lev4.mat'); + output_FG_E0055_deg6_lev4 = output_FG_deg6; + end + figure('Position',[0 0 600 600]) + dof = numel(output_FG_E010_deg4_lev4.fval_t{end}); + semilogy(cell2mat(output_FG_E010_deg4_lev4.alpha_t),'DisplayName',['FG (E/E_D=0.1,deg=4,lev=4), DoF=',num2str(dof)],'LineWidth',lw,'Color','#3D67F5'); + xlabel('{Normalized Time ($\tilde{t}=t/\tilde{\nu}_{ee}$)}','Interpreter','latex'); + ylabel('{RE Production Rate ($\alpha(\tilde{t}))$ [arb. units]}','Interpreter','latex'); + title('Adaptive Sparse Grid (ASG) Convergence of $\alpha$','Interpreter','latex'); + hold on + dof = numel(output_FG_E007_deg6_lev4.fval_t{end}); + semilogy(cell2mat(output_FG_E007_deg6_lev4.alpha_t),'DisplayName',['FG (E/E_D=0.07,deg=6,lev=4), DoF=',num2str(dof)],'LineWidth',lw,'Color','#52A95E'); + dof = numel(output_FG_E0055_deg6_lev4.fval_t{end}); + semilogy(cell2mat(output_FG_E0055_deg6_lev4.alpha_t),'DisplayName',['FG (E/E_D=0.055,deg=6,lev=4), DoF=',num2str(dof)],'LineWidth',lw,'Color','#A569BD'); + + semilogy(alpha_SG(1,:),'DisplayName',['SG (E/E_D=0.1,deg=4,lev=4), DoF=',num2str(dof_SG(1))],'Color','#3D67F5','LineStyle','--'); +% semilogy(alpha_1em1(1,:),'DisplayName',['ASG 1e-1 (E/E_D=0.1,deg=4), DoF=',num2str(dof_1em1(1))],'Marker','s','Color','#3D67F5','MarkerSize',ms,'LineStyle',':'); +% semilogy(alpha_1em2(1,:),'DisplayName',['1e-2 (E/E_D=0.1), DoF=',num2str(dof_1em2(1))],'Marker','o','Color','#3D67F5','MarkerSize',ms); + semilogy(alpha_1em3(1,:),'DisplayName',['ASG 1e-3 (E/E_D=0.1,deg=4), DoF=',num2str(dof_1em3(1))],'Marker','d','Color','#3D67F5','MarkerSize',ms); +% semilogy(alpha_1em4(1,:),'DisplayName',['1e-4 (E/E_D=0.1), DoF=',num2str(dof_1em4(1))],'Marker','*','Color','#3D67F5','MarkerSize',ms); + + semilogy(alpha_SG(2,:),'DisplayName',['SG (E/E_D=0.07,deg=4,lev=4), DoF=',num2str(dof_SG(2))],'Color','#52A95E','LineStyle','--'); +% semilogy(alpha_1em1(2,:),'DisplayName',['ASG 1e-1 (E/E_D=0.07,deg=4), DoF=',num2str(dof_1em1(2))],'Marker','s','Color','#52A95E','MarkerSize',ms,'LineStyle',':'); +% semilogy(alpha_1em2(2,:),'DisplayName',['1e-2 (E/E_D=0.07), DoF=',num2str(dof_1em2(2))],'Marker','o','Color','#52A95E','MarkerSize',ms); +% semilogy(alpha_1em3(2,:),'DisplayName',['1e-3 (E/E_D=0.07), DoF=',num2str(dof_1em3(2))],'Marker','d','Color','#52A95E','MarkerSize',ms); + semilogy(alpha_1em4(2,:),'DisplayName',['ASG 1e-4 (E/E_D=0.07,deg=4), DoF=',num2str(dof_1em4(2))],'Marker','*','Color','#52A95E','MarkerSize',ms); + + semilogy(alpha_SG(3,:),'DisplayName',['SG (E/E_D=0.055,deg=4,lev=4), DoF=',num2str(dof_SG(3))],'Color','#A569BD','LineStyle','--'); +% semilogy(alpha_1em1(3,:),'DisplayName',['ASG 1e-1 (E/E_D=0.055,deg=4), DoF=',num2str(dof_1em1(3))],'Marker','s','Color','#A569BD','MarkerSize',ms,'LineStyle',':'); +% semilogy(alpha_1em2(3,:),'DisplayName',['1e-2 (E/E_D=0.055), DoF=',num2str(dof_1em2(3))],'Marker','o','Color','#A569BD','MarkerSize',ms); +% semilogy(alpha_1em3(3,:),'DisplayName',['1e-3 (E/E_D=0.055), DoF=',num2str(dof_1em3(3))],'Marker','d','Color','#A569BD','MarkerSize',ms); + semilogy(alpha_1em4(3,:),'DisplayName',['ASG 1e-4 (E/E_D=0.055,deg=4), DoF=',num2str(dof_1em4(3))],'Marker','*','Color','#A569BD','MarkerSize',ms); +% semilogy(alpha_1em5(3,:),'DisplayName',['1e-5 (E/E_D=0.055), DoF=',num2str(dof_1em5(3))],'Marker','s','Color','#A569BD','MarkerSize',ms); + legend('FontSize',10) + ylim([10^-8 10^-1]) + hold off + end + +end + + +% Scan over Z +do_Z_scan = false; +if do_Z_scan + Z = linspace(1,10,100); + E_ED = 0.08; + figure + semilogy(Z,connor_hastie_nr(E_ED*cgs.E_D,Z)); + hold on + semilogy(Z,connor_hastie_r(E_ED*cgs.E_D,Z)); + norm_fac = connor_hastie_nr(E_ED*cgs.E_D,1)/kulsrud_Z008(1); + semilogy(kulsrud_E008,kulsrud_Z008*norm_fac,'Marker','s','MarkerSize',16,'MarkerFaceColor','auto'); + % ylim([1e-10 1]); + + Z2 = 1:10; + for i=1:numel(Z2) + args.E = E_ED * SI.E_D / norm.E; % E into asgard is 2*E/E_D per the normalization + args.Z = Z2(i); + args.p_max = 10; + args.v_th = norm.v_th; + args.delta = 0; + args.nu_ee = norm.nu_ee; + args.tau = norm.tau; + args.n = norm.n; + + E_cgs = args.E / 300 / 100; + v_c_cgs = cgs.v_c(E_cgs+1e-6); + v_c_SI = v_c_cgs/100; + v_c_norm = v_c_SI * SI.m_e / norm.p; + disp(['v_c (cm/s): ',num2str(v_c_cgs)]); + disp(['v_c (m/s): ',num2str(v_c_SI)]); + disp(['v_c (norm): ', num2str(v_c_norm)]); + + num_steps = 10; + dt = 2./args.E.^2/num_steps; + disp(i); + [~,~,~,~,~,outputs(i)] = asgard(@mirror2_velocity_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',4,'lev',4,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true); + alpha_Z(i) = outputs(i).alpha_t{end}; + end + + norm_fac = connor_hastie_nr(E_ED*cgs.E_D,1)/alpha_Z(1); + semilogy(Z2,alpha_Z*norm_fac,'Marker','none','MarkerSize',16,'MarkerFaceColor','auto'); + legend('C-H (nr)','C-H (r)','kulsrud (E/E_D=0.08)', 'alpha(Z)'); + hold off +end + +disp(''); + diff --git a/2020-10-mirror_3D_scripts/dpitch_long_i.txt b/2020-10-mirror_3D_scripts/dpitch_long_i.txt new file mode 100644 index 00000000..9bb7cd48 --- /dev/null +++ b/2020-10-mirror_3D_scripts/dpitch_long_i.txt @@ -0,0 +1,15 @@ + 7.952452671E-02 1.129492901E-01 5.941727353E-02 4.820582348E-02 4.205907478E-02 3.804727771E-02 3.518877981E-02 3.304121677E-02 3.137077637E-02 3.004056109E-02 + 2.896447062E-02 2.808543543E-02 2.736411117E-02 2.677256624E-02 2.629055317E-02 2.590320725E-02 2.559957714E-02 2.537166455E-02 2.521378977E-02 2.512217608E-02 + 2.509468969E-02 2.513069855E-02 2.523103142E-02 2.539803169E-02 2.563571299E-02 2.595003751E-02 2.634935658E-02 2.684508125E-02 2.745269801E-02 2.819332669E-02 + 2.909617023E-02 3.020250455E-02 3.157247937E-02 3.329740395E-02 3.552366840E-02 1.852512870E-02 5.273452973E-04 1.051280553E-03 1.574664544E-03 2.093190533E-03 + 2.606449645E-03 3.114289632E-03 3.612702340E-03 4.103848307E-03 4.584888596E-03 5.052951443E-03 5.509961183E-03 5.952774356E-03 6.380680873E-03 6.793063026E-03 + 7.187307084E-03 7.563505927E-03 7.919970508E-03 8.254927667E-03 8.567450786E-03 8.855783065E-03 9.117702407E-03 9.350836405E-03 9.553584580E-03 9.720618113E-03 + 9.849303078E-03 9.936221244E-03 9.972213075E-03 9.952859362E-03 9.867414270E-03 9.702892042E-03 9.449252096E-03 9.080992811E-03 8.580439098E-03 7.927108237E-03 + 7.086565160E-03 6.044876865E-03 4.789057312E-03 3.328063965E-03 1.021491200E-01 1.021491200E-01 3.328063965E-03 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4.97080E-30 4.97080E-30 4.97080E-30 4.97080E-30 4.97080E-30 4.97080E-30 4.97079E-30 + 4.97079E-30 4.97079E-30 4.97079E-30 4.97079E-30 4.97079E-30 4.97078E-30 4.97076E-30 4.97075E-30 4.97073E-30 4.97072E-30 + 4.97070E-30 4.97069E-30 4.97067E-30 4.97066E-30 4.97064E-30 4.97063E-30 4.97062E-30 4.97060E-30 4.97059E-30 4.97058E-30 + 4.97056E-30 4.97055E-30 4.97054E-30 4.97053E-30 4.97052E-30 4.97050E-30 4.97049E-30 4.97048E-30 4.97047E-30 4.97046E-30 + 4.97045E-30 4.97043E-30 4.97042E-30 4.97041E-30 4.97040E-30 4.97039E-30 4.97038E-30 4.97037E-30 4.97036E-30 4.97035E-30 + 2.91687E-30 2.91688E-30 2.91688E-30 2.91689E-30 2.91690E-30 2.91690E-30 2.91691E-30 2.91691E-30 2.91692E-30 2.91693E-30 + 2.91693E-30 2.91694E-30 2.91695E-30 2.91695E-30 2.91696E-30 2.91697E-30 2.91697E-30 2.91698E-30 2.91699E-30 2.91700E-30 + 2.91700E-30 2.91701E-30 2.91702E-30 2.91703E-30 2.91704E-30 2.91704E-30 2.91705E-30 2.91706E-30 2.91707E-30 2.91708E-30 + 2.91709E-30 2.91709E-30 2.91710E-30 2.91711E-30 2.91712E-30 2.91713E-30 2.91713E-30 2.91713E-30 2.91713E-30 2.91713E-30 + 2.91713E-30 2.91713E-30 2.91713E-30 2.91713E-30 2.91714E-30 2.91714E-30 2.91714E-30 2.91714E-30 2.91714E-30 2.91714E-30 + 2.91714E-30 2.91714E-30 2.91715E-30 2.91715E-30 2.91715E-30 2.91715E-30 2.91715E-30 2.91715E-30 2.91716E-30 2.91716E-30 + 2.91716E-30 2.91716E-30 2.91716E-30 2.91716E-30 2.91717E-30 2.91717E-30 2.91717E-30 2.91717E-30 2.91717E-30 2.91717E-30 + 2.91717E-30 2.91717E-30 2.91717E-30 2.91717E-30 2.91717E-30 2.91717E-30 2.91717E-30 2.91717E-30 2.91717E-30 2.91717E-30 + 2.91717E-30 2.91717E-30 2.91717E-30 2.91717E-30 2.91717E-30 2.91717E-30 2.91716E-30 2.91716E-30 2.91716E-30 2.91716E-30 + 2.91716E-30 2.91716E-30 2.91715E-30 2.91715E-30 2.91715E-30 2.91715E-30 2.91715E-30 2.91715E-30 2.91714E-30 2.91714E-30 + 2.91714E-30 2.91714E-30 2.91714E-30 2.91714E-30 2.91714E-30 2.91714E-30 2.91713E-30 2.91713E-30 2.91713E-30 2.91713E-30 + 2.91713E-30 2.91713E-30 2.91713E-30 2.91713E-30 2.91713E-30 2.91712E-30 2.91711E-30 2.91710E-30 2.91709E-30 2.91709E-30 + 2.91708E-30 2.91707E-30 2.91706E-30 2.91705E-30 2.91704E-30 2.91704E-30 2.91703E-30 2.91702E-30 2.91701E-30 2.91700E-30 + 2.91700E-30 2.91699E-30 2.91698E-30 2.91697E-30 2.91697E-30 2.91696E-30 2.91695E-30 2.91695E-30 2.91694E-30 2.91693E-30 + 2.91693E-30 2.91692E-30 2.91691E-30 2.91691E-30 2.91690E-30 2.91690E-30 2.91689E-30 2.91688E-30 2.91688E-30 2.91687E-30 diff --git a/2020-10-mirror_3D_scripts/interpolate_numerical_distribution.m b/2020-10-mirror_3D_scripts/interpolate_numerical_distribution.m new file mode 100644 index 00000000..cfc65965 --- /dev/null +++ b/2020-10-mirror_3D_scripts/interpolate_numerical_distribution.m @@ -0,0 +1,61 @@ +function F_out = interpolate_numerical_distribution() + + function out = F2(u,z) + out = ones(numel(u),numel(z)); + if size(u) == size(z) + for i = 1:numel(u) + for j = 1:numel(z) + out(i,j) = F(u(i),z(j)); + end + end + elseif isscalar(u) + for j = 1:numel(z) + out(j) = F(u,z(j)); + end + end + end + +pitch_file = fopen('pitch_i.txt', 'r'); +vel_file = fopen('u_j.txt', 'r'); +dist_file = fopen('f_ij.txt', 'r'); + +z = fscanf(pitch_file, '%f'); +u = fscanf(vel_file, '%f'); +f_vals = fscanf(dist_file, '%f'); + +size_f = length(f_vals); +num = sqrt(size_f); + +n_o = 8e14; +temp = 1.6022e-10; %temperature in erg +m_e = 9.109*10^-28; +u_th = sqrt(2*temp/m_e); +lIndex = [0 1 2]; + +%[u,z] = meshgrid(vel_vals,pitch_vals); +%maxwell = n_o.*exp(-u.^2./u_th^2).*(z.*0 + 1)./(u_th.^3.*pi^(3/2)); + +analytic = @(x,y) n_o.*exp(-x.^2./u_th^2).*(y.*0 + 1)./(u_th.^3.*pi^(3/2)); +f_vals = reshape(f_vals, [num num]); + +% ax1 = subplot(1,3,1); +% contour(vel_vals,pitch_vals,f_vals); +% ax2 = subplot(1,3,2); +% contour(u,z,analytic(u,z)); + +%u = u'; + +%z = z'; + +F = griddedInterpolant({u,z},f_vals'); +F_out = @F2; + +%ax3 = subplot(1,3,3); +%f_plot = F_out(u(:),z(:)); +%f_plot = reshape(f_plot, size(u)); +%contour(u,z,f_plot); +% + + + +end \ No newline at end of file diff --git a/2020-10-mirror_3D_scripts/pitch_i.txt b/2020-10-mirror_3D_scripts/pitch_i.txt new file mode 100644 index 00000000..0ed041c7 --- /dev/null +++ b/2020-10-mirror_3D_scripts/pitch_i.txt @@ -0,0 +1,15 @@ + 0.00000E+00 1.59049E-01 2.25899E-01 2.77884E-01 3.22310E-01 3.62002E-01 3.98405E-01 4.32379E-01 4.64487E-01 4.95121E-01 + 5.24568E-01 5.53050E-01 5.80739E-01 6.07778E-01 6.34284E-01 6.60359E-01 6.86091E-01 7.11558E-01 7.36834E-01 7.61986E-01 + 7.87078E-01 8.12175E-01 8.37340E-01 8.62637E-01 8.88136E-01 9.13909E-01 9.40036E-01 9.66607E-01 9.93726E-01 1.02151E+00 + 1.05011E+00 1.07971E+00 1.11052E+00 1.14285E+00 1.17711E+00 1.21390E+00 1.21416E+00 1.21495E+00 1.21627E+00 1.21810E+00 + 1.22045E+00 1.22331E+00 1.22668E+00 1.23054E+00 1.23489E+00 1.23971E+00 1.24499E+00 1.25073E+00 1.25690E+00 1.26349E+00 + 1.27049E+00 1.27787E+00 1.28561E+00 1.29371E+00 1.30212E+00 1.31084E+00 1.31983E+00 1.32908E+00 1.33854E+00 1.34818E+00 + 1.35798E+00 1.36788E+00 1.37785E+00 1.38783E+00 1.39776E+00 1.40756E+00 1.41716E+00 1.42646E+00 1.43532E+00 1.44362E+00 + 1.45118E+00 1.45779E+00 1.46327E+00 1.46737E+00 1.46992E+00 1.67167E+00 1.67422E+00 1.67833E+00 1.68380E+00 1.69042E+00 + 1.69797E+00 1.70627E+00 1.71513E+00 1.72443E+00 1.73403E+00 1.74384E+00 1.75377E+00 1.76374E+00 1.77371E+00 1.78362E+00 + 1.79341E+00 1.80306E+00 1.81252E+00 1.82176E+00 1.83075E+00 1.83947E+00 1.84789E+00 1.85598E+00 1.86373E+00 1.87111E+00 + 1.87810E+00 1.88469E+00 1.89086E+00 1.89660E+00 1.90188E+00 1.90670E+00 1.91105E+00 1.91491E+00 1.91828E+00 1.92114E+00 + 1.92349E+00 1.92533E+00 1.92664E+00 1.92743E+00 1.92770E+00 1.96448E+00 1.99874E+00 2.03107E+00 2.06189E+00 2.09148E+00 + 2.12008E+00 2.14787E+00 2.17499E+00 2.20156E+00 2.22768E+00 2.25346E+00 2.27896E+00 2.30425E+00 2.32942E+00 2.35451E+00 + 2.37961E+00 2.40476E+00 2.43003E+00 2.45550E+00 2.48123E+00 2.50731E+00 2.53381E+00 2.56085E+00 2.58854E+00 2.61702E+00 + 2.64647E+00 2.67711E+00 2.70921E+00 2.74319E+00 2.77959E+00 2.81928E+00 2.86371E+00 2.91569E+00 2.98254E+00 3.14159E+00 diff --git a/2020-10-mirror_3D_scripts/pitch_long_i.txt b/2020-10-mirror_3D_scripts/pitch_long_i.txt new file mode 100644 index 00000000..de49d7c6 --- /dev/null +++ b/2020-10-mirror_3D_scripts/pitch_long_i.txt @@ -0,0 +1,15 @@ + 0.000000000E+00 1.590490534E-01 2.258985802E-01 2.778836005E-01 3.223102271E-01 3.620017501E-01 3.984047825E-01 4.323793097E-01 4.644872161E-01 4.951208624E-01 + 5.245683382E-01 5.530498037E-01 5.807392091E-01 6.077780260E-01 6.342843416E-01 6.603591323E-01 6.860907561E-01 7.115582866E-01 7.368340852E-01 7.619858662E-01 + 7.870784373E-01 8.121752455E-01 8.373398344E-01 8.626373084E-01 8.881358978E-01 9.139087343E-01 9.400359728E-01 9.666074475E-01 9.937261353E-01 1.021512844E+00 + 1.050112789E+00 1.079705184E+00 1.110517798E+00 1.142850143E+00 1.177112606E+00 1.213897480E+00 1.214162863E+00 1.214952170E+00 1.216265424E+00 1.218101499E+00 + 1.220451805E+00 1.223314399E+00 1.226680385E+00 1.230539803E+00 1.234888081E+00 1.239709580E+00 1.244993984E+00 1.250729503E+00 1.256899533E+00 1.263490865E+00 + 1.270485659E+00 1.277865479E+00 1.285612671E+00 1.293705420E+00 1.302122526E+00 1.310840321E+00 1.319834092E+00 1.329075726E+00 1.338535765E+00 1.348182895E+00 + 1.357977001E+00 1.367881501E+00 1.377849444E+00 1.387825928E+00 1.397755162E+00 1.407560756E+00 1.417160946E+00 1.426459260E+00 1.435322932E+00 1.443620138E+00 + 1.451177149E+00 1.457793269E+00 1.463266902E+00 1.467371383E+00 1.469923030E+00 1.671669623E+00 1.674221270E+00 1.678325751E+00 1.683799385E+00 1.690415505E+00 + 1.697972515E+00 1.706269722E+00 1.715133393E+00 1.724431707E+00 1.734031898E+00 1.743837491E+00 1.753766726E+00 1.763743210E+00 1.773711152E+00 1.783615652E+00 + 1.793409758E+00 1.803056889E+00 1.812516928E+00 1.821758561E+00 1.830752332E+00 1.839470128E+00 1.847887234E+00 1.855979983E+00 1.863727175E+00 1.871106995E+00 + 1.878101789E+00 1.884693121E+00 1.890863151E+00 1.896598670E+00 1.901883073E+00 1.906704572E+00 1.911052850E+00 1.914912269E+00 1.918278255E+00 1.921140848E+00 + 1.923491154E+00 1.925327229E+00 1.926640483E+00 1.927429790E+00 1.927695174E+00 1.964480048E+00 1.998742511E+00 2.031074856E+00 2.061887470E+00 2.091479865E+00 + 2.120079810E+00 2.147866518E+00 2.174985206E+00 2.201556681E+00 2.227683919E+00 2.253456756E+00 2.278955345E+00 2.304252819E+00 2.329417408E+00 2.354514216E+00 + 2.379606787E+00 2.404758568E+00 2.430034367E+00 2.455501898E+00 2.481233521E+00 2.507308312E+00 2.533814628E+00 2.560853444E+00 2.588542850E+00 2.617024315E+00 + 2.646471791E+00 2.677105438E+00 2.709213344E+00 2.743187871E+00 2.779590904E+00 2.819282426E+00 2.863709053E+00 2.915694073E+00 2.982543600E+00 3.141592654E+00 diff --git a/2020-10-mirror_3D_scripts/plot_mirror_output.m b/2020-10-mirror_3D_scripts/plot_mirror_output.m index 86bc30d9..b57281f3 100644 --- a/2020-10-mirror_3D_scripts/plot_mirror_output.m +++ b/2020-10-mirror_3D_scripts/plot_mirror_output.m @@ -1,45 +1,196 @@ -function plot_mirror_output(nodes, f_nD, f_nD_analytic, pde) +function plot_mirror_output(nodes, outputs, pde, opts) - x = nodes{1}; - y = nodes{2}; - z = nodes{3}; - - nx = numel(x); - ny = numel(y); - nz = numel(z); - - %% + n_cgs = 8e14; %equilibrium density in cm.^-3 + m_e_cgs = 9.109*10^-28; %electron mass in g + m_D_cgs = 3.3443*10^-24; %Deuterium mass in g + m_He_cgs = 6.7*10^-24; %helium 4 mass in g + m_B_cgs = 1.82*10^-23; %Boron 11 mass in g + m_Ne_cgs = 3.3509177*10^-23; %Neon mass in g + temp_cgs = 1.6022e-10; %temperature in erg + params_cgs.a.n = n_cgs; + params_cgs.b.n = n_cgs; + params_cgs.b2.n = n_cgs; + % params_cgs.a.vth = sqrt(2*temp_cgs/m_e_cgs); + % params_cgs.b.vth = sqrt(2*temp_cgs/m_e_cgs); + params_cgs.a.m = m_e_cgs; %beam is electrons + params_cgs.b.m = m_D_cgs; %background ions + params_cgs.b2.m = m_e_cgs; %background electrons + params_cgs.e = 4.803*10^-10; %charge in Fr + params_cgs.c = 3*10^10; %speed of light in cm/s + params_cgs.a.theta = pde.params.a.T_eV/(params_cgs.a.m*params_cgs.c^2); + nu_ee = 4*pi*params_cgs.a.n.*params_cgs.e.^4*pde.params.ln_delt/(params_cgs.a.theta^(3/2)... + *params_cgs.a.m^3*params_cgs.c^3); + franz_conduct = params_cgs.a.n*params_cgs.e^2/(pde.params.b.Z*params_cgs.a.m*nu_ee); + x = nodes{1}; + y = nodes{2}; + nx = numel(x); + ny = numel(y); + sx = max(1, floor(nx/2)); + sy = max(1, floor(2*ny/8)); + energy_func_v = @(x) 0.5*pde.params.a.m.*x.^2/(1.602*10^-19); + energy_func_z = @(z) z.*0 + 2*pi; + current_func_v = @(x) 2*pi*pde.params.a.Z.*pde.params.e.*x; + current_func_z = @(x) cos(x); + coord = get_realspace_coords(pde,nodes); + mass_func = @(x) x.*0 + sqrt(2*pi); + zero_func = @(x) x.*0; + num_dims = numel(pde.dimensions); + moment_func_nD{1} = energy_func_v; + moment_func_nD{2} = energy_func_z; + mass_func_nD{1} = mass_func; + mass_func_nD{2} = mass_func; + current_func_nD{1} = current_func_v; + current_func_nD{2} = current_func_z; + x_E = 0.5.*pde.params.a.m*x.^2/pde.params.e; + num_steps = length(outputs.time_array); + spitzer_conduct = (3/(4*sqrt(2*pi)))*(4*pi*pde.params.eps0)^2*(1.38e-23*pde.params.a.T_eV*11604)^(3/2)... + /(pde.params.b.Z*pde.params.e^2*pde.params.a.m^(1/2)*pde.params.ln_delt); + spitzer_conduct2 = 4*pi*pde.params.eps0^2*(pde.params.a.m*pde.params.a.vth^2)^(3/2) ... + /(pde.params.a.m^(1/2)*pde.params.e^2*pde.params.ln_delt*pde.params.b2.Z); + f1d_analytic = outputs.f_realspace_analytic_nD_t{1,num_steps}; + f1d_ic = outputs.f_realspace_analytic_nD_t{1,1}; + %getting energy density + lev_vec = [opts.lev, opts.lev]; + % data = struct2cell(outputs); + % f_data = cell2mat(data{6,1}); + % f_data = reshape(f_data, [num_steps size(f1d_ic)]); +% [x_grid, y_grid] = meshgrid(outputs.time_array,x_E); + outputs.time_array(1) = 0; +for i = 1:numel(outputs.time_array) + f_data(i,:) = outputs.f_realspace_nD_t{i}(ny/2,:); +end + %contourf(outputs.time_array,x_E,real(f_data)',50); +% f_data = permute(f_data,[1 3 2]); + +% contour(outputs.time_array',x',squeeze(f_data(:,:,sy))'); +for j = 1:num_steps + %plot(x,f1d); + hold on + fval_realspace = reshape(outputs.f_realspace_nD_t{j}, [numel(f1d_ic) 1]); + mass_vals(j) = moment_integral(lev_vec, opts.deg, coord, fval_realspace, mass_func_nD, pde.dimensions); + mass = moment_integral(lev_vec, opts.deg, coord, fval_realspace, mass_func_nD, pde.dimensions); + conduct_vals(j) = moment_integral(lev_vec,opts.deg,coord,fval_realspace, current_func_nD,pde.dimensions)/(pde.params.E); + conduct_vals(j) = conduct_vals(j)/spitzer_conduct; + energy_vals(j) = moment_integral(lev_vec, opts.deg, coord, fval_realspace, moment_func_nD, pde.dimensions)./mass; + % vel_vals(i) = sum(outputs.f_realspace_nD_t{1,i}(:).*coord{:,:}*1e-4); +% x_hint_t = @(t) -x_hint(t,pde.params.a.vel_vals(j),pde.params.a,pde.params.b); + %e_hint = integral(x_hint_t, 0, outputs.time_array(j)); + %hint_func(j) = energy_vals(1)*exp(-e_hint); + for i = 1:length(x) + f1d_new(i) = fval_realspace(i); + f1d_analytic_new(i) = f1d_analytic(i); + end + time = outputs.dt*j; + %loglog(x,f_data(j,:),'DisplayName',[num2str(time)]); + hold on +end +legend(); +hold off + %formulating the Hinton solution + % timespan = [0 1e-3]; %time span in seconds + % x0 = 3e3; %initial energy in eV + % y = @(x) sqrt(1.602e-19.*x./(0.5.*3.3443e-27)); %velocity function in terms of energy + % [t,E] = ode45(@(t,E) (-params.nu_E(y(E),params.a,params.b)-params.nu_E(y(E),params.a,params.b2)).*E,timespan,x0); + %plot(x,f1d_ic,'--'); + %plotting Hinton solution alongside numerical values + %x = x./x0; + %hold on + %plot(t,E,'r','LineWidth', 2); + %plot(outputs.time_array,energy_vals,'-o','LineWidth',1); + %figure + %plot(outputs.time_array,mass_vals,'-o','LineWidth',2); + %hold off + %f_slice = outputs.f_realspace_nD_t{1,num_steps}; + %v_norm = x./pde.params.b.vth; + %plot(v_norm,f_slice); + %figure + plot(outputs.time_array,conduct_vals,'-','LineWidth',2); + hold on + %loglog(x_E,f1d_analytic_new, '-o'); + %semilogy(outputs.time_array,hint_func,'k'); + % hold off +% hold off; +% y = nodes{2}; +% z = nodes{3}; +% nx = numel(x); +% ny = numel(y); +% ax1 = subplot(2,2,1); +% contourf(y,x,squeeze(f_nD{1,1}(:,:))'); +% ax2 = subplot(2,2,2); +% contourf(y,x,squeeze(f_nD{1,num_steps}(:,:))'); + %title('Pitch vs Velocity'); + +% sy = numel(f_nD{1,1}(:,1))/4; +% sx = 1; +% f1d = f_nD{1,num_steps}(:,sx); +% f1d_ic = f_nD{1,1}(:,sx); +% ax3 = subplot(2,2,3); +% plot(y,f1d,'-o'); +% hold on +% plot(y,f1d_ic, '-'); +% hold off +% f1d = f_nD{1,num_steps}(sy,:); +% f1d_ic = f_nD{1,1}(sy,:); +% ax4 = subplot(2,2,4); +% plot(x,f1d,'-o'); +% hold on +% plot(x,f1d_ic, '-'); + +% nz = numel(z); +% num_dims = 3; +% subset_dimensions = 2; +% deg = 6; +% space_func = @(x) x.*0 + 1; +% energy_func = @(x) x.^2; +% perp_func = @(x) sin(x).^2; +% par_func = @(x) cos(x).^2; +% coord = get_realspace_coords(pde,nodes); +% moment_func_nD = {energy_func,perp_func,space_func}; +% % v_perp_temp = moment_integral(pde.get_lev_vec,deg,coord,f_nD,moment_func_nD,pde.dimensions,subset_dimensions); +% moment_func_nD = {energy_func,par_func,space_func}; +% % v_par_temp = moment_integral(pde.get_lev_vec,deg,coord,f_nD,moment_func_nD,pde.dimensions,subset_dimensions); +% %% % Plot a 1D line through the solution + for i = 1:nx + for j = 1:ny + v_par(i,j) = x(i).*cos(y(j)); + v_perp(i,j) = x(i).*sin(y(j)); + end + end +% +% sz = numel(f_nD{1,1}(:,1,1))/2 + 1; + - sz = numel(f_nD(:,1,1))/2; - sy = numel(f_nD(1,:,1))/2; - sx = numel(f_nD(1,1,:)) - 1; - +% contourf(v_par,v_perp,outputs.f_realspace_nD_t{1,num_steps}(:,sx)); +% hold on +%plot(v_par,fval_realspace); +% plot(z,v_perp_temp, 'r'); +% plot(z,v_par_temp, 'b'); +% hold off %plotting - f1d = f_nD(:,sy,sx); - f1d = f1d(1,:); - x = nodes{1}; - y = nodes{2}; - z = nodes{3}; - x = 9.109*10^-31*x.^2/(1.602*10^-19); - plot(z,f1d,'-o'); +% f1d = f1d(1,:); +% x = nodes{1}; +% y = nodes{2}; +% z = nodes{3}; +% x = 9.109*10^-31*x.^2/(1.602*10^-19); %xlim([0.01,1e4]); %ylim([0.01,1e4]); - title('Mirror 2D Relaxation'); - - %% - - %% - % Overplot analytic solution - - if pde.checkAnalytic - f_1d_analytic = f_nD_analytic(:,sy,sx); - f_1d_analytic = f_1d_analytic(1,:); - hold on; - plot(z,f_1d_analytic,'-'); - hold off; - end - +% title('Mirror 2D Relaxation'); +% +% %% +% +% %% +% % Overplot analytic solution +% +% % if pde.checkAnalytic +% % f_1d_analytic = f_nD_analytic(:,sy,sx); +% % f_1d_analytic = f_1d_analytic(1,:); +% hold on; +% f_1d_analytic = f_nD_analytic{1,2}; +% plot(x,f_1d_analytic,'-'); +% hold off; +% % end +% % sx = max(1,floor(nx/2)); % if nx > 2 % sx = sx+2; % just to get off the exact middle @@ -56,12 +207,22 @@ function plot_mirror_output(nodes, f_nD, f_nD_analytic, pde) % %% % % Plot 2D % -% ax1 = subplot(2,2,3); -% f_nD_with_noise = f_nD; -% f_nD_with_noise(1,1) = f_nD_with_noise(1,1)*1.0001; -% contourf(x,y,f_nD_with_noise,'LineColor','none'); -% title('numeric 2D solution'); +% ax1 = subplot(2,3,1); +% contourf(z,y,squeeze(f_nD{1,num_steps}(:,:,sx))'); +% title('Space vs. Pitch'); +% ax2 = subplot(2,3,2); +% contourf(z,x,squeeze(f_nD{1,num_steps}(:,sy,:))'); +% title('Space vs. Velocity'); +% %sx = 46; +% ax3 = subplot(2,3,3); +% % - - +% n_total = zeros(nz, num_steps); +% for i = 1:num_steps +% n_total(:,i) = squeeze(sum(f_nD{1,i}, [2 3])); +% end +% ax4 = subplot(2,3,5); +% contourf(z,time_array,squeeze(n_total(:,:))'); +% title('Number Density vs. Time'); + end diff --git a/2020-10-mirror_3D_scripts/spitzer_test.m b/2020-10-mirror_3D_scripts/spitzer_test.m new file mode 100644 index 00000000..d4e17e65 --- /dev/null +++ b/2020-10-mirror_3D_scripts/spitzer_test.m @@ -0,0 +1,35 @@ +function spitzer_test() + +% modify PDE +m_D_cgs = 3.3443*10^-24; %Deuterium mass in g +m_He_cgs = 6.7*10^-24; %helium 4 mass in g +m_B_cgs = 1.82*10^-23; %Boron 11 mass in g +m_vals = 0.001.*[m_D_cgs,m_He_cgs,m_B_cgs]; +z_vals = [1,2,5]; +vals.E = 9.17e-05; +vals.E_D = 73.84; +vals.Z = 1; +vals.m = m_vals(1); +vals.dt = 3.9e-6; +args = {'timestep_method','BE','case',3,'lev',4, 'deg', 4, 'num_steps', 5,'quiet',true,'save_output',true, 'cmd_args', vals,'update_params_each_timestep', true}; +opts = OPTS(args); +pde = mirror2_velocity_div(opts); +ratio_max = 0.1; +N = 15; +ratio = linspace(0.02,ratio_max,N); + +for i = 1:length(ratio) + vals.E = ratio(i)*pde.params.E_dreicer_si; + vals.dt = 3.9e-6*vals.E/vals.E_D; + vals.num_steps = 12*3.9e-6/vals.dt; + args{16} = vals; + opts = OPTS(args); + pde = mirror2_velocity_div(opts); + [~,~,~,nodes,~,outputs(i)] = asgard_run_pde(opts,pde); + alpha_nr(i,vals.Z) = outputs(i).alpha_t{end}; + %plot_mirror_output(nodes,outputs,pde,opts); + %legend( sprintf('Z = %g', vals.Z) ); +end +semilogy(ratio,alpha_nr(:,1),'LineWidth',5,'DisplayName','ASGarD (nr, Z=1)','color','red'); + +end \ No newline at end of file diff --git a/2020-10-mirror_3D_scripts/spitzer_test.m.bak b/2020-10-mirror_3D_scripts/spitzer_test.m.bak new file mode 100644 index 00000000..3c0002b4 --- /dev/null +++ b/2020-10-mirror_3D_scripts/spitzer_test.m.bak @@ -0,0 +1,59 @@ +function spitzer_test() + +m_D_cgs = 3.3443*10^-24; %Deuterium mass in g +m_He_cgs = 6.7*10^-24; %helium 4 mass in g +m_B_cgs = 1.82*10^-23; %Boron 11 mass in g +m_Ne_cgs = 3.3509177*10^-23; %Neon mass in g +m_vals = [m_D_cgs,m_He_cgs,m_B_cgs,m_Ne_cgs]/1000; + +z_vals = [1,2,5,10]; +dt = 0.001; + +for i = 1:length(z_vals) + args = {'timestep_method','BE','dt',dt,'lev',4,'deg', 3,'num_steps',3,'update_params_each_timestep', true,'save_output',true,'quiet',true}; + opts = OPTS(args); + pde = mirror2_velocity_div(opts); + lev_vec = [opts.lev, opts.lev]; + pde.params.a.m = 9.1093*10^-31; + pde.params.b.m = m_vals(i); + pde.params.b.Z = z_vals(i); + pde.params.a.T_eV = 1000; + pde.params.b.T_eV = pde.params.a.T_eV; + pde.params.b2.T_eV = pde.params.a.T_eV; + pde.params.a.vth = pde.params.v_th(pde.params.a.T_eV,pde.params.a.m); + pde.params.b.vth = pde.params.v_th(pde.params.b.T_eV,pde.params.b.m); + pde.params.b2.vth = pde.params.v_th(pde.params.b2.T_eV,pde.params.b2.m); + pde.params.ln_delt = 15; + pde.params.a.n = 8e20; + pde.params.e = 1.602*10^-19; %charge in Coulombs + E_dreicer_si = pde.params.a.n.*pde.params.e^3*pde.params.ln_delt/(2*pi*pde.params.eps0^2*pde.params.a.m ... + *pde.params.a.vth^2); + frac = 1e-3; + pde.params.E = frac*E_dreicer_si; + %vel_norm = @(v,vth) v./vth; %normalized velocity to thermal velocity + pde.params.maxwell = @(v,offset,vth) pde.params.a.n/(pi.^(3/2)*vth^3).*exp(-((v-offset)/vth).^2); + pde.params.soln_v = @(v,p,t) solution_v(v,p,t); + pde.params.f0_v = @(v) pde.params.maxwell(v,0,pde.params.a.vth); + pde.params.init_cond_v = @(v,p,t) pde.params.f0_v(v); + [err,fval,fval_realspace,nodes,err_realspace] = asgard_run_pde(opts,pde); + close all; + load('asgard-out-l'+ lev_vec(1) + '-d'+ opts.deg(1) +'-SG-dt'+dt+'-adapt-n.mat'); + num_steps = length(outputs.time_array); + coord = get_realspace_coords(pde,nodes); + f1d_ic = outputs.f_realspace_analytic_nD_t{1,1}; + fval_realspace = reshape(outputs.f_realspace_nD_t{num_steps}, [numel(f1d_ic) 1]); + current_func_v = @(x) 2*pi*pde.params.a.Z.*pde.params.e.*x; + current_func_z = @(x) cos(x); + current_func_nD{1} = current_func_v; + current_func_nD{2} = current_func_z; + conduct_vals(i) = moment_integral(lev_vec,opts.deg,coord,fval_realspace, current_func_nD,pde.dimensions)/(pde.params.E); + func = (1 + 1.198*pde.params.b.Z + 0.222*pde.params.b.Z^2)/(1 + 2.966*pde.params.b.Z + 0.753*pde.params.b.Z^2); + spitzer_conduct = func*(3/(4*sqrt(2*pi)))*(4*pi*pde.params.eps0)^2*(1.38e-23*pde.params.a.T_eV*11604)^(3/2)... + /(pde.params.b.Z*pde.params.e^2*pde.params.a.m^(1/2)*pde.params.ln_delt); + conduct_vals(i) = conduct_vals(i)/spitzer_conduct; +end + +plot(z_vals,conduct_vals); + + +end \ No newline at end of file diff --git a/2020-10-mirror_3D_scripts/u_j.txt b/2020-10-mirror_3D_scripts/u_j.txt new file mode 100644 index 00000000..be3d167f --- /dev/null +++ b/2020-10-mirror_3D_scripts/u_j.txt @@ -0,0 +1,15 @@ + 0.00000E+00 2.52242E+07 5.04485E+07 7.56727E+07 1.00897E+08 1.26121E+08 1.51345E+08 1.76570E+08 2.01794E+08 2.27018E+08 + 2.52242E+08 2.77467E+08 3.02691E+08 3.27915E+08 3.53139E+08 3.78364E+08 4.03588E+08 4.28812E+08 4.54036E+08 4.79261E+08 + 5.04485E+08 5.29709E+08 5.54933E+08 5.80157E+08 6.05382E+08 6.30606E+08 6.55830E+08 6.81054E+08 7.06279E+08 7.31503E+08 + 7.56727E+08 7.81951E+08 8.07176E+08 8.32400E+08 8.57624E+08 8.82848E+08 9.08073E+08 9.33297E+08 9.58521E+08 9.83745E+08 + 1.00897E+09 1.03419E+09 1.05942E+09 1.08464E+09 1.10987E+09 1.13509E+09 1.16031E+09 1.18554E+09 1.21076E+09 1.23599E+09 + 1.26121E+09 1.28644E+09 1.31166E+09 1.33688E+09 1.36211E+09 1.38733E+09 1.41256E+09 1.43778E+09 1.46301E+09 1.48823E+09 + 1.51345E+09 1.53868E+09 1.56390E+09 1.58913E+09 1.61435E+09 1.63958E+09 1.66480E+09 1.69002E+09 1.71525E+09 1.74047E+09 + 1.76570E+09 1.79092E+09 1.81615E+09 1.84137E+09 1.86659E+09 1.89182E+09 1.91704E+09 1.94227E+09 1.96749E+09 1.99271E+09 + 2.01794E+09 2.04316E+09 2.06839E+09 2.09361E+09 2.11884E+09 2.14406E+09 2.16928E+09 2.19451E+09 2.21973E+09 2.24496E+09 + 2.27018E+09 2.29541E+09 2.32063E+09 2.34585E+09 2.37108E+09 2.39630E+09 2.42153E+09 2.44675E+09 2.47198E+09 2.49720E+09 + 2.52242E+09 2.54765E+09 2.57287E+09 2.59810E+09 2.62332E+09 2.64854E+09 2.67377E+09 2.69899E+09 2.72422E+09 2.74944E+09 + 2.77467E+09 2.79989E+09 2.82511E+09 2.85034E+09 2.87556E+09 2.90079E+09 2.92601E+09 2.95124E+09 2.97646E+09 3.00168E+09 + 3.02691E+09 3.05213E+09 3.07736E+09 3.10258E+09 3.12781E+09 3.15303E+09 3.17825E+09 3.20348E+09 3.22870E+09 3.25393E+09 + 3.27915E+09 3.30438E+09 3.32960E+09 3.35482E+09 3.38005E+09 3.40527E+09 3.43050E+09 3.45572E+09 3.48094E+09 3.50617E+09 + 3.53139E+09 3.55662E+09 3.58184E+09 3.60707E+09 3.63229E+09 3.65751E+09 3.68274E+09 3.70796E+09 3.73319E+09 3.75841E+09 diff --git a/DIMENSION.m b/DIMENSION.m index 16cfdeeb..94317584 100644 --- a/DIMENSION.m +++ b/DIMENSION.m @@ -8,6 +8,7 @@ lev = 3; init_cond_fn = @(x,p) x.*0; moment_dV = @(x,p,t,d) x.*0 + 1; + mass_mat = []; end diff --git a/MD_TERM.m b/MD_TERM.m index ef3c9cfd..c723d37e 100644 --- a/MD_TERM.m +++ b/MD_TERM.m @@ -25,6 +25,7 @@ t.terms_1D = terms_1D_; + end end diff --git a/Meval.mat b/Meval.mat deleted file mode 100644 index 81a0a77e..00000000 Binary files a/Meval.mat and /dev/null differ diff --git a/OPTS.m b/OPTS.m index 6e62cf82..7078cda1 100644 --- a/OPTS.m +++ b/OPTS.m @@ -33,7 +33,9 @@ calculate_mass = true; % calculate and print the mass normalize_by_mass = false; % normalize the analytic solution by the initial cond mass start_time = 0; - num_steps = 5; + num_steps = 5; + cmd_args = ''; + update_params_each_timestep = false; end @@ -80,8 +82,11 @@ addOptional(input_parser,'use_connectivity',opts.use_connectivity,@islogical); addOptional(input_parser,'use_sparse_A',opts.use_sparse_A,@islogical); addOptional(input_parser,'case',opts.case_,@isnumeric); + addOptional(input_parser,'cmd_args',opts.cmd_args); % can be anything addOptional(input_parser,'calculate_mass',opts.calculate_mass,@islogical); addOptional(input_parser,'normalize_by_mass',opts.normalize_by_mass,@islogical); + addOptional(input_parser,'update_params_each_timestep',opts.update_params_each_timestep,@islogical); + parse(input_parser,varargin{:}{:}) @@ -132,10 +137,12 @@ opts.use_connectivity = input_parser.Results.use_connectivity; opts.use_sparse_A = input_parser.Results.use_sparse_A; opts.case_ = input_parser.Results.case; + opts.cmd_args = input_parser.Results.cmd_args; opts.calculate_mass = input_parser.Results.calculate_mass; opts.normalize_by_mass = input_parser.Results.normalize_by_mass; opts.num_steps = input_parser.Results.num_steps; opts.start_time = input_parser.Results.start_time; + opts.update_params_each_timestep = input_parser.Results.update_params_each_timestep; opts.build_A = false; if sum(strcmp(opts.timestep_method,{'BE','CN','time_independent','matrix_exponential'}))>0 @@ -187,6 +194,13 @@ end end + if ~strcmp(opts.output_grid,'quadrature') + + opts.calculate_mass = false; + opts.normalize_by_mass = false; + + end + if ~isempty(fieldnames(input_parser.Unmatched)) disp('Extra inputs:') disp(input_parser.Unmatched) diff --git a/PDE/advect_blob1.m b/PDE/advect_blob1.m new file mode 100644 index 00000000..3eb37cff --- /dev/null +++ b/PDE/advect_blob1.m @@ -0,0 +1,73 @@ +function pde = advect_blob1(opts) +% 1D advect a blob across a domain. Use for feature tracking testing in the adaptiviy. +% +% df/dt == -v * df/dx +% +% Run with +% +% asgard(@advect_blob1,'deg',5','lev',4,'num_steps',5,'dt',0.002) +% +% Notes: +% DLG - analytic solution won't work past about t = 0.002*500 + +%% Define the dimensions + +dim_x = DIMENSION(-1,+1); +dimensions = {dim_x}; +num_dims = numel(dimensions); + +%% Define some parameters and add to pde object. + +params.v = 2; % blob speed +params.sig = 0.1; % blob width + +%% Define the analytic solution (optional). + +a_x = @(x,p,t) exp(-(x-p.v*t).^2/p.sig.^2)+exp(-(x-p.v*t+2).^2/p.sig.^2); +a_t = @(t,p) t.*0+1; +sol1 = new_md_func(num_dims,{a_x,a_t}); +solutions = {sol1}; + +%% Define the initial conditions + +initial_conditions = {sol1}; + +%% Define the terms of the PDE + +% -2 * df/dx + +g1 = @(x,p,t,dat) x.*0-p.v; +pterm1 = GRAD(num_dims,g1,-1,'P','P'); + +term1_x = SD_TERM({pterm1}); +term1 = MD_TERM(num_dims,{term1_x}); + +%% +% Add terms to the pde object + +terms = {term1}; + +%% Define sources + +sources = {}; + +%% Define function to set time step + + function dt=set_dt(pde,CFL) + + dim = pde.dimensions{1}; + lev = dim.lev; + xMax = dim.max; + xMin = dim.min; + xRange = xMax-xMin; + dx = xRange/(2^lev); + dt = CFL*dx; + end + +%% Construct PDE + +pde = PDE(opts,dimensions,terms,[],sources,params,@set_dt,[],initial_conditions,solutions); + +end + + diff --git a/PDE/advect_blob2.m b/PDE/advect_blob2.m new file mode 100644 index 00000000..015f1d1c --- /dev/null +++ b/PDE/advect_blob2.m @@ -0,0 +1,75 @@ +function pde = advect_blob2(opts) +% 2D advect a blob across a domain. Use for feature tracking testing in the adaptiviy. +% +% df/dt == -v * df/dx +% +% Run with +% +% asgard(@advect_blob2,'deg',5','lev',4,'num_steps',5,'dt',0.002) +% +% Notes: +% DLG - analytic solution won't work past about t = 0.002*500 + +%% Define the dimensions + +dim_x = DIMENSION(-1,+1); +dim_y = DIMENSION(-1,+1); +dimensions = {dim_x,dim_y}; +num_dims = numel(dimensions); + +%% Define some parameters and add to pde object. + +params.v = 2; % blob speed +params.sig = 0.1; % blob width + +%% Define the analytic solution (optional). + +a_x = @(x,p,t) exp(-(x-p.v*t).^2/p.sig.^2)+exp(-(x-p.v*t+2).^2/p.sig.^2); +a_y = @(x,p,t) exp(-x.^2/p.sig.^2); +a_t = @(t,p) t.*0+1; +sol1 = new_md_func(num_dims,{a_x,a_y,a_t}); +solutions = {sol1}; + +%% Define the initial conditions + +initial_conditions = {sol1}; + +%% Define the terms of the PDE + +% -2 * df/dx + +g1 = @(x,p,t,dat) x.*0-p.v; +pterm1 = GRAD(num_dims,g1,-1,'P','P'); + +term1_x = SD_TERM({pterm1}); +term1 = MD_TERM(num_dims,{term1_x,[]}); + +%% +% Add terms to the pde object + +terms = {term1}; + +%% Define sources + +sources = {}; + +%% Define function to set time step + + function dt=set_dt(pde,CFL) + + dim = pde.dimensions{1}; + lev = dim.lev; + xMax = dim.max; + xMin = dim.min; + xRange = xMax-xMin; + dx = xRange/(2^lev); + dt = CFL*dx; + end + +%% Construct PDE + +pde = PDE(opts,dimensions,terms,[],sources,params,@set_dt,[],initial_conditions,solutions); + +end + + diff --git a/PDE/advect_blob3.m b/PDE/advect_blob3.m new file mode 100644 index 00000000..3ddc831d --- /dev/null +++ b/PDE/advect_blob3.m @@ -0,0 +1,77 @@ +function pde = advect_blob3(opts) +% 3D advect a blob across a domain. Use for feature tracking testing in the adaptiviy. +% +% df/dt == -v * df/dx +% +% Run with +% +% asgard(@advect_blob3,'deg',5','lev',4,'num_steps',5,'dt',0.002) +% +% Notes: +% DLG - analytic solution won't work past about t = 0.002*500 + +%% Define the dimensions + +dim_x = DIMENSION(-1,+1); +dim_y = DIMENSION(-1,+1); +dim_z = DIMENSION(-1,+1); +dimensions = {dim_x,dim_y,dim_z}; +num_dims = numel(dimensions); + +%% Define some parameters and add to pde object. + +params.v = 2; % blob speed +params.sig = 0.1; % blob width + +%% Define the analytic solution (optional). + +a_x = @(x,p,t) exp(-(x-p.v*t).^2/p.sig.^2)+exp(-(x-p.v*t+2).^2/p.sig.^2); +a_y = @(x,p,t) exp(-x.^2/p.sig.^2); +a_z = @(x,p,t) exp(-x.^2/p.sig.^2); +a_t = @(t,p) t.*0+1; +sol1 = new_md_func(num_dims,{a_x,a_y,a_z,a_t}); +solutions = {sol1}; + +%% Define the initial conditions + +initial_conditions = {sol1}; + +%% Define the terms of the PDE + +% -2 * df/dx + +g1 = @(x,p,t,dat) x.*0-p.v; +pterm1 = GRAD(num_dims,g1,-1,'P','P'); + +term1_x = SD_TERM({pterm1}); +term1 = MD_TERM(num_dims,{term1_x,[],[]}); + +%% +% Add terms to the pde object + +terms = {term1}; + +%% Define sources + +sources = {}; + +%% Define function to set time step + + function dt=set_dt(pde,CFL) + + dim = pde.dimensions{1}; + lev = dim.lev; + xMax = dim.max; + xMin = dim.min; + xRange = xMax-xMin; + dx = xRange/(2^lev); + dt = CFL*dx; + end + +%% Construct PDE + +pde = PDE(opts,dimensions,terms,[],sources,params,@set_dt,[],initial_conditions,solutions); + +end + + diff --git a/PDE/advect_blob4.m b/PDE/advect_blob4.m new file mode 100644 index 00000000..51ee2558 --- /dev/null +++ b/PDE/advect_blob4.m @@ -0,0 +1,79 @@ +function pde = advect_blob4(opts) +% 4D advect a blob across a domain. Use for feature tracking testing in the adaptiviy. +% +% df/dt == -v * df/dx +% +% Run with +% +% asgard(@advect_blob4,'deg',5','lev',4,'num_steps',5,'dt',0.002) +% +% Notes: +% DLG - analytic solution won't work past about t = 0.002*500 + +%% Define the dimensions + +dim_x = DIMENSION(-1,+1); +dim_y = DIMENSION(-1,+1); +dim_z = DIMENSION(-1,+1); +dim_vx = DIMENSION(-1,+1); +dimensions = {dim_x,dim_y,dim_z,dim_vx}; +num_dims = numel(dimensions); + +%% Define some parameters and add to pde object. + +params.v = 2; % blob speed +params.sig = 0.1; % blob width + +%% Define the analytic solution (optional). + +a_x = @(x,p,t) exp(-(x-p.v*t).^2/p.sig.^2)+exp(-(x-p.v*t+2).^2/p.sig.^2); +a_y = @(x,p,t) exp(-x.^2/p.sig.^2); +a_z = @(x,p,t) exp(-x.^2/p.sig.^2); +a_vx = @(x,p,t) exp(-x.^2/p.sig.^2); +a_t = @(t,p) t.*0+1; +sol1 = new_md_func(num_dims,{a_x,a_y,a_z,a_vx,a_t}); +solutions = {sol1}; + +%% Define the initial conditions + +initial_conditions = {sol1}; + +%% Define the terms of the PDE + +% -2 * df/dx + +g1 = @(x,p,t,dat) x.*0-p.v; +pterm1 = GRAD(num_dims,g1,-1,'P','P'); + +term1_x = SD_TERM({pterm1}); +term1 = MD_TERM(num_dims,{term1_x,[],[],[]}); + +%% +% Add terms to the pde object + +terms = {term1}; + +%% Define sources + +sources = {}; + +%% Define function to set time step + + function dt=set_dt(pde,CFL) + + dim = pde.dimensions{1}; + lev = dim.lev; + xMax = dim.max; + xMin = dim.min; + xRange = xMax-xMin; + dx = xRange/(2^lev); + dt = CFL*dx; + end + +%% Construct PDE + +pde = PDE(opts,dimensions,terms,[],sources,params,@set_dt,[],initial_conditions,solutions); + +end + + diff --git a/PDE/advect_blob_test.m b/PDE/advect_blob_test.m new file mode 100644 index 00000000..106e7403 --- /dev/null +++ b/PDE/advect_blob_test.m @@ -0,0 +1,49 @@ +function tests = advect_blob_test() +fh = localfunctions; +tests = functiontests(fh); +end + +function advect_blob1_test(testCase) +addpath(genpath(pwd)); +disp('Testing advect_blob1'); +% setup PDE +args = {'lev',4,'deg',5,'dt',0.002,'quiet',true,'num_steps',5}; +opts = OPTS(args); +pde = advect_blob1(opts); +% modify PDE - not needed here +% run PDE +[err,fval,fval_realspace,nodes,err_realspace] = asgard_run_pde(opts,pde); +% assert on correctness +rel_err = err / norm(fval); +verifyLessThan(testCase,rel_err,2e-4); +end + +function advect_blob2_test(testCase) +addpath(genpath(pwd)); +disp('Testing advect_blob2'); +% setup PDE +args = {'lev',4,'deg',5,'dt',0.002,'quiet',true,'num_steps',5}; +opts = OPTS(args); +pde = advect_blob2(opts); +% modify PDE - not needed here +% run PDE +[err,fval,fval_realspace,nodes,err_realspace] = asgard_run_pde(opts,pde); +% assert on correctness +rel_err = err / norm(fval); +verifyLessThan(testCase,rel_err,3e-4); +end + +function advect_blob3_test(testCase) +addpath(genpath(pwd)); +disp('Testing advect_blob3'); +% setup PDE +args = {'lev',4,'deg',5,'dt',0.002,'quiet',true,'num_steps',5}; +opts = OPTS(args); +pde = advect_blob3(opts); +% modify PDE - not needed here +% run PDE +[err,fval,fval_realspace,nodes,err_realspace] = asgard_run_pde(opts,pde); +% assert on correctness +rel_err = err / norm(fval); +verifyLessThan(testCase,rel_err,3e-4); +end \ No newline at end of file diff --git a/pdes/continuity1_div.m b/PDE/advection1_LF.m similarity index 56% rename from pdes/continuity1_div.m rename to PDE/advection1_LF.m index bb27ff7a..f16aa568 100644 --- a/pdes/continuity1_div.m +++ b/PDE/advection1_LF.m @@ -1,45 +1,52 @@ -function pde = continuity1_div(opts) -% 1D test case using continuity equation, i.e., +function pde = advection1_LF(opts) +% 1D test case where the advection coefficient switches sign within the domain [-pi,+pi]. +% (see mathematica worksheet advection1_LF.nb) % -% df/dt == -df/dx +% df/dt == -x * df/dx +% +% f(t=0) = Exp[-(x - 1)^2/sig] + Exp[-(x + 1)^2/sig]; +% sig = 0.1; % % Run with % -% explicit -% asgard(@continuity1_div,'lev',4,'deg',3) +% asgard(@advection1_LF,'dt',0.01,'num_steps',100,'timestep_method','matrix_exponential','lev',4,'deg',4) % -% implicit -% asgard(@continuity1_div,'timestep_method','CN') +% Notes +% DLG - this works fine with central(0) or left(-1) flux, but fails with +% right(+1). Why? + %% Define the dimensions -dim_x = DIMENSION(-1,+1); +dim_x = DIMENSION(-pi,+pi); dimensions = {dim_x}; num_dims = numel(dimensions); %% Define the analytic solution (optional). -% This requires nDims+time function handles. + function ans = solution(x,p,t) + ep = (-1+x.*exp(-t)).^2; + em = (+1+x.*exp(-t)).^2; + ans = exp( -t -10*em -10*ep ) .* ( exp(10*em) + exp(10*ep) ); + end -a_x = @(x,p,t) cos(2*pi*x); -a_t = @(t,p) sin(t); +a_x = @solution; +a_t = @(t,p) 1; sol1 = new_md_func(num_dims,{a_x,a_t}); solutions = {sol1}; %% Define the initial conditions -ic_x = @(x,p,t) x.*0; +ic_x = @solution; ic1 = new_md_func(num_dims,{ic_x}); initial_conditions = {ic1}; %% Define the terms of the PDE -% -% Here we have 1 term1, having only nDims=1 (x) operators. %% % -df/dx -g1 = @(x,p,t,dat) x.*0-1; -pterm1 = DIV(num_dims,g1,'',-1,'P','P'); +g1 = @(x,p,t,dat) -x; +pterm1 = GRAD(num_dims,g1,0,'N','N'); term1_x = SD_TERM({pterm1}); term1 = MD_TERM(num_dims,{term1_x}); @@ -57,19 +64,7 @@ %% 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left(-1) flux, but fails with +% right(+1). Why? + + +%% Define the dimensions + +dim_x = DIMENSION(-pi,+pi); +dim_y = DIMENSION(-pi,+pi); +dimensions = {dim_x,dim_y}; +num_dims = numel(dimensions); + +%% Define the analytic solution (optional). + function ans = solution(x,p,t) + ep = (-1+x.*exp(-t)).^2; + em = (+1+x.*exp(-t)).^2; + ans = exp( -t -10*em -10*ep ) .* ( exp(10*em) + exp(10*ep) ); + end + +a_x = @solution; +a_y = a_x; +a_t = @(t,p) 1; +sol1 = new_md_func(num_dims,{a_x,a_y,a_t}); +solutions = {sol1}; + +%% Define the initial conditions + +ic_x = @solution; +ic_y = ic_x; +ic1 = new_md_func(num_dims,{ic_x,ic_y}); +initial_conditions = {ic1}; + +%% Define the terms of the PDE + +%% +% -x*df/dx + +g1 = @(x,p,t,dat) -x; +pterm1 = GRAD(num_dims,g1,0,'N','N'); + +term1_x = SD_TERM({pterm1}); +term1 = MD_TERM(num_dims,{term1_x,[]}); + +%% +% -y*df/dy + +g1 = @(y,p,t,dat) -y; +pterm1 = GRAD(num_dims,g1,0,'N','N'); + +term2_y = SD_TERM({pterm1}); +term2 = MD_TERM(num_dims,{[],term2_y}); + +%% +% Add terms to the pde object + +terms = {term1,term2}; + +%% Define some parameters and add to pde object. +% These might be used within the various functions below. + +params.parameter1 = 0; +params.parameter2 = 1; + +%% Define sources + +sources = {}; + +%% Define function to set time step + + function dt=set_dt(pde,CFL) + + dim = pde.dimensions{1}; + lev = dim.lev; + xMax = dim.max; + xMin = dim.min; + xRange = xMax-xMin; + dx = xRange/(2^lev); + dt = CFL*dx; + end + +%% Construct PDE + +pde = PDE(opts,dimensions,terms,[],sources,params,@set_dt,[],initial_conditions,solutions); + +end + + diff --git a/PDE/advection_LF_test.m b/PDE/advection_LF_test.m new file mode 100644 index 00000000..aa456d3e --- /dev/null +++ b/PDE/advection_LF_test.m @@ -0,0 +1,35 @@ +function tests = advection1_LF_test() +fh = localfunctions; +tests = functiontests(fh); +end + +function advection1_LF_left_test(testCase) +addpath(genpath(pwd)); +disp('Testing advection1_LF the left(-1) flux'); +% setup PDE +args = {'lev',4,'deg',4,'dt',1e-2,'quiet',true,'num_steps',20,'timestep_method','matrix_exponential'}; +opts = OPTS(args); +pde = advection1_LF(opts); +% modify PDE - not needed here +% run PDE +[err,fval,fval_realspace,nodes,err_realspace] = asgard_run_pde(opts,pde); +% assert on correctness +rel_err = err / norm(fval); +verifyLessThan(testCase,rel_err,1e-3); +end + +function advection2_LF_left_test(testCase) +addpath(genpath(pwd)); +disp('Testing advection2_LF the left(-1) flux'); +% setup PDE +args = {'lev',4,'deg',4,'dt',1e-2,'quiet',true,'num_steps',15,'timestep_method','BE'}; +opts = OPTS(args); +pde = advection2_LF(opts); +% modify PDE - not needed here +% run PDE +[err,fval,fval_realspace,nodes,err_realspace] = asgard_run_pde(opts,pde); +% assert on correctness +rel_err = err / norm(fval); +verifyLessThan(testCase,rel_err,8e-3); +end + diff --git a/PDE/mirror2_test_div.m b/PDE/mirror2_test_div.m new file mode 100644 index 00000000..a812495b --- /dev/null +++ b/PDE/mirror2_test_div.m @@ -0,0 +1,95 @@ +function pde = mirror2_test_div(opts) + +% Two-dimensional test of spatial and pitch-angle variation in magnetic +% mirror where f coefficients change signs throughout the domain +% +% df/dt == 1/(sin(th)) d/dth (sin(th) sin(th)/2B dB/ds f_a) +% - 1/B d (B cos(th)f)/ds +% Run with +% +% asgard(@mirror2_space_pitch_div,'timestep_method','BE','case',3,'dt',1e-8,'lev',3,'deg', 3,'num_steps',20) + +dim_th = DIMENSION(0,pi); +dV_th = @(x,p,t,d) sin(x); +dim_th.moment_dV = dV_th; + +dimensions = {dim_th}; +num_dims = numel(dimensions); + +params = mirror_parameters(); + +%% Define the initial conditions + +params.init_cond_z = @(z,p,t,dat) cos(z); +ic1 = new_md_func(num_dims,{params.init_cond_z}); +initial_conditions = {ic1}; + +%% Define the boundary conditions + +BCL = new_md_func(num_dims,{... + @(x,p,t,dat) cos(x), ... + @(t,p) 0*t+1}); + +BCR = new_md_func(num_dims,{... + @(x,p,t,dat) cos(x), ... + @(t,p) 0*t+1}); + +%% Define the terms of the PDE + +%% Advection term + +%termZa is a done combining mass ad div defining C(th) = sin(th) and using +%the function mag(s) = dB/ds/(2*B). This applies to the domain where +% mag(s) > 0 and therefore we use upwinding +%eq1: df/dt == div(mag(s) f) [pterm1: div(g(th)=C(th),-1, BCL=N,BCR=N)] + +dV_th = @(x,p,t,d) sin(x); +%dV_th = @(x,p,t,d) 0*x+1; + +C = @(z) sin(z); +%C = @(z) 1./sin(z); +%C = @(z) 0*z+1; +g2 = @(z,p,t,dat) C(z); +pterm2 = DIV(num_dims,g2,'',-1,'N','D','','','',dV_th); +termZa_z = SD_TERM({pterm2}); + +termZa = MD_TERM(num_dims,{termZa_z}); + +g2 = @(z,p,t,dat) -cos(z); +pterm2 = MASS(g2,'','',dV_th); +termZa_mass = SD_TERM({pterm2}); +term_mass = MD_TERM(num_dims,{termZa_mass}); + +terms = {termZa,term_mass}; +%terms = {termZa}; + + + +%% Define the analytic solution (optional) + + +soln1_z = @(z,p,t,d) cos(z); +solution = new_md_func(num_dims,{soln1_z}); +solutions = {solution}; + + +%% Define sources +%source1_v = @(x,p,t,d) p.f0_v(x); +%source1_z = @(x,p,t,d) (sin(x)).^2 - (cos(x)).^2; +%source1 = new_md_func(num_dims,{source1_z,[]}); +%sources = {source1}; +sources = {}; + +%% Define function to set time step + function dt=set_dt(pde,CFL) + Lmax = pde.dimensions{1}.max; + LevX = pde.dimensions{1}.lev; + dt = Lmax/2^LevX*CFL; + end + + + +%% Construct PDE + +pde = PDE(opts,dimensions,terms,[],sources,params,@set_dt,[],initial_conditions,solutions); +end \ No newline at end of file diff --git a/adapt.m b/adapt.m index 209570a5..72cfcfc1 100644 --- a/adapt.m +++ b/adapt.m @@ -112,7 +112,7 @@ % and is labeled as a leaf if element_max <= coarsen_threshold ... - && min(hash_table.elements.lev_p1(idx,:)>=2) % level must be >= 1 at present + && min(hash_table.elements.lev_p1(idx,:)>=1) % level must be >= 0 at present %&& hash_table.elements.type(idx) == 2 %% @@ -408,6 +408,8 @@ lev_vec(d) = max(hash_table.elements.lev_p1(:,d)-1); end +%pde = compute_dimension_mass_mat(opts,pde); + if opts.max_lev_coeffs pde = get_coeff_mats_rechain(pde, deg, lev_vec); end @@ -439,7 +441,11 @@ for d=1:num_dims if strcmp(opts.output_grid,'fixed') - num_fixed_grid = 51; + if d==1 + num_fixed_grid = 51; + else + num_fixed_grid = 21; + end nodes_nodups{d} = ... linspace(pde.dimensions{d}.min,pde.dimensions{d}.max,num_fixed_grid); [Meval{d},nodes{d},nodes_count{d}] = ... @@ -491,7 +497,7 @@ subplot(4,3,4) f2d = singleD_to_multiD(num_dims,fval_realspace0,nodes0); if strcmp(opts.output_grid,'fixed') - f2d = remove_duplicates(num_dims,f2d,nodes_nodups,nodes_count); + f2d = remove_duplicates(num_dims,f2d,nodes_nodups0,nodes_count0); end x = nodes_nodups0{1}; y = nodes_nodups0{2}; diff --git a/apply_M.m b/apply_M.m new file mode 100644 index 00000000..52482ccf --- /dev/null +++ b/apply_M.m @@ -0,0 +1,144 @@ +function [ftmp] = apply_M (pde,opts,A_data,f) + +%----------------------------------- +% Multiply Matrix M by a vector f +%----------------------------------- +dof = size(f,1); +use_sparse_ftmp = 0; +if (use_sparse_ftmp) + ftmp=sparse(dof,1); +else + ftmp = zeros(dof,1); +end +use_kronmultd = 1; + +deg = opts.deg; + +num_dims = numel(pde.dimensions); + +%% +% Tensor product encoding over DOF within an element, i.e., over "deg" (A_Data), +% i.e., tmpA and tmpB are deg_1 x deg_2 x deg_D matricies + +num_elem = numel(A_data.element_global_row_index); + +ftmpA = ftmp; + +element_DOF = deg^num_dims; + +total_DOF = num_elem * element_DOF; + +if opts.use_connectivity + connectivity = pde.connectivity; + num_A = 0; + for i=1:num_elem + num_A = num_A + numel(pde.connectivity{i}); + end + num_A = num_A * element_DOF^2; +else + num_A = total_DOF * total_DOF; +end + +cnt = 1; + +for elem=1:num_elem + + if opts.use_connectivity + num_connected = numel(connectivity{elem}); + else + num_connected = num_elem; % Simply assume all are connected. + end + + for d=1:num_dims + element_idx1D_D{d} = A_data.element_local_index_D{d}(elem); + end + + % Expand out the local and global indicies for this compressed item + + global_row = element_DOF*(elem-1) + [1:element_DOF]'; +% global_1D_row = deg*(elem-1) + [1:deg]'; + + for d=1:num_dims + myDeg = opts.deg; + Index_I{d} = (element_idx1D_D{d}-1)*myDeg + [1:myDeg]'; + end + + for j=1:num_connected + + if opts.use_connectivity + connected_col_j = connectivity{elem}(j); + else + connected_col_j = j; + end + + for d=1:num_dims + connected_idx1D_D{d} = A_data.element_local_index_D{d}(connected_col_j); + end + + % Expand out the global col indicies for this compressed + % connected item. + + global_col = element_DOF*(connected_col_j-1) + [1:element_DOF]'; + + for d=1:num_dims + myDeg = opts.deg; + Index_J{d} = (connected_idx1D_D{d}-1)*myDeg + [1:myDeg]'; + end + + %% + % Apply operator matrices to present state using the pde spec + % Y = A * X + % where A is tensor product encoded. + + if opts.build_A && opts.use_sparse_A + num_view = element_DOF * element_DOF; + [gr,gc] = meshgrid(global_col,global_row); + A_s1(cnt:cnt+num_view-1) = gr(:); + A_s2(cnt:cnt+num_view-1) = gc(:); + end + + %% + % Construct the list of matrices for the kron_mult for this + % operator (which has dimension many entries). + for d=1:num_dims + idx_i = Index_I{d}; + idx_j = Index_J{d}; + tmp = pde.dimensions{d}.mass_mat; + kron_mat_list{d} = tmp(idx_i,idx_j); % List of tmpA, tmpB, ... tmpD used in kron_mult + end + + + %% + % Apply kron_mult to return A*Y (explicit time advance) + X = f(global_col); + if use_kronmultd + Y = kron_multd(num_dims,kron_mat_list,X); + else + Y = kron_multd_full(num_dims,kron_mat_list,X); + end + + use_globalRow = 0; + if (use_globalRow) + ftmpA(global_row) = ftmpA(global_row) + Y; + else + % ------------------------------------------------------ + % globalRow = elementDOF*(workItem-1) + [1:elementDOF]'; + % ------------------------------------------------------ + i1 = element_DOF*(elem-1) + 1; + i2 = element_DOF*(elem-1) + element_DOF; + ftmpA(i1:i2) = ftmpA(i1:i2) + Y; + end + + %% + % Overwrite previous approach with PDE spec approch + ftmp = ftmpA; + + if opts.use_sparse_A; cnt = cnt + num_view; end + + end + + assert(elem==elem); + +end + +end diff --git a/asgard.m b/asgard.m index c7d1f751..b25f00bb 100644 --- a/asgard.m +++ b/asgard.m @@ -1,6 +1,6 @@ %% MATLAB (reference) version of the ASGarD solver -function [err,fval,fval_realspace,nodes,err_realspace,outputs] = asgard(pde_handle,varargin) +function [err,fval,fval_realspace,nodes,err_realspace,outputs,opts] = asgard(pde_handle,varargin) format short e folder = fileparts(which(mfilename)); @@ -20,7 +20,18 @@ pde = pde_handle(opts); %% Launch ASGarD with this PDE -[err,fval,fval_realspace,nodes,err_realspace,outputs] = asgard_run_pde(opts,pde); +output_filename = create_output_filename(opts); +if exist(output_filename,'file') && opts.save_output + err=-1; + fval=-1; + fval_realspace=-1; + nodes=-1; + err_realspace=-1; + outputs=-1; + disp('Output already exists ... skipping'); +else + [err,fval,fval_realspace,nodes,err_realspace,outputs,opts] = asgard_run_pde(opts,pde); +end end diff --git a/asgard_run_pde.m b/asgard_run_pde.m index 4f1aa8af..f009d22b 100644 --- a/asgard_run_pde.m +++ b/asgard_run_pde.m @@ -1,4 +1,4 @@ -function [err,fval,fval_realspace,nodes,err_realspace,outputs] = ... +function [err,fval,fval_realspace,nodes,err_realspace,outputs,opts] = ... asgard_run_pde(opts,pde) root_directory = get_root_folder(); @@ -43,6 +43,8 @@ connectivity = []; end +%% Generate 1D mass matrices in each dimension (used in L2 projections) +pde = compute_dimension_mass_mat(opts,pde); %% Generate initial conditions (both 1D and multi-D). if ~opts.quiet; disp('Calculate 2D initial condition on the sparse-grid'); end @@ -98,8 +100,8 @@ if num_dims <=3 %% - % Get the real space solution - + % Get the real space solution + fval_realspace = wavelet_to_realspace(pde,opts,Meval,fval,hash_table); if ~isempty(pde.solutions) fval_realspace_analytic = get_analytic_realspace_solution_D(pde,opts,coord,t); @@ -107,8 +109,11 @@ end % construct the moment function handle list for calculating the mass - if opts.calculate_mass - [mass,mass_analytic] = calculate_mass(pde,opts,coord,fval_realspace,fval_realspace_analytic); + if opts.calculate_mass + mass = calculate_mass(pde,opts,coord,fval_realspace); + if ~isempty(pde.solutions) + mass_analytic = calculate_mass(pde,opts,coord,fval_realspace_analytic); + end mass_t(1) = mass; end @@ -156,7 +161,10 @@ % fval_realspace_SG = real_space_solution_at_coordinates_irregular(pde,fval,coordinates); if opts.calculate_mass - [mass,mass_analytic] = calculate_mass(pde,opts,coord,fval_realspace,fval_realspace_analytic); + mass = calculate_mass(pde,opts,coord,fval_realspace); + if ~isempty(pde.solutions) + mass_analytic = calculate_mass(pde,opts,coord,fval_realspace_analytic); + end mass_t(1) = mass; end @@ -232,7 +240,9 @@ % need to clean up this interface! outputs = save_output([],0,pde,opts,num_dims,fval,fval_realspace,f_realspace_analytic_nD,nodes,nodes_nodups,nodes_count,t,dt,toc,root_directory,hash_table); -outputs.mass_t = mass_t; +if opts.calculate_mass + outputs.mass_t = mass_t; +end %% Time Loop count=1; @@ -273,7 +283,7 @@ E = E * pde.Et(t,params); Emax = max(abs(Meval{2}*E)); % TODO : this clearly is problem dependent end - + if ~opts.quiet; disp(' Calculate time dependent matrix coeffs'); end if num_dims==2 if (pde.applySpecifiedE || pde.solvePoisson) @@ -440,32 +450,35 @@ err = err_wavelet; end - %% - % Plot results + % Reshape realspace solution and plot - if mod(L,opts.plot_freq)==0 && ~opts.quiet + if num_dims <= 3 - if isfield(figs,'solution') - figure(figs.solution); + f_realspace_nD = singleD_to_multiD(num_dims,fval_realspace,nodes); + if strcmp(opts.output_grid,'fixed') || strcmp(opts.output_grid,'elements') + f_realspace_nD = ... + remove_duplicates(num_dims,f_realspace_nD,nodes_nodups,nodes_count); + end + + f_realspace_analytic_nD = get_analytic_realspace_solution_D(pde,opts,coord_nodups,t+dt); + + element_coordinates = []; + if opts.use_oldhash else - figs.solution = figure('Name','Solution','Units','normalized','Position',[0.1,0.1,0.5,0.5]); + element_coordinates = get_sparse_grid_coordinates(pde,opts,hash_table); end - if num_dims <= 3 - - f_realspace_nD = singleD_to_multiD(num_dims,fval_realspace,nodes); - if strcmp(opts.output_grid,'fixed') || strcmp(opts.output_grid,'elements') - f_realspace_nD = ... - remove_duplicates(num_dims,f_realspace_nD,nodes_nodups,nodes_count); - end - - f_realspace_analytic_nD = get_analytic_realspace_solution_D(pde,opts,coord_nodups,t+dt); + %% + % Plot results + + if mod(L,opts.plot_freq)==0 && ~opts.quiet - element_coordinates = []; - if opts.use_oldhash + if isfield(figs,'solution') + figure(figs.solution); else - element_coordinates = get_sparse_grid_coordinates(pde,opts,hash_table); + figs.solution = figure('Name','Solution','Units','normalized','Position',[0.1,0.1,0.5,0.5]); end + plot_fval(pde,nodes_nodups,f_realspace_nD,f_realspace_analytic_nD,element_coordinates); % this is just for the RE paper @@ -484,13 +497,19 @@ figure(87) contour(ppar,pper,f2d,levs) end - end - + + end end count=count+1; t1 = toc; if ~opts.quiet; disp(['Took ' num2str(t1) ' [s]']); end + + + % Hack right now to update the params data every time step + + + % Save output outputs = save_output(outputs,L,pde,opts,num_dims,fval,fval_realspace,f_realspace_analytic_nD,nodes,nodes_nodups,nodes_count,t,dt,toc,root_directory,hash_table); @@ -508,8 +527,56 @@ ylim([0,2]); end + + % Hack right now to update the params data every time step + + if opts.update_params_each_timestep + + f_v0 = f_realspace_nD(:,1); % get the f(0,z) value (or as close to p=0 as the nodes allow) +% alpha_z = @(z) (2/sqrt(pi)-interp1(nodes{2},f_p0,z,'spline','extrap'))/dt; +% alpha_z = @(z) (pde.params.f0_v(nodes{1}(1))-interp1(nodes{2},f_v0,z,'spline','extrap'))/dt; +% pde.params.f0_v(nodes_nodups{1}(1))-f_v0 + alpha_z = @(z) (pde.params.f0_v(nodes_nodups{1}(1))-interp1(nodes_nodups{2},f_v0,z,'spline','extrap'))/dt; +% alpha_z = @(z) z.*0; %+ f_v0(1)./dt; + pde.params.alpha_z = alpha_z; +% z = linspace(0,pi,100); + outputs.alpha_t0{L+1} = alpha_z; +% outputs.alpha_t{L+1} = sum(alpha_z(z)); + outputs.alpha_t{L+1} = alpha_z(0); + alpha_z(0) + + background_species = [pde.params.b, pde.params.b2]; + uVals = nodes{1}; +% for k = 1:numel(background_species) +% % for i = 1:length(uVals) +% % uVal = uVals(i); +% for j = 1:length(lIndex) +% gamma_a = 4*pi*(params.a.Z)^2*e^4/((params.a.m)^2); +% % numerVals = mirror_FokkerPlanckCoeffs(numer_func,uVal,lIndex(j),z,params,background_species(k)); +% coeffVals = @(x) mirror_FokkerPlanckCoeffs(func,x,lIndex(j),z,params,background_species(k)); +% test_Avals(j) = test_Avals(j) + testVals(1); +% test_Bvals(j) = test_Bvals(j) + testVals(2); +% test_Cvals(j) = test_Cvals(j) + testVals(3); +% test_Dvals(j) = test_Dvals(j) + testVals(4); +% test_Evals(j) = test_Evals(j) + testVals(5); +% test_Fvals(j) = test_Fvals(j) + testVals(6); +% end +% % total_numA(i) = sum(numer_Avals(i,:)); +% % total_numB(i) = sum(numer_Bvals(i,:)); +% % total_numC(i) = sum(numer_Cvals(i,:)); +% % total_numD(i) = sum(numer_Dvals(i,:)); +% % total_numE(i) = sum(numer_Evals(i,:)); +% % total_numF(i) = sum(numer_Fvals(i,:)); +% pde.params.fp_Coeffs = coeffVals; +% end +% % end +% end + end +outputs.pde = pde; +outputs.opts = opts; + % delta_mass(1) = 0; % for i=1:numel(outputs.mass_t)-1 % z=outputs.nodes_t{end}{2}; diff --git a/asgard_test.m b/asgard_test.m index 3f762fef..13a73d71 100644 --- a/asgard_test.m +++ b/asgard_test.m @@ -9,14 +9,14 @@ function asgard_advection1_explicit_test(testCase) addpath(genpath(pwd)); disp('Testing advection1 (RK3)'); [err, act_f, act_frs] = asgard(@advection1,'quiet',true,'num_steps',5); -verifyLessThan(testCase, err, 9e-4); +verifyLessThan(testCase, err, 1e-3); end function asgard_advection1reverse_explicit_test(testCase) addpath(genpath(pwd)); disp('Testing advection1_reverse_flow (RK3)'); [err, act_f, act_frs] = asgard(@advection1_reverse_flow,'quiet',true,'num_steps', 5); -verifyLessThan(testCase, err, 9e-4); +verifyLessThan(testCase, err, 1e-3); end function asgard_advection1_implicit_test(testCase) @@ -253,7 +253,7 @@ function asgard_fokkerplanck1_momentum_C_ode15s_test(testCase) disp('Testing fokkerplanck1_momentum_C (ode15s)'); [err,act_f,act_frs] = asgard(@fokkerplanck1_momentum_C,... 'timestep_method','ode15s','lev',3,'num_steps',1,'dt',1.875*30,'quiet',true,'case',2); -verifyLessThan(testCase,err,3.8e-2); +verifyLessThan(testCase,err,5.4e-2); end function asgard_fokkerplanck1_momentum_C_CN_test(testCase) @@ -261,7 +261,7 @@ function asgard_fokkerplanck1_momentum_C_CN_test(testCase) disp('Testing fokkerplanck1_momentum_C (CN)'); [err,act_f,act_frs] = asgard(@fokkerplanck1_momentum_C,... 'timestep_method','CN','lev',3,'num_steps',30,'dt',1.875,'quiet',true,'case',2); -verifyLessThan(testCase,err,3.8e-2); +verifyLessThan(testCase,err,5.4e-2); end function asgard_fokkerplanck1_momentum_C_CN_TIA_test(testCase) @@ -270,7 +270,7 @@ function asgard_fokkerplanck1_momentum_C_CN_TIA_test(testCase) [err,act_f,act_frs] = asgard(@fokkerplanck1_momentum_C,... 'timestep_method','CN','lev',3,'num_steps',30,'dt',1.875,... 'quiet',true,'time_independent_A',true,'case',2); -verifyLessThan(testCase,err,3.8e-2); +verifyLessThan(testCase,err,5.4e-2); end function asgard_fokkerplanck1_momentum_C_BE_test(testCase) @@ -278,7 +278,7 @@ function asgard_fokkerplanck1_momentum_C_BE_test(testCase) disp('Testing fokkerplanck1_momentum_C (BE)'); [err,act_f,act_frs] = asgard(@fokkerplanck1_momentum_C,... 'timestep_method','BE','lev',3,'num_steps',30,'dt',1.875,'quiet',true,'case',2); -verifyLessThan(testCase,err,3.8e-2); +verifyLessThan(testCase,err,5.4e-2); end function asgard_fokkerplanck1_momentum_C_BE_TIA_test(testCase) @@ -287,38 +287,47 @@ function asgard_fokkerplanck1_momentum_C_BE_TIA_test(testCase) [err,act_f,act_frs] = asgard(@fokkerplanck1_momentum_C,... 'timestep_method','BE','lev',3,'num_steps',30,'dt',1.875,... 'quiet',true,'time_independent_A',true,'case',2); -verifyLessThan(testCase,err,3.8e-2); +verifyLessThan(testCase,err,5.4e-2); end function asgard_fokkerplanck1_momentum_C_implicit_BE_test(testCase) addpath(genpath(pwd)); -disp('Testing fokkerplanck1_momentum_C (BE / with LHS)'); -[err,act_f,act_frs] = asgard(@fokkerplanck1_momentum_C_LHS,'timestep_method','BE', ... +disp('Testing fokkerplanck1_momentum_C (BE)'); +[err,act_f,act_frs] = asgard(@fokkerplanck1_momentum_C,'timestep_method','BE', ... 'lev',3,'num_steps',30,'CFL',1.5,'quiet',true); -verifyLessThan(testCase,err,2.5e-2); +verifyLessThan(testCase,err,5.4e-2); end function asgard_fokkerplanck1_momentum_C_implicit_BE_TIA_test(testCase) addpath(genpath(pwd)); -disp('Testing fokkerplanck1_momentum_C (BE / with LHS / TIA)'); -[err,act_f,act_frs] = asgard(@fokkerplanck1_momentum_C_LHS,'timestep_method','BE', ... +disp('Testing fokkerplanck1_momentum_C (BE / TIA)'); +[err,act_f,act_frs] = asgard(@fokkerplanck1_momentum_C,'timestep_method','BE', ... 'lev',3,'num_steps',30,'CFL',1.5,'quiet',true,'time_independent_A',true); -verifyLessThan(testCase,err,2.5e-2); +verifyLessThan(testCase,err,5.4e-2); end function asgard_fokkerplanck1_momentum_C_implicit_CN_test(testCase) addpath(genpath(pwd)); -disp('Testing fokkerplanck1_momentum_C (CN / with LHS)'); -[err,act_f,act_frs] = asgard(@fokkerplanck1_momentum_C_LHS,'timestep_method','CN', ... +disp('Testing fokkerplanck1_momentum_C (CN)'); +[err,act_f,act_frs] = asgard(@fokkerplanck1_momentum_C,'timestep_method','CN', ... 'lev',3,'num_steps',30,'CFL',1.5,'quiet',true); -verifyLessThan(testCase,err,2.5e-2); +verifyLessThan(testCase,err,5.4e-2); end function asgard_fokkerplanck1_momentum_C_implicit_CN_TIA_test(testCase) addpath(genpath(pwd)); -disp('Testing fokkerplanck1_momentum_C (CN / with LHS / TIA)'); -[err,act_f,act_frs] = asgard(@fokkerplanck1_momentum_C_LHS,'timestep_method','CN', ... +disp('Testing fokkerplanck1_momentum_C (CN / TIA)'); +[err,act_f,act_frs] = asgard(@fokkerplanck1_momentum_C,'timestep_method','CN', ... 'lev',3,'num_steps',30,'CFL',1.5,'quiet',true,'time_independent_A',true); +verifyLessThan(testCase,err,5.4e-2); +end + +function asgard_mirror1_collision_div_test(testCase) +addpath(genpath(pwd)); +disp('Testing mirror1_collision_div (matrix_exponential)'); +[err,act_f,act_frs] = asgard(@mirror1_collision_div,'timestep_method','BE', ... + 'lev',4, 'deg', 5,'dt',1e-3,'num_steps',20,'quiet',false,'calculate_mass', true, ... + 'normalize_by_mass', true); verifyLessThan(testCase,err,2.5e-2); end @@ -395,18 +404,18 @@ function matrix_exponential_bcs2_test(testCase) verifyLessThan(testCase,rel_err,1e-5); end -function matrix_exponential_LHS_test(testCase) +function matrix_exponential_test(testCase) addpath(genpath(pwd)); disp('Testing matrix exponential with LHS'); -[err,fval]=asgard(@fokkerplanck2_E_LHS,'timestep_method','matrix_exponential','lev',3,'deg',4,'num_steps',1,'dt',0.01,'quiet',true,'case',3); +[err,fval]=asgard(@fokkerplanck2_E,'timestep_method','matrix_exponential','lev',3,'deg',4,'num_steps',1,'dt',0.01,'quiet',true,'case',3); rel_err = err / norm(fval); verifyLessThan(testCase,rel_err,2e-5); end -function ode15s_LHS_test(testCase) +function ode15s_test(testCase) addpath(genpath(pwd)); disp('Testing ode15s with LHS'); -[err,fval]=asgard(@fokkerplanck2_E_LHS,'timestep_method','ode15s','lev',3,'deg',3,'num_steps',1,'dt',0.01,'quiet',true,'case',3); +[err,fval]=asgard(@fokkerplanck2_E,'timestep_method','ode15s','lev',3,'deg',3,'num_steps',1,'dt',0.01,'quiet',true,'case',3); rel_err = err / norm(fval); verifyLessThan(testCase,rel_err,1e-4); end diff --git a/boundary_condition_vector.m b/boundary_condition_vector.m index cdf34a17..c2f0303c 100644 --- a/boundary_condition_vector.m +++ b/boundary_condition_vector.m @@ -28,12 +28,12 @@ for tt = 1:num_terms % Construct a BC object for each term - term_nD = terms{tt}; + md_term = terms{tt}; for d1 = 1:num_dims dim = dims{d1}; - term_1D = term_nD.terms_1D{d1}; + sd_term = md_term.terms_1D{d1}; xMin = dim.min; xMax = dim.max; @@ -41,9 +41,9 @@ lev = dim.lev; dof = deg * 2^lev; - for p=1:numel(term_1D.pterms) + for p=1:numel(sd_term.pterms) - pterm = term_1D.pterms{p}; + pterm = sd_term.pterms{p}; this_type = pterm.type; this_g = pterm.g; @@ -75,13 +75,28 @@ %% % Get boundary functions for all dims + % The d2=d1 index of this loop is overwritten. All + % other dims will have a mass term. for d2=1:num_dims + sd_term_oth_dim = md_term.terms_1D{d2}; + mass_pterm = sd_term_oth_dim.pterms{p}; + BC_func = @(x,p,t) BCL_fList{d2}(x,p,t).*mass_pterm.g(x,p,t); bcL{d1}{d2} = forward_wavelet_transform(opts.deg,pde.dimensions{d2}.lev,... pde.dimensions{d2}.min,pde.dimensions{d2}.max,... - BCL_fList{d2},pde.params,pde.transform_blocks,time); + BC_func,mass_pterm.dV,pde.params,pde.transform_blocks,time); + %Apply inverse mat + N = numel(bcL{d1}{d2}); + bcL{d1}{d2} = mass_pterm.LHS_mass_mat(1:N,1:N) \ bcL{d1}{d2}; + %Apply previous pterms + for q=1:p-1 + bcL{d1}{d2} = sd_term_oth_dim.pterms{q}.mat(1:N,1:N) * bcL{d1}{d2}; + end end + + + %% % Overwrite the trace (boundary) value just for this dim % Func*v|_xMin and Func*v|_xMax @@ -94,14 +109,14 @@ % Apply LHS_mass_mat for this pterm M = pterm.LHS_mass_mat; - bcL_tmp = inv(M) * bcL_tmp; + bcL_tmp = M(1:dof,1:dof) \ bcL_tmp; %% % Apply mats from preceeding pterms when chaining (p>1) preceeding_mat = eye(dof); for nn=1:p-1 - preceeding_mat = preceeding_mat * term_1D.pterms{nn}.mat; + preceeding_mat = preceeding_mat * sd_term.pterms{nn}.mat(1:dof,1:dof); end bcL_tmp = preceeding_mat * bcL_tmp; @@ -119,11 +134,23 @@ %% % Get boundary functions for all dims + % The d2=d1 index of this loop is overwritten. All + % other dims will have mass term. for d2=1:num_dims + sd_term_oth_dim = md_term.terms_1D{d2}; + mass_pterm = sd_term_oth_dim.pterms{p}; + BC_func = @(x,p,t) BCR_fList{d2}(x,p,t).*mass_pterm.g(x,p,t); bcR{d1}{d2} = forward_wavelet_transform(opts.deg,pde.dimensions{d2}.lev,... pde.dimensions{d2}.min,pde.dimensions{d2}.max,... - BCR_fList{d2},pde.params,pde.transform_blocks,time); + BC_func,mass_pterm.dV,pde.params,pde.transform_blocks,time); + %Apply inverse mat + N = numel(bcL{d1}{d2}); + bcR{d1}{d2} = mass_pterm.LHS_mass_mat(1:N,1:N) \ bcR{d1}{d2}; + %Apply previous pterms + for q=1:p-1 + bcR{d1}{d2} = sd_term_oth_dim.pterms{q}.mat(1:N,1:N) * bcR{d1}{d2}; + end end %% @@ -138,14 +165,14 @@ % Apply LHS_mass_mat for this pterm M = pterm.LHS_mass_mat; - bcR_tmp = inv(M) * bcR_tmp; + bcR_tmp = M(1:dof,1:dof) \ bcR_tmp; %% % Apply mats from preceeding terms when chaining (p>1) preceeding_mat = eye(dof); for nn=1:p-1 - preceeding_mat = preceeding_mat * term_1D.pterms{nn}.mat; + preceeding_mat = preceeding_mat * sd_term.pterms{nn}.mat(1:dof,1:dof); end bcR_tmp = preceeding_mat * bcR_tmp; diff --git a/calculate_mass.m b/calculate_mass.m index 062ccb3a..3972e0d0 100644 --- a/calculate_mass.m +++ b/calculate_mass.m @@ -1,4 +1,4 @@ -function [mass,mass_analytic] = calculate_mass(pde,opts,coord,fval_realspace,fval_realspace_analytic) +function [mass] = calculate_mass(pde,opts,coord,fval_realspace) num_dims = numel(pde.dimensions); @@ -8,8 +8,5 @@ end mass = moment_integral(pde.get_lev_vec,opts.deg,coord,fval_realspace,moment_func_nD,pde.dimensions); -if ~isempty(pde.solutions) && nargin>4 - mass_analytic = moment_integral(pde.get_lev_vec,opts.deg,coord,fval_realspace_analytic,moment_func_nD,pde.dimensions); -end end \ No newline at end of file diff --git a/compute_dimension_mass_mat.m b/compute_dimension_mass_mat.m new file mode 100644 index 00000000..c1d3d11c --- /dev/null +++ b/compute_dimension_mass_mat.m @@ -0,0 +1,22 @@ +function [pde] = compute_dimension_mass_mat(opts,pde) +%Computing mass matrix using the moment_dV volume jacobian. +%Needed when determining L2 projections with non-cartesian coordinates. + +num_dims = numel(pde.dimensions); +dims = pde.dimensions; + + +for d = 1:num_dims + dim = dims{d}; + construction_level = dim.lev; + if opts.max_lev_coeffs + construction_level = opts.max_lev; + end + g1 = @(x,p,t,d) 0*x+1; + pterm = MASS(g1,[],[],dim.moment_dV); + [M,~] = coeff_matrix(opts.deg,0,dim,pterm,pde.params,pde.transform_blocks,construction_level); + pde.dimensions{d}.mass_mat = M; +end + +end + diff --git a/diff b/diff new file mode 100644 index 00000000..c66967dd --- /dev/null +++ b/diff @@ -0,0 +1,8945 @@ +diff --git a/2020-07-runaway-electron-paper-scripts/runaway_electron_rate_plots.m b/2020-07-runaway-electron-paper-scripts/runaway_electron_rate_plots.m +index 8ea2b73..2477f96 100644 +--- a/2020-07-runaway-electron-paper-scripts/runaway_electron_rate_plots.m ++++ b/2020-07-runaway-electron-paper-scripts/runaway_electron_rate_plots.m +@@ -45,12 +45,14 @@ disp(['E_R V/m (from cgs 2): ',num2str(cgs.E_D*300*100*cgs.kB*T_e_K/(cgs.m_e*cgs + disp(['E_D / E_R : ', num2str(cgs.E_D/cgs.E_R)]); + disp(['v_th m/s (from cgs): ',num2str(cgs.v_th/100)]); + ++ + % calculate Dreicer E field in SI + + SI.n_e = cgs.n_e*1e6; + SI.v_th = sqrt(T_e_eV*SI.e/SI.m_e); + SI.coulomb_ln = coulomb_ln; +-SI.E_D = 1/(4*pi*SI.eps0^2) * SI.n_e * SI.e^3 * SI.coulomb_ln / (SI.m_e * SI.v_th^2); ++SI.E_D = SI.n_e*SI.e^3*SI.coulomb_ln/(2*pi*SI.eps0^2*SI.m_e ... ++ *SI.v_th^2);%1/(4*pi*SI.eps0^2) * SI.n_e * SI.e^3 * SI.coulomb_ln / (SI.m_e * SI.v_th^2); + disp(['E_D V/m (from SI): ', num2str(SI.E_D)]); + disp(['v_th m/s (from SI): ',num2str(SI.v_th)]); + +@@ -61,12 +63,13 @@ cgs.nu_ee = 4*pi * cgs.n_e * cgs.e^4 * cgs.coulomb_ln / (cgs.m_e^2 * cgs.v_th^3) + disp(['nu_ee 1/s (from cgs): ',num2str(cgs.nu_ee)]); + disp(['nu_ee 1/s (from cgs 2): ',num2str(cgs.nu_ee2)]); + +-% normalized (norm) parameters for use in FokkerPlanck2_complete_div ++% normalized (norm) parameters for use in mirror2_velocity_div + % here we have 3 types of variables ... + % 1) T,n,v_th - absolute values in SI + % 2) T_ref, n_ref, v_th_ref - these are the "reference values" (or the "tilde" values in the manuscript) + % 3) T_norm, n_norm, v_th_norm - these are T_norm = T / T_ref + ++ + ref.energy_eV = 20e3; + ref.T_eV = 2/3*ref.energy_eV; + ref.T_K = ref.T_eV * 11605; +@@ -93,9 +96,9 @@ disp(['n: ', num2str(norm.n)]); + + % Scan over E/E_D (0 to 0.6) for Zb=1 - compare with Fig 9 (pg 68) of Franz + +-ratio_max = 0.2; +-N = 100; +-ratio = linspace(0.,ratio_max,N); ++ratio_max = 0.3; ++N = 15; ++ratio = linspace(0.2,ratio_max,N); + + % Franz + Cn = 1/SI.n_e; +@@ -137,7 +140,7 @@ CH_normfac_r = CH_normfac_nr; + KB_normfac = 1/(kruskal_bernstein(0.1)/kulsrud_Z1(end)); + + % Scan over E/E_D ratio +-do_E_scan = false; ++do_E_scan = true; + if do_E_scan + figure + semilogy(ratio,kruskal_bernstein(ratio)*KB_normfac,'LineWidth',10,'Color','#E8E7E7','DisplayName','K-B (nr)'); +@@ -154,61 +157,85 @@ if do_E_scan + + N2 = 15; + ratio_max2 = 0.1; +- ratio2 = linspace(0.02,ratio_max2,N2); ++ ratio2 = linspace(0.002,ratio_max2,N2); + args.p_max = 10; +- args.v_th = norm.v_th; ++ args.v_th = ref.v_th; + args.nu_ee = norm.nu_ee; + args.tau = norm.tau; +- args.n = norm.n; ++ args.n = ref.n_e_m3; + num_steps = 10; + ++ m_D = 3.3443*10^-27; %Deuterium mass in kg ++ m_He = 6.7*10^-27; %helium 4 mass in kg ++ m_Ne = 3.3509177*10^-26; %neon 20 in kg ++ + % Non-relativistic + args.delta = 0; +- for Z = [1 2 10] +- for i=1:N2 +- args.E = ratio2(i) * SI.E_D / norm.E; % E into asgard is 2*E/E_D per the normalization +- args.Z = Z; +- dt = 2./args.E.^2/num_steps; +- if dt > 2000 +- dt = 2000; ++ args.Z = 1; ++ args.m = m_D; ++ % for Z = [1 2 10] ++ for i=1:N2 ++ % args.E = 0.2*ratio2(i) * SI.E_D ; % E into asgard is 2*E/E_D per the normalization ++ args.E_D = SI.E_D; ++ args.frac = 0.005*ratio2(i); ++ %args.Z = Z6 ++% if Z == 1 ++% args.m = m_D; ++% elseif Z == 2 ++% args.m = m_He; ++% else ++% args.m = m_Ne; ++% end ++ dt = 6.125e-04; ++ if dt > 2000 ++ dt = 2000; ++ end ++ num_steps = 1; ++ [~,~,~,~,~,outputs(i)] = asgard(@mirror2_velocity_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',4,'lev',4,'case',3,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true,'normalize_by_mass',true); ++ alpha_nr(i,1) = outputs(i).alpha_t{end}; ++ dt_nr(i,1) = dt; + end +- [~,~,~,~,~,outputs(i)] = asgard(@fokkerplanck2_complete_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',4,'lev',4,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true); +- alpha_nr(i,Z) = outputs(i).alpha_t{end}; +- end +- end +- +- % Relativistic +- args.delta = norm.delta; +- for Z = [1 2 10] +- for i=1:N2 +- args.E = ratio2(i) * SI.E_D / norm.E; % E into asgard is 2*E/E_D per the normalization +- args.Z = Z; +- dt = 2./args.E.^2/num_steps; +- if dt > 2000 +- dt = 2000; +- end +- [~,~,~,~,~,outputs(i)] = asgard(@fokkerplanck2_complete_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',4,'lev',4,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true); +- alpha_r(i,Z) = outputs(i).alpha_t{end}; +- end +- end ++% end ++% semilogy(dt_nr,alpha_nr(:,1)); ++% % Relativistic ++% args.delta = norm.delta; ++% for Z = [1 2 10] ++% for i=1:N2 ++% args.E = ratio2(i) * SI.E_D; % E into asgard is 2*E/E_D per the normalization ++% args.Z = Z; ++% if Z == 1 ++% args.m = m_D; ++% elseif Z == 2 ++% args.m = m_He; ++% else ++% args.m = m_Ne; ++% end ++% dt = 1e-4;%2./args.E.^2/num_steps; ++% if dt > 2000 ++% dt = 2000; ++% end ++% [~,~,~,~,~,outputs(i)] = asgard(@mirror2_velocity_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',4,'lev',4,'case',3,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true); ++% alpha_r(i,Z) = outputs(i).alpha_t{end}; ++% end ++% end + + norm_fac = kulsrud_Z1(end)/alpha_nr(N2,1); + disp(['norm_fac: ',num2str(norm_fac)]); + hold on +- semilogy(ratio2,alpha_nr(:,1)*norm_fac,'LineWidth',5,'DisplayName','ASGarD (nr, Z=1)','color','red'); +- semilogy(ratio2,alpha_nr(:,2)*norm_fac,'LineWidth',5,'DisplayName','ASGarD (nr, Z=2)','color','green'); +- semilogy(ratio2,alpha_nr(:,10)*norm_fac,'LineWidth',5,'DisplayName','ASGarD (nr, Z=10)','color','blue'); ++ semilogy(ratio2,alpha_nr(:,1)*norm_fac,'LineWidth',5,'DisplayName','ASGarD (nr, Z=1)','color','red'); ++ % semilogy(ratio2,alpha_nr(:,2)*norm_fac,'LineWidth',5,'DisplayName','ASGarD (nr, Z=2)','color','green'); ++ % semilogy(ratio2,alpha_nr(:,10)*norm_fac,'LineWidth',5,'DisplayName','ASGarD (nr, Z=10)','color','blue'); + +- semilogy(ratio2,alpha_r(:,1)*norm_fac,'LineWidth',5,'DisplayName','ASGarD (r, Z=1)','color','red','LineStyle',':'); +- semilogy(ratio2,alpha_r(:,2)*norm_fac,'LineWidth',5,'DisplayName','ASGarD (r, Z=2)','color','green','LineStyle',':'); +- semilogy(ratio2,alpha_r(:,10)*norm_fac,'LineWidth',5,'DisplayName','ASGarD (r, Z=10)','color','blue','LineStyle',':'); ++ % semilogy(ratio2,alpha_r(:,1)*norm_fac,'LineWidth',5,'DisplayName','ASGarD (r, Z=1)','color','red','LineStyle',':'); ++ %semilogy(ratio2,alpha_r(:,2)*norm_fac,'LineWidth',5,'DisplayName','ASGarD (r, Z=2)','color','green','LineStyle',':'); ++ %semilogy(ratio2,alpha_r(:,10)*norm_fac,'LineWidth',5,'DisplayName','ASGarD (r, Z=10)','color','blue','LineStyle',':'); + legend + hold off + end + + % Compare DoF required for given accuracy in alpha + +-do_dof_scan = true; ++do_dof_scan = false; + if do_dof_scan + + args.p_max = 10; +@@ -236,19 +263,19 @@ if do_dof_scan + % considerable time. + do_FG = false; + if do_FG +- [~,~,~,~,~,output_FG_deg4] = asgard(@fokkerplanck2_complete_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',4,'lev',lev,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','FG','update_params_each_timestep',true,'output_grid','fixed'); ++ [~,~,~,~,~,output_FG_deg4] = asgard(@mirror2_velocity_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',4,'lev',lev,'case',3,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','FG','update_params_each_timestep',true,'output_grid','fixed'); + save(['output_FG_E',E_string{i},'_deg4_lev',lev_str','.mat'],'output_FG_deg4'); + clear output_FG_deg4; + +- [~,~,~,~,~,output_FG_deg5] = asgard(@fokkerplanck2_complete_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',5,'lev',lev,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','FG','update_params_each_timestep',true,'output_grid','fixed'); ++ [~,~,~,~,~,output_FG_deg5] = asgard(@mirror2_velocity_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',5,'lev',lev,'case',3,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','FG','update_params_each_timestep',true,'output_grid','fixed'); + save(['output_FG_E',E_string{i},'_deg5_lev',lev_str','.mat'],'output_FG_deg5'); + clear output_FG_deg5; + +- [~,~,~,~,~,output_FG_deg6] = asgard(@fokkerplanck2_complete_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',6,'lev',lev,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','FG','update_params_each_timestep',true,'output_grid','fixed'); ++ [~,~,~,~,~,output_FG_deg6] = asgard(@mirror2_velocity_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',6,'lev',lev,'case',3,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','FG','update_params_each_timestep',true,'output_grid','fixed'); + save(['output_FG_E',E_string{i},'_deg6_lev',lev_str','.mat'],'output_FG_deg6'); + clear output_FG_deg6; + +- [~,~,~,~,~,output_FG_deg7] = asgard(@fokkerplanck2_complete_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',7,'lev',lev,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','FG','update_params_each_timestep',true,'output_grid','fixed'); ++ [~,~,~,~,~,output_FG_deg7] = asgard(@mirror2_velocity_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',7,'lev',lev,'case',3,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','FG','update_params_each_timestep',true,'output_grid','fixed'); + save(['output_FG_E',E_string{i},'_deg7_lev',lev_str','.mat'],'output_FG_deg7'); + clear output_FG_deg7; + end +@@ -257,14 +284,14 @@ if do_dof_scan + % results. + do_SG = true; + if do_SG +- [~,~,~,~,~,output_SG] = asgard(@fokkerplanck2_complete_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',deg,'lev',lev,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true,'output_grid','fixed'); +- [~,~,~,~,~,output_SG_deg6] = asgard(@fokkerplanck2_complete_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',6,'lev',lev,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true,'output_grid','fixed'); +- [~,~,~,~,~,output_1em0] = asgard(@fokkerplanck2_complete_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',deg,'lev',lev,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true,'adapt',true,'adapt_threshold',1e0,'output_grid','fixed','adapt_initial_condition',true); +- [~,~,~,~,~,output_1em1] = asgard(@fokkerplanck2_complete_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',deg,'lev',lev,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true,'adapt',true,'adapt_threshold',1e-1,'output_grid','fixed','adapt_initial_condition',true); +- [~,~,~,~,~,output_1em2] = asgard(@fokkerplanck2_complete_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',deg,'lev',lev,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true,'adapt',true,'adapt_threshold',1e-2,'output_grid','fixed','adapt_initial_condition',true); +- [~,~,~,~,~,output_1em3] = asgard(@fokkerplanck2_complete_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',deg,'lev',lev,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true,'adapt',true,'adapt_threshold',1e-3,'output_grid','fixed','adapt_initial_condition',true); +- [~,~,~,~,~,output_1em4] = asgard(@fokkerplanck2_complete_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',deg,'lev',lev,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true,'adapt',true,'adapt_threshold',1e-4,'output_grid','fixed','adapt_initial_condition',true); +- [~,~,~,~,~,output_1em5] = asgard(@fokkerplanck2_complete_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',deg,'lev',lev,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true,'adapt',true,'adapt_threshold',1e-5,'output_grid','fixed','adapt_initial_condition',true); ++ [~,~,~,~,~,output_SG] = asgard(@mirror2_velocity_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',deg,'lev',lev,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true,'output_grid','fixed'); ++ [~,~,~,~,~,output_SG_deg6] = asgard(@mirror2_velocity_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',6,'lev',lev,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true,'output_grid','fixed'); ++ [~,~,~,~,~,output_1em0] = asgard(@mirror2_velocity_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',deg,'lev',lev,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true,'adapt',true,'adapt_threshold',1e0,'output_grid','fixed','adapt_initial_condition',true); ++ [~,~,~,~,~,output_1em1] = asgard(@mirror2_velocity_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',deg,'lev',lev,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true,'adapt',true,'adapt_threshold',1e-1,'output_grid','fixed','adapt_initial_condition',true); ++ [~,~,~,~,~,output_1em2] = asgard(@mirror2_velocity_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',deg,'lev',lev,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true,'adapt',true,'adapt_threshold',1e-2,'output_grid','fixed','adapt_initial_condition',true); ++ [~,~,~,~,~,output_1em3] = asgard(@mirror2_velocity_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',deg,'lev',lev,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true,'adapt',true,'adapt_threshold',1e-3,'output_grid','fixed','adapt_initial_condition',true); ++ [~,~,~,~,~,output_1em4] = asgard(@mirror2_velocity_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',deg,'lev',lev,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true,'adapt',true,'adapt_threshold',1e-4,'output_grid','fixed','adapt_initial_condition',true); ++ [~,~,~,~,~,output_1em5] = asgard(@mirror2_velocity_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',deg,'lev',lev,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true,'adapt',true,'adapt_threshold',1e-5,'output_grid','fixed','adapt_initial_condition',true); + + alpha_SG(i,:) = cell2mat(output_SG.alpha_t); + alpha_SG_deg6(i,:) = cell2mat(output_SG_deg6.alpha_t); +@@ -497,7 +524,7 @@ if do_Z_scan + num_steps = 10; + dt = 2./args.E.^2/num_steps; + disp(i); +- [~,~,~,~,~,outputs(i)] = asgard(@fokkerplanck2_complete_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',4,'lev',4,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true); ++ [~,~,~,~,~,outputs(i)] = asgard(@mirror2_velocity_div,'timestep_method','BE','num_steps',num_steps,'dt',dt,'deg',4,'lev',4,'case',5,'cmd_args',args,'quiet',true,'calculate_mass',true,'grid_type','SG','update_params_each_timestep',true); + alpha_Z(i) = outputs(i).alpha_t{end}; + end + +diff --git a/2020-10-mirror_3D_scripts/dpitch_long_i.txt b/2020-10-mirror_3D_scripts/dpitch_long_i.txt +new file mode 100644 +index 0000000..9bb7cd4 +--- /dev/null ++++ b/2020-10-mirror_3D_scripts/dpitch_long_i.txt +@@ -0,0 +1,15 @@ ++ 7.952452671E-02 1.129492901E-01 5.941727353E-02 4.820582348E-02 4.205907478E-02 3.804727771E-02 3.518877981E-02 3.304121677E-02 3.137077637E-02 3.004056109E-02 ++ 2.896447062E-02 2.808543543E-02 2.736411117E-02 2.677256624E-02 2.629055317E-02 2.590320725E-02 2.559957714E-02 2.537166455E-02 2.521378977E-02 2.512217608E-02 ++ 2.509468969E-02 2.513069855E-02 2.523103142E-02 2.539803169E-02 2.563571299E-02 2.595003751E-02 2.634935658E-02 2.684508125E-02 2.745269801E-02 2.819332669E-02 ++ 2.909617023E-02 3.020250455E-02 3.157247937E-02 3.329740395E-02 3.552366840E-02 1.852512870E-02 5.273452973E-04 1.051280553E-03 1.574664544E-03 2.093190533E-03 ++ 2.606449645E-03 3.114289632E-03 3.612702340E-03 4.103848307E-03 4.584888596E-03 5.052951443E-03 5.509961183E-03 5.952774356E-03 6.380680873E-03 6.793063026E-03 ++ 7.187307084E-03 7.563505927E-03 7.919970508E-03 8.254927667E-03 8.567450786E-03 8.855783065E-03 9.117702407E-03 9.350836405E-03 9.553584580E-03 9.720618113E-03 ++ 9.849303078E-03 9.936221244E-03 9.972213075E-03 9.952859362E-03 9.867414270E-03 9.702892042E-03 9.449252096E-03 9.080992811E-03 8.580439098E-03 7.927108237E-03 ++ 7.086565160E-03 6.044876865E-03 4.789057312E-03 3.328063965E-03 1.021491200E-01 1.021491200E-01 3.328063965E-03 4.789057312E-03 6.044876865E-03 7.086565160E-03 ++ 7.927108237E-03 8.580439098E-03 9.080992811E-03 9.449252096E-03 9.702892042E-03 9.867414270E-03 9.952859362E-03 9.972213075E-03 9.936221244E-03 9.849303078E-03 ++ 9.720618113E-03 9.553584580E-03 9.350836405E-03 9.117702407E-03 8.855783065E-03 8.567450786E-03 8.254927667E-03 7.919970508E-03 7.563505927E-03 7.187307084E-03 ++ 6.793063026E-03 6.380680873E-03 5.952774356E-03 5.509961183E-03 5.052951443E-03 4.584888596E-03 4.103848307E-03 3.612702340E-03 3.114289632E-03 2.606449645E-03 ++ 2.093190533E-03 1.574664544E-03 1.051280553E-03 5.273452973E-04 1.852512870E-02 3.552366840E-02 3.329740395E-02 3.157247937E-02 3.020250455E-02 2.909617023E-02 ++ 2.819332669E-02 2.745269801E-02 2.684508125E-02 2.634935658E-02 2.595003751E-02 2.563571299E-02 2.539803169E-02 2.523103142E-02 2.513069855E-02 2.509468969E-02 ++ 2.512217608E-02 2.521378977E-02 2.537166455E-02 2.559957714E-02 2.590320725E-02 2.629055317E-02 2.677256624E-02 2.736411117E-02 2.808543543E-02 2.896447062E-02 ++ 3.004056109E-02 3.137077637E-02 3.304121677E-02 3.518877981E-02 3.804727771E-02 4.205907478E-02 4.820582348E-02 5.941727353E-02 1.129492901E-01 7.952452671E-02 +diff --git a/2020-10-mirror_3D_scripts/f_ij.txt b/2020-10-mirror_3D_scripts/f_ij.txt +new file mode 100644 +index 0000000..88512d9 +--- /dev/null ++++ b/2020-10-mirror_3D_scripts/f_ij.txt +@@ -0,0 +1,2250 @@ ++ 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 ++ 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 ++ 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 ++ 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 ++ 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 ++ 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 ++ 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 ++ 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 ++ 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 ++ 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 ++ 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 ++ 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 ++ 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 ++ 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 ++ 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 6.88657E-13 ++ 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 ++ 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 ++ 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 ++ 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 ++ 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 ++ 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 ++ 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 ++ 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 ++ 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 ++ 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 ++ 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 ++ 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 ++ 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 ++ 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 ++ 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 6.87307E-13 ++ 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 ++ 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 ++ 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 ++ 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 ++ 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 ++ 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 ++ 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 ++ 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 ++ 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 ++ 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 ++ 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 ++ 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 ++ 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 ++ 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 ++ 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 6.83278E-13 ++ 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 ++ 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 ++ 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 ++ 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 ++ 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 ++ 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 ++ 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 ++ 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 ++ 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 ++ 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 ++ 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 ++ 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 ++ 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 ++ 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 ++ 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 6.76719E-13 ++ 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 ++ 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 ++ 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 ++ 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 ++ 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 ++ 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 ++ 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 ++ 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 ++ 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 ++ 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 ++ 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 ++ 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 ++ 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 ++ 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 ++ 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 6.67864E-13 ++ 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 ++ 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 ++ 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 ++ 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 ++ 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 ++ 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 ++ 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 ++ 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 ++ 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 ++ 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 ++ 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 ++ 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 ++ 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 ++ 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 ++ 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 6.56807E-13 ++ 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 ++ 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 ++ 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 ++ 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 ++ 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 ++ 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 ++ 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 ++ 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 ++ 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 ++ 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 ++ 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 ++ 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 ++ 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 ++ 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 ++ 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 6.43647E-13 ++ 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 ++ 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 ++ 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 ++ 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 ++ 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 ++ 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 ++ 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 ++ 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 ++ 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 ++ 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 ++ 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 ++ 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 ++ 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 ++ 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 ++ 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 6.28510E-13 ++ 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 ++ 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 ++ 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 ++ 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 ++ 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 ++ 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 ++ 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 ++ 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 ++ 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 ++ 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 ++ 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 ++ 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 ++ 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 ++ 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 ++ 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 6.11541E-13 ++ 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 ++ 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 ++ 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 ++ 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 ++ 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 ++ 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 ++ 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 ++ 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 ++ 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 ++ 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 ++ 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 ++ 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 ++ 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 ++ 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 ++ 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 5.92905E-13 ++ 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 ++ 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 ++ 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 ++ 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 ++ 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 ++ 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 ++ 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 ++ 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 ++ 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 ++ 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 ++ 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 ++ 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 ++ 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 ++ 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 ++ 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 5.72781E-13 ++ 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 ++ 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 ++ 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 ++ 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 ++ 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 ++ 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 ++ 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 ++ 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 ++ 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 ++ 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 ++ 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 ++ 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 ++ 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 ++ 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 ++ 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 5.51358E-13 ++ 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 ++ 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 ++ 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 ++ 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 ++ 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 ++ 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 ++ 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 ++ 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 ++ 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 ++ 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 ++ 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 ++ 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 ++ 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 ++ 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 ++ 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 5.28835E-13 ++ 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 ++ 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 ++ 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 ++ 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 ++ 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 ++ 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 ++ 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 ++ 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 ++ 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 ++ 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 ++ 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 ++ 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 ++ 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 ++ 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 ++ 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 5.05412E-13 ++ 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 ++ 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 ++ 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 ++ 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 ++ 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 ++ 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 ++ 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 ++ 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 ++ 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 ++ 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 ++ 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 ++ 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 ++ 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 ++ 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 ++ 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 4.81294E-13 ++ 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 ++ 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 ++ 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 ++ 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 ++ 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 ++ 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 ++ 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 ++ 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 ++ 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 ++ 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 ++ 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 ++ 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 ++ 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 ++ 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 ++ 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 4.56680E-13 ++ 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 ++ 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 ++ 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 ++ 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 ++ 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 ++ 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 ++ 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 ++ 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 ++ 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 ++ 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 ++ 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 ++ 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 ++ 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 ++ 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 ++ 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 4.31769E-13 ++ 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 ++ 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 ++ 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 ++ 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 ++ 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 ++ 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 ++ 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 ++ 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 ++ 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 ++ 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 ++ 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 ++ 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 ++ 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 ++ 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 ++ 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 4.06750E-13 ++ 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 ++ 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 ++ 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 ++ 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 ++ 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 ++ 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 ++ 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 ++ 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 ++ 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 ++ 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 ++ 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 ++ 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 ++ 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 ++ 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 ++ 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 3.81804E-13 ++ 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 ++ 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 ++ 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 ++ 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 ++ 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 ++ 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 ++ 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 ++ 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 ++ 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 ++ 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 ++ 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 ++ 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 ++ 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 ++ 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 ++ 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 3.57098E-13 ++ 3.32789E-13 3.32789E-13 3.32789E-13 3.32789E-13 3.32789E-13 3.32789E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 ++ 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 ++ 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 ++ 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 ++ 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 ++ 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 ++ 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 ++ 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 ++ 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 ++ 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 ++ 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 ++ 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 ++ 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 ++ 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 ++ 3.32790E-13 3.32790E-13 3.32790E-13 3.32790E-13 3.32789E-13 3.32789E-13 3.32789E-13 3.32789E-13 3.32789E-13 3.32789E-13 ++ 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 ++ 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 ++ 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 ++ 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 ++ 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 ++ 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 ++ 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 ++ 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 ++ 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 ++ 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 ++ 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 ++ 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 ++ 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 ++ 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 ++ 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 3.09020E-13 ++ 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 ++ 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 ++ 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 ++ 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 ++ 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 ++ 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 ++ 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 ++ 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 ++ 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 ++ 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 ++ 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 ++ 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 ++ 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 ++ 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 ++ 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 2.85915E-13 ++ 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 ++ 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 ++ 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 ++ 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 ++ 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 ++ 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 ++ 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 ++ 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 ++ 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 ++ 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 ++ 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 ++ 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 ++ 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 ++ 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 ++ 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 2.63585E-13 ++ 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 ++ 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 ++ 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 ++ 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 ++ 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 ++ 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 ++ 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 ++ 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 ++ 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 ++ 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 ++ 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 ++ 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 ++ 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 ++ 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 ++ 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 2.42124E-13 ++ 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 ++ 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 ++ 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 ++ 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 ++ 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 ++ 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 ++ 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 ++ 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 ++ 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 ++ 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 ++ 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 ++ 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 ++ 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 ++ 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 ++ 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 2.21609E-13 ++ 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 ++ 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 ++ 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 ++ 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 ++ 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 ++ 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 ++ 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 ++ 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 ++ 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 ++ 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 ++ 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 ++ 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 ++ 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 ++ 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 ++ 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 2.02101E-13 ++ 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 ++ 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 ++ 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 ++ 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 ++ 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 ++ 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 ++ 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 ++ 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 ++ 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 ++ 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 ++ 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 ++ 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 ++ 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 ++ 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 ++ 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 1.83646E-13 ++ 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 ++ 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 ++ 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 ++ 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 ++ 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 ++ 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 ++ 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 ++ 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 ++ 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 ++ 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 ++ 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 ++ 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 ++ 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 ++ 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 ++ 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 1.66275E-13 ++ 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 ++ 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 ++ 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 ++ 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 ++ 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 ++ 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 ++ 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 ++ 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 ++ 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 ++ 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 ++ 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 ++ 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 ++ 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 ++ 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 ++ 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 1.50004E-13 ++ 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 ++ 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 ++ 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 ++ 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 ++ 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 ++ 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 ++ 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 ++ 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 ++ 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 ++ 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 ++ 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 ++ 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 ++ 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 ++ 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 ++ 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 1.34837E-13 ++ 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 ++ 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 ++ 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 ++ 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 ++ 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 ++ 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 ++ 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 ++ 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 ++ 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 ++ 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 ++ 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 ++ 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 ++ 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 ++ 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 ++ 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 1.20766E-13 ++ 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 ++ 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 ++ 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 ++ 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 ++ 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 ++ 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 ++ 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 ++ 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 ++ 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 ++ 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 ++ 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 ++ 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 ++ 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 ++ 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 ++ 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 1.07774E-13 ++ 9.58318E-14 9.58318E-14 9.58318E-14 9.58318E-14 9.58318E-14 9.58318E-14 9.58318E-14 9.58318E-14 9.58318E-14 9.58318E-14 ++ 9.58318E-14 9.58318E-14 9.58318E-14 9.58318E-14 9.58318E-14 9.58318E-14 9.58318E-14 9.58318E-14 9.58319E-14 9.58319E-14 ++ 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 ++ 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 ++ 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 ++ 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 ++ 9.58320E-14 9.58320E-14 9.58320E-14 9.58320E-14 9.58320E-14 9.58320E-14 9.58320E-14 9.58320E-14 9.58320E-14 9.58320E-14 ++ 9.58320E-14 9.58320E-14 9.58320E-14 9.58320E-14 9.58320E-14 9.58320E-14 9.58320E-14 9.58320E-14 9.58320E-14 9.58320E-14 ++ 9.58320E-14 9.58320E-14 9.58320E-14 9.58320E-14 9.58320E-14 9.58320E-14 9.58320E-14 9.58320E-14 9.58320E-14 9.58320E-14 ++ 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 ++ 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 ++ 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 ++ 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 9.58319E-14 ++ 9.58319E-14 9.58319E-14 9.58318E-14 9.58318E-14 9.58318E-14 9.58318E-14 9.58318E-14 9.58318E-14 9.58318E-14 9.58318E-14 ++ 9.58318E-14 9.58318E-14 9.58318E-14 9.58318E-14 9.58318E-14 9.58318E-14 9.58318E-14 9.58318E-14 9.58318E-14 9.58318E-14 ++ 8.49056E-14 8.49056E-14 8.49056E-14 8.49056E-14 8.49056E-14 8.49056E-14 8.49056E-14 8.49056E-14 8.49056E-14 8.49056E-14 ++ 8.49056E-14 8.49056E-14 8.49056E-14 8.49056E-14 8.49056E-14 8.49056E-14 8.49056E-14 8.49056E-14 8.49056E-14 8.49057E-14 ++ 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 ++ 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 ++ 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 ++ 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 ++ 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49058E-14 ++ 8.49058E-14 8.49058E-14 8.49058E-14 8.49058E-14 8.49058E-14 8.49058E-14 8.49058E-14 8.49058E-14 8.49058E-14 8.49058E-14 ++ 8.49058E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 ++ 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 ++ 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 ++ 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 ++ 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 8.49057E-14 ++ 8.49057E-14 8.49056E-14 8.49056E-14 8.49056E-14 8.49056E-14 8.49056E-14 8.49056E-14 8.49056E-14 8.49056E-14 8.49056E-14 ++ 8.49056E-14 8.49056E-14 8.49056E-14 8.49056E-14 8.49056E-14 8.49056E-14 8.49056E-14 8.49056E-14 8.49056E-14 8.49056E-14 ++ 7.49536E-14 7.49536E-14 7.49536E-14 7.49536E-14 7.49536E-14 7.49536E-14 7.49536E-14 7.49536E-14 7.49536E-14 7.49536E-14 ++ 7.49536E-14 7.49536E-14 7.49536E-14 7.49536E-14 7.49536E-14 7.49536E-14 7.49536E-14 7.49536E-14 7.49537E-14 7.49537E-14 ++ 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 ++ 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 ++ 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 ++ 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 ++ 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49538E-14 7.49538E-14 ++ 7.49538E-14 7.49538E-14 7.49538E-14 7.49538E-14 7.49538E-14 7.49538E-14 7.49538E-14 7.49538E-14 7.49538E-14 7.49538E-14 ++ 7.49538E-14 7.49538E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 ++ 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 ++ 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 ++ 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 ++ 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 7.49537E-14 ++ 7.49537E-14 7.49537E-14 7.49536E-14 7.49536E-14 7.49536E-14 7.49536E-14 7.49536E-14 7.49536E-14 7.49536E-14 7.49536E-14 ++ 7.49536E-14 7.49536E-14 7.49536E-14 7.49536E-14 7.49536E-14 7.49536E-14 7.49536E-14 7.49536E-14 7.49536E-14 7.49536E-14 ++ 6.59292E-14 6.59292E-14 6.59292E-14 6.59292E-14 6.59292E-14 6.59292E-14 6.59292E-14 6.59292E-14 6.59292E-14 6.59292E-14 ++ 6.59293E-14 6.59293E-14 6.59293E-14 6.59293E-14 6.59293E-14 6.59293E-14 6.59293E-14 6.59293E-14 6.59293E-14 6.59293E-14 ++ 6.59293E-14 6.59293E-14 6.59293E-14 6.59293E-14 6.59293E-14 6.59293E-14 6.59293E-14 6.59293E-14 6.59293E-14 6.59293E-14 ++ 6.59293E-14 6.59293E-14 6.59293E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 ++ 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 ++ 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 ++ 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 ++ 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 ++ 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 ++ 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 ++ 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 ++ 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59294E-14 6.59293E-14 6.59293E-14 6.59293E-14 ++ 6.59293E-14 6.59293E-14 6.59293E-14 6.59293E-14 6.59293E-14 6.59293E-14 6.59293E-14 6.59293E-14 6.59293E-14 6.59293E-14 ++ 6.59293E-14 6.59293E-14 6.59293E-14 6.59293E-14 6.59293E-14 6.59293E-14 6.59293E-14 6.59293E-14 6.59293E-14 6.59293E-14 ++ 6.59292E-14 6.59292E-14 6.59292E-14 6.59292E-14 6.59292E-14 6.59292E-14 6.59292E-14 6.59292E-14 6.59292E-14 6.59292E-14 ++ 5.77820E-14 5.77820E-14 5.77820E-14 5.77820E-14 5.77820E-14 5.77820E-14 5.77820E-14 5.77820E-14 5.77820E-14 5.77820E-14 ++ 5.77820E-14 5.77820E-14 5.77821E-14 5.77821E-14 5.77821E-14 5.77821E-14 5.77821E-14 5.77821E-14 5.77821E-14 5.77821E-14 ++ 5.77821E-14 5.77821E-14 5.77821E-14 5.77821E-14 5.77821E-14 5.77821E-14 5.77821E-14 5.77821E-14 5.77821E-14 5.77821E-14 ++ 5.77821E-14 5.77821E-14 5.77821E-14 5.77821E-14 5.77821E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 ++ 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 ++ 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 ++ 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 ++ 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 ++ 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 ++ 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 ++ 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 ++ 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77822E-14 5.77821E-14 5.77821E-14 5.77821E-14 5.77821E-14 5.77821E-14 ++ 5.77821E-14 5.77821E-14 5.77821E-14 5.77821E-14 5.77821E-14 5.77821E-14 5.77821E-14 5.77821E-14 5.77821E-14 5.77821E-14 ++ 5.77821E-14 5.77821E-14 5.77821E-14 5.77821E-14 5.77821E-14 5.77821E-14 5.77821E-14 5.77821E-14 5.77820E-14 5.77820E-14 ++ 5.77820E-14 5.77820E-14 5.77820E-14 5.77820E-14 5.77820E-14 5.77820E-14 5.77820E-14 5.77820E-14 5.77820E-14 5.77820E-14 ++ 5.04587E-14 5.04587E-14 5.04588E-14 5.04588E-14 5.04588E-14 5.04588E-14 5.04588E-14 5.04588E-14 5.04588E-14 5.04588E-14 ++ 5.04588E-14 5.04588E-14 5.04588E-14 5.04588E-14 5.04588E-14 5.04588E-14 5.04588E-14 5.04588E-14 5.04588E-14 5.04588E-14 ++ 5.04588E-14 5.04588E-14 5.04588E-14 5.04588E-14 5.04588E-14 5.04588E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 ++ 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 ++ 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 ++ 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 ++ 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 ++ 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 ++ 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 ++ 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 ++ 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 ++ 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 ++ 5.04589E-14 5.04589E-14 5.04589E-14 5.04589E-14 5.04588E-14 5.04588E-14 5.04588E-14 5.04588E-14 5.04588E-14 5.04588E-14 ++ 5.04588E-14 5.04588E-14 5.04588E-14 5.04588E-14 5.04588E-14 5.04588E-14 5.04588E-14 5.04588E-14 5.04588E-14 5.04588E-14 ++ 5.04588E-14 5.04588E-14 5.04588E-14 5.04588E-14 5.04588E-14 5.04588E-14 5.04588E-14 5.04588E-14 5.04587E-14 5.04587E-14 ++ 4.39045E-14 4.39045E-14 4.39045E-14 4.39045E-14 4.39045E-14 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 ++ 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 ++ 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 ++ 4.39046E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 ++ 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 ++ 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 ++ 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 ++ 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 ++ 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 ++ 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 ++ 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 ++ 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39047E-14 4.39046E-14 ++ 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 ++ 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 ++ 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 4.39046E-14 4.39045E-14 4.39045E-14 4.39045E-14 4.39045E-14 4.39045E-14 ++ 3.80637E-14 3.80637E-14 3.80637E-14 3.80637E-14 3.80637E-14 3.80637E-14 3.80637E-14 3.80638E-14 3.80638E-14 3.80638E-14 ++ 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 ++ 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 ++ 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 ++ 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 ++ 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 ++ 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 ++ 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 ++ 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 ++ 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 ++ 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 ++ 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80639E-14 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 ++ 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 ++ 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 3.80638E-14 ++ 3.80638E-14 3.80638E-14 3.80638E-14 3.80637E-14 3.80637E-14 3.80637E-14 3.80637E-14 3.80637E-14 3.80637E-14 3.80637E-14 ++ 3.28808E-14 3.28808E-14 3.28808E-14 3.28808E-14 3.28808E-14 3.28808E-14 3.28808E-14 3.28808E-14 3.28808E-14 3.28808E-14 ++ 3.28808E-14 3.28808E-14 3.28808E-14 3.28808E-14 3.28808E-14 3.28808E-14 3.28808E-14 3.28808E-14 3.28808E-14 3.28809E-14 ++ 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 ++ 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 ++ 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 ++ 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 ++ 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 ++ 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 ++ 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 ++ 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 ++ 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 ++ 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 ++ 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 3.28809E-14 ++ 3.28809E-14 3.28808E-14 3.28808E-14 3.28808E-14 3.28808E-14 3.28808E-14 3.28808E-14 3.28808E-14 3.28808E-14 3.28808E-14 ++ 3.28808E-14 3.28808E-14 3.28808E-14 3.28808E-14 3.28808E-14 3.28808E-14 3.28808E-14 3.28808E-14 3.28808E-14 3.28808E-14 ++ 2.83010E-14 2.83010E-14 2.83010E-14 2.83010E-14 2.83010E-14 2.83010E-14 2.83010E-14 2.83011E-14 2.83011E-14 2.83011E-14 ++ 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 ++ 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 ++ 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 ++ 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 ++ 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 ++ 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 ++ 2.83012E-14 2.83012E-14 2.83012E-14 2.83012E-14 2.83012E-14 2.83012E-14 2.83012E-14 2.83012E-14 2.83012E-14 2.83012E-14 ++ 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 ++ 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 ++ 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 ++ 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 ++ 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 ++ 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 2.83011E-14 ++ 2.83011E-14 2.83011E-14 2.83011E-14 2.83010E-14 2.83010E-14 2.83010E-14 2.83010E-14 2.83010E-14 2.83010E-14 2.83010E-14 ++ 2.42712E-14 2.42712E-14 2.42712E-14 2.42712E-14 2.42712E-14 2.42712E-14 2.42712E-14 2.42712E-14 2.42712E-14 2.42712E-14 ++ 2.42712E-14 2.42712E-14 2.42712E-14 2.42712E-14 2.42712E-14 2.42712E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 ++ 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 ++ 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 ++ 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 ++ 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 ++ 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 ++ 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 ++ 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 ++ 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 ++ 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 ++ 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 ++ 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 ++ 2.42713E-14 2.42713E-14 2.42713E-14 2.42713E-14 2.42712E-14 2.42712E-14 2.42712E-14 2.42712E-14 2.42712E-14 2.42712E-14 ++ 2.42712E-14 2.42712E-14 2.42712E-14 2.42712E-14 2.42712E-14 2.42712E-14 2.42712E-14 2.42712E-14 2.42712E-14 2.42712E-14 ++ 2.07400E-14 2.07400E-14 2.07400E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 ++ 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 ++ 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 ++ 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 ++ 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 ++ 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 ++ 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 ++ 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 ++ 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 ++ 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 ++ 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 ++ 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 ++ 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 ++ 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 ++ 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07401E-14 2.07400E-14 2.07400E-14 2.07400E-14 ++ 1.76586E-14 1.76586E-14 1.76586E-14 1.76586E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 ++ 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 ++ 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 ++ 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 ++ 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 ++ 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 ++ 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 ++ 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 ++ 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 ++ 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 ++ 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 ++ 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 ++ 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 ++ 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 ++ 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76587E-14 1.76586E-14 1.76586E-14 1.76586E-14 1.76586E-14 ++ 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 ++ 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 ++ 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 ++ 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 ++ 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 ++ 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 ++ 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 ++ 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 ++ 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 ++ 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 ++ 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 ++ 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49809E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 ++ 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 ++ 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 ++ 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 1.49808E-14 ++ 1.26631E-14 1.26631E-14 1.26631E-14 1.26631E-14 1.26631E-14 1.26631E-14 1.26631E-14 1.26631E-14 1.26631E-14 1.26632E-14 ++ 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 ++ 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 ++ 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 ++ 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 ++ 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 ++ 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 ++ 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 ++ 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 ++ 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 ++ 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 ++ 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 ++ 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 ++ 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 1.26632E-14 ++ 1.26632E-14 1.26631E-14 1.26631E-14 1.26631E-14 1.26631E-14 1.26631E-14 1.26631E-14 1.26631E-14 1.26631E-14 1.26631E-14 ++ 1.06654E-14 1.06654E-14 1.06654E-14 1.06654E-14 1.06654E-14 1.06654E-14 1.06654E-14 1.06654E-14 1.06654E-14 1.06654E-14 ++ 1.06654E-14 1.06654E-14 1.06654E-14 1.06654E-14 1.06654E-14 1.06654E-14 1.06654E-14 1.06654E-14 1.06655E-14 1.06655E-14 ++ 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 ++ 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 ++ 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 ++ 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 ++ 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 ++ 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 ++ 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 ++ 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 ++ 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 ++ 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 ++ 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 1.06655E-14 ++ 1.06655E-14 1.06655E-14 1.06654E-14 1.06654E-14 1.06654E-14 1.06654E-14 1.06654E-14 1.06654E-14 1.06654E-14 1.06654E-14 ++ 1.06654E-14 1.06654E-14 1.06654E-14 1.06654E-14 1.06654E-14 1.06654E-14 1.06654E-14 1.06654E-14 1.06654E-14 1.06654E-14 ++ 8.95045E-15 8.95045E-15 8.95045E-15 8.95045E-15 8.95045E-15 8.95046E-15 8.95046E-15 8.95046E-15 8.95046E-15 8.95046E-15 ++ 8.95046E-15 8.95047E-15 8.95047E-15 8.95047E-15 8.95047E-15 8.95047E-15 8.95047E-15 8.95047E-15 8.95048E-15 8.95048E-15 ++ 8.95048E-15 8.95048E-15 8.95048E-15 8.95048E-15 8.95049E-15 8.95049E-15 8.95049E-15 8.95049E-15 8.95049E-15 8.95049E-15 ++ 8.95050E-15 8.95050E-15 8.95050E-15 8.95050E-15 8.95050E-15 8.95050E-15 8.95050E-15 8.95050E-15 8.95050E-15 8.95050E-15 ++ 8.95050E-15 8.95050E-15 8.95050E-15 8.95050E-15 8.95050E-15 8.95050E-15 8.95050E-15 8.95050E-15 8.95050E-15 8.95050E-15 ++ 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 ++ 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 ++ 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 ++ 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 ++ 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 8.95051E-15 ++ 8.95050E-15 8.95050E-15 8.95050E-15 8.95050E-15 8.95050E-15 8.95050E-15 8.95050E-15 8.95050E-15 8.95050E-15 8.95050E-15 ++ 8.95050E-15 8.95050E-15 8.95050E-15 8.95050E-15 8.95050E-15 8.95050E-15 8.95050E-15 8.95050E-15 8.95050E-15 8.95050E-15 ++ 8.95049E-15 8.95049E-15 8.95049E-15 8.95049E-15 8.95049E-15 8.95049E-15 8.95048E-15 8.95048E-15 8.95048E-15 8.95048E-15 ++ 8.95048E-15 8.95048E-15 8.95047E-15 8.95047E-15 8.95047E-15 8.95047E-15 8.95047E-15 8.95047E-15 8.95047E-15 8.95046E-15 ++ 8.95046E-15 8.95046E-15 8.95046E-15 8.95046E-15 8.95046E-15 8.95045E-15 8.95045E-15 8.95045E-15 8.95045E-15 8.95045E-15 ++ 7.48414E-15 7.48414E-15 7.48415E-15 7.48415E-15 7.48415E-15 7.48415E-15 7.48415E-15 7.48415E-15 7.48415E-15 7.48416E-15 ++ 7.48416E-15 7.48416E-15 7.48416E-15 7.48416E-15 7.48416E-15 7.48416E-15 7.48417E-15 7.48417E-15 7.48417E-15 7.48417E-15 ++ 7.48417E-15 7.48417E-15 7.48417E-15 7.48418E-15 7.48418E-15 7.48418E-15 7.48418E-15 7.48418E-15 7.48418E-15 7.48418E-15 ++ 7.48418E-15 7.48419E-15 7.48419E-15 7.48419E-15 7.48419E-15 7.48419E-15 7.48419E-15 7.48419E-15 7.48419E-15 7.48419E-15 ++ 7.48419E-15 7.48419E-15 7.48419E-15 7.48419E-15 7.48419E-15 7.48419E-15 7.48419E-15 7.48419E-15 7.48419E-15 7.48419E-15 ++ 7.48419E-15 7.48419E-15 7.48419E-15 7.48419E-15 7.48419E-15 7.48420E-15 7.48420E-15 7.48420E-15 7.48420E-15 7.48420E-15 ++ 7.48420E-15 7.48420E-15 7.48420E-15 7.48420E-15 7.48420E-15 7.48420E-15 7.48420E-15 7.48420E-15 7.48420E-15 7.48420E-15 ++ 7.48420E-15 7.48420E-15 7.48420E-15 7.48420E-15 7.48420E-15 7.48420E-15 7.48420E-15 7.48420E-15 7.48420E-15 7.48420E-15 ++ 7.48420E-15 7.48420E-15 7.48420E-15 7.48420E-15 7.48420E-15 7.48420E-15 7.48420E-15 7.48420E-15 7.48420E-15 7.48420E-15 ++ 7.48420E-15 7.48420E-15 7.48420E-15 7.48420E-15 7.48420E-15 7.48419E-15 7.48419E-15 7.48419E-15 7.48419E-15 7.48419E-15 ++ 7.48419E-15 7.48419E-15 7.48419E-15 7.48419E-15 7.48419E-15 7.48419E-15 7.48419E-15 7.48419E-15 7.48419E-15 7.48419E-15 ++ 7.48419E-15 7.48419E-15 7.48419E-15 7.48419E-15 7.48419E-15 7.48419E-15 7.48419E-15 7.48419E-15 7.48419E-15 7.48418E-15 ++ 7.48418E-15 7.48418E-15 7.48418E-15 7.48418E-15 7.48418E-15 7.48418E-15 7.48418E-15 7.48417E-15 7.48417E-15 7.48417E-15 ++ 7.48417E-15 7.48417E-15 7.48417E-15 7.48417E-15 7.48416E-15 7.48416E-15 7.48416E-15 7.48416E-15 7.48416E-15 7.48416E-15 ++ 7.48416E-15 7.48415E-15 7.48415E-15 7.48415E-15 7.48415E-15 7.48415E-15 7.48415E-15 7.48415E-15 7.48414E-15 7.48414E-15 ++ 6.23548E-15 6.23548E-15 6.23549E-15 6.23549E-15 6.23549E-15 6.23549E-15 6.23549E-15 6.23549E-15 6.23549E-15 6.23549E-15 ++ 6.23550E-15 6.23550E-15 6.23550E-15 6.23550E-15 6.23550E-15 6.23550E-15 6.23550E-15 6.23550E-15 6.23551E-15 6.23551E-15 ++ 6.23551E-15 6.23551E-15 6.23551E-15 6.23551E-15 6.23551E-15 6.23551E-15 6.23552E-15 6.23552E-15 6.23552E-15 6.23552E-15 ++ 6.23552E-15 6.23552E-15 6.23552E-15 6.23552E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 ++ 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 ++ 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 ++ 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 ++ 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 ++ 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 ++ 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 ++ 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 ++ 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23553E-15 6.23552E-15 6.23552E-15 6.23552E-15 6.23552E-15 ++ 6.23552E-15 6.23552E-15 6.23552E-15 6.23552E-15 6.23551E-15 6.23551E-15 6.23551E-15 6.23551E-15 6.23551E-15 6.23551E-15 ++ 6.23551E-15 6.23551E-15 6.23550E-15 6.23550E-15 6.23550E-15 6.23550E-15 6.23550E-15 6.23550E-15 6.23550E-15 6.23550E-15 ++ 6.23549E-15 6.23549E-15 6.23549E-15 6.23549E-15 6.23549E-15 6.23549E-15 6.23549E-15 6.23549E-15 6.23548E-15 6.23548E-15 ++ 5.17642E-15 5.17642E-15 5.17642E-15 5.17642E-15 5.17642E-15 5.17642E-15 5.17642E-15 5.17642E-15 5.17643E-15 5.17643E-15 ++ 5.17643E-15 5.17643E-15 5.17643E-15 5.17643E-15 5.17643E-15 5.17643E-15 5.17643E-15 5.17644E-15 5.17644E-15 5.17644E-15 ++ 5.17644E-15 5.17644E-15 5.17644E-15 5.17644E-15 5.17644E-15 5.17644E-15 5.17644E-15 5.17645E-15 5.17645E-15 5.17645E-15 ++ 5.17645E-15 5.17645E-15 5.17645E-15 5.17645E-15 5.17645E-15 5.17645E-15 5.17645E-15 5.17645E-15 5.17645E-15 5.17645E-15 ++ 5.17645E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 ++ 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 ++ 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 ++ 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 ++ 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 ++ 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 ++ 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17646E-15 5.17645E-15 ++ 5.17645E-15 5.17645E-15 5.17645E-15 5.17645E-15 5.17645E-15 5.17645E-15 5.17645E-15 5.17645E-15 5.17645E-15 5.17645E-15 ++ 5.17645E-15 5.17645E-15 5.17645E-15 5.17644E-15 5.17644E-15 5.17644E-15 5.17644E-15 5.17644E-15 5.17644E-15 5.17644E-15 ++ 5.17644E-15 5.17644E-15 5.17644E-15 5.17643E-15 5.17643E-15 5.17643E-15 5.17643E-15 5.17643E-15 5.17643E-15 5.17643E-15 ++ 5.17643E-15 5.17643E-15 5.17642E-15 5.17642E-15 5.17642E-15 5.17642E-15 5.17642E-15 5.17642E-15 5.17642E-15 5.17642E-15 ++ 4.28173E-15 4.28174E-15 4.28174E-15 4.28174E-15 4.28174E-15 4.28174E-15 4.28174E-15 4.28174E-15 4.28174E-15 4.28174E-15 ++ 4.28174E-15 4.28174E-15 4.28175E-15 4.28175E-15 4.28175E-15 4.28175E-15 4.28175E-15 4.28175E-15 4.28175E-15 4.28175E-15 ++ 4.28175E-15 4.28175E-15 4.28176E-15 4.28176E-15 4.28176E-15 4.28176E-15 4.28176E-15 4.28176E-15 4.28176E-15 4.28176E-15 ++ 4.28176E-15 4.28176E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 ++ 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 ++ 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 ++ 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 ++ 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 ++ 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 ++ 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 ++ 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 ++ 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28177E-15 4.28176E-15 4.28176E-15 ++ 4.28176E-15 4.28176E-15 4.28176E-15 4.28176E-15 4.28176E-15 4.28176E-15 4.28176E-15 4.28176E-15 4.28175E-15 4.28175E-15 ++ 4.28175E-15 4.28175E-15 4.28175E-15 4.28175E-15 4.28175E-15 4.28175E-15 4.28175E-15 4.28175E-15 4.28174E-15 4.28174E-15 ++ 4.28174E-15 4.28174E-15 4.28174E-15 4.28174E-15 4.28174E-15 4.28174E-15 4.28174E-15 4.28174E-15 4.28174E-15 4.28173E-15 ++ 3.52892E-15 3.52892E-15 3.52892E-15 3.52892E-15 3.52892E-15 3.52893E-15 3.52893E-15 3.52893E-15 3.52893E-15 3.52893E-15 ++ 3.52893E-15 3.52893E-15 3.52893E-15 3.52893E-15 3.52893E-15 3.52893E-15 3.52893E-15 3.52894E-15 3.52894E-15 3.52894E-15 ++ 3.52894E-15 3.52894E-15 3.52894E-15 3.52894E-15 3.52894E-15 3.52894E-15 3.52894E-15 3.52894E-15 3.52894E-15 3.52895E-15 ++ 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 ++ 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 ++ 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 ++ 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 ++ 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 ++ 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 ++ 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 ++ 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 ++ 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 3.52895E-15 ++ 3.52895E-15 3.52894E-15 3.52894E-15 3.52894E-15 3.52894E-15 3.52894E-15 3.52894E-15 3.52894E-15 3.52894E-15 3.52894E-15 ++ 3.52894E-15 3.52894E-15 3.52894E-15 3.52893E-15 3.52893E-15 3.52893E-15 3.52893E-15 3.52893E-15 3.52893E-15 3.52893E-15 ++ 3.52893E-15 3.52893E-15 3.52893E-15 3.52893E-15 3.52893E-15 3.52892E-15 3.52892E-15 3.52892E-15 3.52892E-15 3.52892E-15 ++ 2.89799E-15 2.89799E-15 2.89799E-15 2.89799E-15 2.89799E-15 2.89799E-15 2.89799E-15 2.89799E-15 2.89799E-15 2.89799E-15 ++ 2.89799E-15 2.89799E-15 2.89800E-15 2.89800E-15 2.89800E-15 2.89800E-15 2.89800E-15 2.89800E-15 2.89800E-15 2.89800E-15 ++ 2.89800E-15 2.89800E-15 2.89800E-15 2.89800E-15 2.89800E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 ++ 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 ++ 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 ++ 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 ++ 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89802E-15 2.89802E-15 2.89802E-15 2.89802E-15 2.89802E-15 2.89802E-15 ++ 2.89802E-15 2.89802E-15 2.89802E-15 2.89802E-15 2.89802E-15 2.89802E-15 2.89802E-15 2.89802E-15 2.89802E-15 2.89802E-15 ++ 2.89802E-15 2.89802E-15 2.89802E-15 2.89802E-15 2.89802E-15 2.89802E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 ++ 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 ++ 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 ++ 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 ++ 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89801E-15 2.89800E-15 2.89800E-15 2.89800E-15 2.89800E-15 2.89800E-15 ++ 2.89800E-15 2.89800E-15 2.89800E-15 2.89800E-15 2.89800E-15 2.89800E-15 2.89800E-15 2.89800E-15 2.89799E-15 2.89799E-15 ++ 2.89799E-15 2.89799E-15 2.89799E-15 2.89799E-15 2.89799E-15 2.89799E-15 2.89799E-15 2.89799E-15 2.89799E-15 2.89799E-15 ++ 2.37128E-15 2.37128E-15 2.37128E-15 2.37128E-15 2.37129E-15 2.37129E-15 2.37129E-15 2.37129E-15 2.37129E-15 2.37129E-15 ++ 2.37129E-15 2.37129E-15 2.37129E-15 2.37129E-15 2.37129E-15 2.37129E-15 2.37129E-15 2.37129E-15 2.37129E-15 2.37129E-15 ++ 2.37130E-15 2.37130E-15 2.37130E-15 2.37130E-15 2.37130E-15 2.37130E-15 2.37130E-15 2.37130E-15 2.37130E-15 2.37130E-15 ++ 2.37130E-15 2.37130E-15 2.37130E-15 2.37130E-15 2.37130E-15 2.37130E-15 2.37130E-15 2.37130E-15 2.37130E-15 2.37130E-15 ++ 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 ++ 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 ++ 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 ++ 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 ++ 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 ++ 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 ++ 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 2.37131E-15 ++ 2.37130E-15 2.37130E-15 2.37130E-15 2.37130E-15 2.37130E-15 2.37130E-15 2.37130E-15 2.37130E-15 2.37130E-15 2.37130E-15 ++ 2.37130E-15 2.37130E-15 2.37130E-15 2.37130E-15 2.37130E-15 2.37130E-15 2.37130E-15 2.37130E-15 2.37130E-15 2.37130E-15 ++ 2.37129E-15 2.37129E-15 2.37129E-15 2.37129E-15 2.37129E-15 2.37129E-15 2.37129E-15 2.37129E-15 2.37129E-15 2.37129E-15 ++ 2.37129E-15 2.37129E-15 2.37129E-15 2.37129E-15 2.37129E-15 2.37129E-15 2.37128E-15 2.37128E-15 2.37128E-15 2.37128E-15 ++ 1.93332E-15 1.93332E-15 1.93332E-15 1.93332E-15 1.93332E-15 1.93332E-15 1.93332E-15 1.93332E-15 1.93332E-15 1.93332E-15 ++ 1.93332E-15 1.93332E-15 1.93332E-15 1.93332E-15 1.93333E-15 1.93333E-15 1.93333E-15 1.93333E-15 1.93333E-15 1.93333E-15 ++ 1.93333E-15 1.93333E-15 1.93333E-15 1.93333E-15 1.93333E-15 1.93333E-15 1.93333E-15 1.93333E-15 1.93333E-15 1.93333E-15 ++ 1.93333E-15 1.93333E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 ++ 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 ++ 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 ++ 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 ++ 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 ++ 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 ++ 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 ++ 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 ++ 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93334E-15 1.93333E-15 1.93333E-15 ++ 1.93333E-15 1.93333E-15 1.93333E-15 1.93333E-15 1.93333E-15 1.93333E-15 1.93333E-15 1.93333E-15 1.93333E-15 1.93333E-15 ++ 1.93333E-15 1.93333E-15 1.93333E-15 1.93333E-15 1.93333E-15 1.93333E-15 1.93332E-15 1.93332E-15 1.93332E-15 1.93332E-15 ++ 1.93332E-15 1.93332E-15 1.93332E-15 1.93332E-15 1.93332E-15 1.93332E-15 1.93332E-15 1.93332E-15 1.93332E-15 1.93332E-15 ++ 1.57057E-15 1.57057E-15 1.57057E-15 1.57057E-15 1.57057E-15 1.57057E-15 1.57057E-15 1.57057E-15 1.57057E-15 1.57057E-15 ++ 1.57057E-15 1.57057E-15 1.57057E-15 1.57057E-15 1.57057E-15 1.57057E-15 1.57057E-15 1.57057E-15 1.57058E-15 1.57058E-15 ++ 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 ++ 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 ++ 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 ++ 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 ++ 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57059E-15 1.57059E-15 1.57059E-15 1.57059E-15 ++ 1.57059E-15 1.57059E-15 1.57059E-15 1.57059E-15 1.57059E-15 1.57059E-15 1.57059E-15 1.57059E-15 1.57059E-15 1.57059E-15 ++ 1.57059E-15 1.57059E-15 1.57059E-15 1.57059E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 ++ 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 ++ 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 ++ 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 ++ 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 1.57058E-15 ++ 1.57058E-15 1.57058E-15 1.57057E-15 1.57057E-15 1.57057E-15 1.57057E-15 1.57057E-15 1.57057E-15 1.57057E-15 1.57057E-15 ++ 1.57057E-15 1.57057E-15 1.57057E-15 1.57057E-15 1.57057E-15 1.57057E-15 1.57057E-15 1.57057E-15 1.57057E-15 1.57057E-15 ++ 1.27129E-15 1.27129E-15 1.27129E-15 1.27129E-15 1.27129E-15 1.27129E-15 1.27129E-15 1.27129E-15 1.27129E-15 1.27129E-15 ++ 1.27129E-15 1.27129E-15 1.27129E-15 1.27129E-15 1.27129E-15 1.27129E-15 1.27129E-15 1.27129E-15 1.27129E-15 1.27129E-15 ++ 1.27129E-15 1.27129E-15 1.27129E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 ++ 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 ++ 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 ++ 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 ++ 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 ++ 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 ++ 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 ++ 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 ++ 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 ++ 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 ++ 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27130E-15 1.27129E-15 1.27129E-15 1.27129E-15 ++ 1.27129E-15 1.27129E-15 1.27129E-15 1.27129E-15 1.27129E-15 1.27129E-15 1.27129E-15 1.27129E-15 1.27129E-15 1.27129E-15 ++ 1.27129E-15 1.27129E-15 1.27129E-15 1.27129E-15 1.27129E-15 1.27129E-15 1.27129E-15 1.27129E-15 1.27129E-15 1.27129E-15 ++ 1.02533E-15 1.02533E-15 1.02533E-15 1.02533E-15 1.02533E-15 1.02533E-15 1.02533E-15 1.02533E-15 1.02533E-15 1.02533E-15 ++ 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 ++ 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 ++ 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 ++ 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 ++ 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 ++ 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 ++ 1.02535E-15 1.02535E-15 1.02535E-15 1.02535E-15 1.02535E-15 1.02535E-15 1.02535E-15 1.02535E-15 1.02535E-15 1.02535E-15 ++ 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 ++ 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 ++ 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 ++ 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 ++ 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 ++ 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 1.02534E-15 ++ 1.02533E-15 1.02533E-15 1.02533E-15 1.02533E-15 1.02533E-15 1.02533E-15 1.02533E-15 1.02533E-15 1.02533E-15 1.02533E-15 ++ 8.23986E-16 8.23987E-16 8.23987E-16 8.23987E-16 8.23987E-16 8.23988E-16 8.23988E-16 8.23988E-16 8.23989E-16 8.23989E-16 ++ 8.23989E-16 8.23989E-16 8.23990E-16 8.23990E-16 8.23990E-16 8.23991E-16 8.23991E-16 8.23991E-16 8.23991E-16 8.23992E-16 ++ 8.23992E-16 8.23992E-16 8.23992E-16 8.23993E-16 8.23993E-16 8.23993E-16 8.23994E-16 8.23994E-16 8.23994E-16 8.23994E-16 ++ 8.23995E-16 8.23995E-16 8.23995E-16 8.23996E-16 8.23996E-16 8.23996E-16 8.23996E-16 8.23996E-16 8.23996E-16 8.23996E-16 ++ 8.23996E-16 8.23996E-16 8.23996E-16 8.23996E-16 8.23996E-16 8.23996E-16 8.23996E-16 8.23996E-16 8.23997E-16 8.23997E-16 ++ 8.23997E-16 8.23997E-16 8.23997E-16 8.23997E-16 8.23997E-16 8.23997E-16 8.23997E-16 8.23997E-16 8.23997E-16 8.23997E-16 ++ 8.23997E-16 8.23997E-16 8.23997E-16 8.23997E-16 8.23997E-16 8.23997E-16 8.23997E-16 8.23997E-16 8.23997E-16 8.23997E-16 ++ 8.23997E-16 8.23997E-16 8.23997E-16 8.23997E-16 8.23998E-16 8.23998E-16 8.23997E-16 8.23997E-16 8.23997E-16 8.23997E-16 ++ 8.23997E-16 8.23997E-16 8.23997E-16 8.23997E-16 8.23997E-16 8.23997E-16 8.23997E-16 8.23997E-16 8.23997E-16 8.23997E-16 ++ 8.23997E-16 8.23997E-16 8.23997E-16 8.23997E-16 8.23997E-16 8.23997E-16 8.23997E-16 8.23997E-16 8.23997E-16 8.23997E-16 ++ 8.23997E-16 8.23997E-16 8.23996E-16 8.23996E-16 8.23996E-16 8.23996E-16 8.23996E-16 8.23996E-16 8.23996E-16 8.23996E-16 ++ 8.23996E-16 8.23996E-16 8.23996E-16 8.23996E-16 8.23996E-16 8.23996E-16 8.23996E-16 8.23995E-16 8.23995E-16 8.23995E-16 ++ 8.23994E-16 8.23994E-16 8.23994E-16 8.23994E-16 8.23993E-16 8.23993E-16 8.23993E-16 8.23992E-16 8.23992E-16 8.23992E-16 ++ 8.23992E-16 8.23991E-16 8.23991E-16 8.23991E-16 8.23991E-16 8.23990E-16 8.23990E-16 8.23990E-16 8.23989E-16 8.23989E-16 ++ 8.23989E-16 8.23989E-16 8.23988E-16 8.23988E-16 8.23988E-16 8.23987E-16 8.23987E-16 8.23987E-16 8.23987E-16 8.23986E-16 ++ 6.59797E-16 6.59797E-16 6.59798E-16 6.59798E-16 6.59798E-16 6.59798E-16 6.59799E-16 6.59799E-16 6.59799E-16 6.59799E-16 ++ 6.59800E-16 6.59800E-16 6.59800E-16 6.59800E-16 6.59800E-16 6.59801E-16 6.59801E-16 6.59801E-16 6.59801E-16 6.59802E-16 ++ 6.59802E-16 6.59802E-16 6.59802E-16 6.59803E-16 6.59803E-16 6.59803E-16 6.59803E-16 6.59804E-16 6.59804E-16 6.59804E-16 ++ 6.59804E-16 6.59805E-16 6.59805E-16 6.59805E-16 6.59805E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 ++ 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 ++ 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 ++ 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59807E-16 6.59807E-16 6.59807E-16 ++ 6.59807E-16 6.59807E-16 6.59807E-16 6.59807E-16 6.59807E-16 6.59807E-16 6.59807E-16 6.59807E-16 6.59807E-16 6.59807E-16 ++ 6.59807E-16 6.59807E-16 6.59807E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 ++ 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 ++ 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 ++ 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59806E-16 6.59805E-16 6.59805E-16 6.59805E-16 6.59805E-16 6.59804E-16 ++ 6.59804E-16 6.59804E-16 6.59804E-16 6.59803E-16 6.59803E-16 6.59803E-16 6.59803E-16 6.59802E-16 6.59802E-16 6.59802E-16 ++ 6.59802E-16 6.59801E-16 6.59801E-16 6.59801E-16 6.59801E-16 6.59800E-16 6.59800E-16 6.59800E-16 6.59800E-16 6.59800E-16 ++ 6.59799E-16 6.59799E-16 6.59799E-16 6.59799E-16 6.59798E-16 6.59798E-16 6.59798E-16 6.59798E-16 6.59797E-16 6.59797E-16 ++ 5.26425E-16 5.26425E-16 5.26425E-16 5.26425E-16 5.26425E-16 5.26426E-16 5.26426E-16 5.26426E-16 5.26426E-16 5.26426E-16 ++ 5.26427E-16 5.26427E-16 5.26427E-16 5.26427E-16 5.26427E-16 5.26428E-16 5.26428E-16 5.26428E-16 5.26428E-16 5.26428E-16 ++ 5.26429E-16 5.26429E-16 5.26429E-16 5.26429E-16 5.26429E-16 5.26430E-16 5.26430E-16 5.26430E-16 5.26430E-16 5.26430E-16 ++ 5.26431E-16 5.26431E-16 5.26431E-16 5.26431E-16 5.26431E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 ++ 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 ++ 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 ++ 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 ++ 5.26432E-16 5.26433E-16 5.26433E-16 5.26433E-16 5.26433E-16 5.26433E-16 5.26433E-16 5.26433E-16 5.26433E-16 5.26432E-16 ++ 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 ++ 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 ++ 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 ++ 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26432E-16 5.26431E-16 5.26431E-16 5.26431E-16 5.26431E-16 5.26431E-16 ++ 5.26430E-16 5.26430E-16 5.26430E-16 5.26430E-16 5.26430E-16 5.26429E-16 5.26429E-16 5.26429E-16 5.26429E-16 5.26429E-16 ++ 5.26428E-16 5.26428E-16 5.26428E-16 5.26428E-16 5.26428E-16 5.26427E-16 5.26427E-16 5.26427E-16 5.26427E-16 5.26427E-16 ++ 5.26426E-16 5.26426E-16 5.26426E-16 5.26426E-16 5.26426E-16 5.26425E-16 5.26425E-16 5.26425E-16 5.26425E-16 5.26425E-16 ++ 4.18502E-16 4.18502E-16 4.18502E-16 4.18503E-16 4.18503E-16 4.18503E-16 4.18503E-16 4.18503E-16 4.18503E-16 4.18504E-16 ++ 4.18504E-16 4.18504E-16 4.18504E-16 4.18504E-16 4.18504E-16 4.18505E-16 4.18505E-16 4.18505E-16 4.18505E-16 4.18505E-16 ++ 4.18505E-16 4.18506E-16 4.18506E-16 4.18506E-16 4.18506E-16 4.18506E-16 4.18506E-16 4.18507E-16 4.18507E-16 4.18507E-16 ++ 4.18507E-16 4.18507E-16 4.18507E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 ++ 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 ++ 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 ++ 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18509E-16 4.18509E-16 4.18509E-16 4.18509E-16 4.18509E-16 4.18509E-16 ++ 4.18509E-16 4.18509E-16 4.18509E-16 4.18509E-16 4.18509E-16 4.18509E-16 4.18509E-16 4.18509E-16 4.18509E-16 4.18509E-16 ++ 4.18509E-16 4.18509E-16 4.18509E-16 4.18509E-16 4.18509E-16 4.18509E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 ++ 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 ++ 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 ++ 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18508E-16 4.18507E-16 4.18507E-16 4.18507E-16 ++ 4.18507E-16 4.18507E-16 4.18507E-16 4.18506E-16 4.18506E-16 4.18506E-16 4.18506E-16 4.18506E-16 4.18506E-16 4.18505E-16 ++ 4.18505E-16 4.18505E-16 4.18505E-16 4.18505E-16 4.18505E-16 4.18504E-16 4.18504E-16 4.18504E-16 4.18504E-16 4.18504E-16 ++ 4.18504E-16 4.18503E-16 4.18503E-16 4.18503E-16 4.18503E-16 4.18503E-16 4.18503E-16 4.18502E-16 4.18502E-16 4.18502E-16 ++ 3.31509E-16 3.31509E-16 3.31509E-16 3.31509E-16 3.31509E-16 3.31509E-16 3.31510E-16 3.31510E-16 3.31510E-16 3.31510E-16 ++ 3.31510E-16 3.31510E-16 3.31510E-16 3.31511E-16 3.31511E-16 3.31511E-16 3.31511E-16 3.31511E-16 3.31511E-16 3.31511E-16 ++ 3.31511E-16 3.31512E-16 3.31512E-16 3.31512E-16 3.31512E-16 3.31512E-16 3.31512E-16 3.31512E-16 3.31513E-16 3.31513E-16 ++ 3.31513E-16 3.31513E-16 3.31513E-16 3.31513E-16 3.31513E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 ++ 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 ++ 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 ++ 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 ++ 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 ++ 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 ++ 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 ++ 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 ++ 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31514E-16 3.31513E-16 3.31513E-16 3.31513E-16 3.31513E-16 3.31513E-16 ++ 3.31513E-16 3.31513E-16 3.31512E-16 3.31512E-16 3.31512E-16 3.31512E-16 3.31512E-16 3.31512E-16 3.31512E-16 3.31511E-16 ++ 3.31511E-16 3.31511E-16 3.31511E-16 3.31511E-16 3.31511E-16 3.31511E-16 3.31511E-16 3.31510E-16 3.31510E-16 3.31510E-16 ++ 3.31510E-16 3.31510E-16 3.31510E-16 3.31510E-16 3.31509E-16 3.31509E-16 3.31509E-16 3.31509E-16 3.31509E-16 3.31509E-16 ++ 2.61655E-16 2.61655E-16 2.61655E-16 2.61655E-16 2.61655E-16 2.61655E-16 2.61655E-16 2.61656E-16 2.61656E-16 2.61656E-16 ++ 2.61656E-16 2.61656E-16 2.61656E-16 2.61656E-16 2.61656E-16 2.61657E-16 2.61657E-16 2.61657E-16 2.61657E-16 2.61657E-16 ++ 2.61657E-16 2.61657E-16 2.61657E-16 2.61657E-16 2.61658E-16 2.61658E-16 2.61658E-16 2.61658E-16 2.61658E-16 2.61658E-16 ++ 2.61658E-16 2.61658E-16 2.61658E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 ++ 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 ++ 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 ++ 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 ++ 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 ++ 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 ++ 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 ++ 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 ++ 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61659E-16 2.61658E-16 2.61658E-16 2.61658E-16 ++ 2.61658E-16 2.61658E-16 2.61658E-16 2.61658E-16 2.61658E-16 2.61658E-16 2.61657E-16 2.61657E-16 2.61657E-16 2.61657E-16 ++ 2.61657E-16 2.61657E-16 2.61657E-16 2.61657E-16 2.61657E-16 2.61656E-16 2.61656E-16 2.61656E-16 2.61656E-16 2.61656E-16 ++ 2.61656E-16 2.61656E-16 2.61656E-16 2.61655E-16 2.61655E-16 2.61655E-16 2.61655E-16 2.61655E-16 2.61655E-16 2.61655E-16 ++ 2.05778E-16 2.05778E-16 2.05778E-16 2.05778E-16 2.05778E-16 2.05779E-16 2.05779E-16 2.05779E-16 2.05779E-16 2.05779E-16 ++ 2.05779E-16 2.05779E-16 2.05779E-16 2.05779E-16 2.05779E-16 2.05779E-16 2.05780E-16 2.05780E-16 2.05780E-16 2.05780E-16 ++ 2.05780E-16 2.05780E-16 2.05780E-16 2.05780E-16 2.05780E-16 2.05780E-16 2.05781E-16 2.05781E-16 2.05781E-16 2.05781E-16 ++ 2.05781E-16 2.05781E-16 2.05781E-16 2.05781E-16 2.05781E-16 2.05781E-16 2.05781E-16 2.05781E-16 2.05781E-16 2.05781E-16 ++ 2.05781E-16 2.05781E-16 2.05781E-16 2.05781E-16 2.05781E-16 2.05781E-16 2.05781E-16 2.05781E-16 2.05781E-16 2.05781E-16 ++ 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 ++ 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 ++ 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 ++ 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 ++ 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 2.05782E-16 ++ 2.05781E-16 2.05781E-16 2.05781E-16 2.05781E-16 2.05781E-16 2.05781E-16 2.05781E-16 2.05781E-16 2.05781E-16 2.05781E-16 ++ 2.05781E-16 2.05781E-16 2.05781E-16 2.05781E-16 2.05781E-16 2.05781E-16 2.05781E-16 2.05781E-16 2.05781E-16 2.05781E-16 ++ 2.05781E-16 2.05781E-16 2.05781E-16 2.05781E-16 2.05780E-16 2.05780E-16 2.05780E-16 2.05780E-16 2.05780E-16 2.05780E-16 ++ 2.05780E-16 2.05780E-16 2.05780E-16 2.05780E-16 2.05779E-16 2.05779E-16 2.05779E-16 2.05779E-16 2.05779E-16 2.05779E-16 ++ 2.05779E-16 2.05779E-16 2.05779E-16 2.05779E-16 2.05779E-16 2.05778E-16 2.05778E-16 2.05778E-16 2.05778E-16 2.05778E-16 ++ 1.61253E-16 1.61253E-16 1.61253E-16 1.61253E-16 1.61253E-16 1.61253E-16 1.61253E-16 1.61253E-16 1.61253E-16 1.61253E-16 ++ 1.61253E-16 1.61253E-16 1.61253E-16 1.61254E-16 1.61254E-16 1.61254E-16 1.61254E-16 1.61254E-16 1.61254E-16 1.61254E-16 ++ 1.61254E-16 1.61254E-16 1.61254E-16 1.61254E-16 1.61254E-16 1.61254E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 ++ 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 ++ 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 ++ 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 ++ 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61256E-16 1.61256E-16 1.61256E-16 1.61256E-16 1.61256E-16 ++ 1.61256E-16 1.61256E-16 1.61256E-16 1.61256E-16 1.61256E-16 1.61256E-16 1.61256E-16 1.61256E-16 1.61256E-16 1.61256E-16 ++ 1.61256E-16 1.61256E-16 1.61256E-16 1.61256E-16 1.61256E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 ++ 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 ++ 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 ++ 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 ++ 1.61255E-16 1.61255E-16 1.61255E-16 1.61255E-16 1.61254E-16 1.61254E-16 1.61254E-16 1.61254E-16 1.61254E-16 1.61254E-16 ++ 1.61254E-16 1.61254E-16 1.61254E-16 1.61254E-16 1.61254E-16 1.61254E-16 1.61254E-16 1.61253E-16 1.61253E-16 1.61253E-16 ++ 1.61253E-16 1.61253E-16 1.61253E-16 1.61253E-16 1.61253E-16 1.61253E-16 1.61253E-16 1.61253E-16 1.61253E-16 1.61253E-16 ++ 1.25907E-16 1.25907E-16 1.25908E-16 1.25908E-16 1.25908E-16 1.25908E-16 1.25908E-16 1.25908E-16 1.25908E-16 1.25908E-16 ++ 1.25908E-16 1.25908E-16 1.25908E-16 1.25908E-16 1.25908E-16 1.25908E-16 1.25908E-16 1.25908E-16 1.25908E-16 1.25909E-16 ++ 1.25909E-16 1.25909E-16 1.25909E-16 1.25909E-16 1.25909E-16 1.25909E-16 1.25909E-16 1.25909E-16 1.25909E-16 1.25909E-16 ++ 1.25909E-16 1.25909E-16 1.25909E-16 1.25909E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 ++ 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 ++ 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 ++ 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 ++ 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 ++ 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 ++ 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 ++ 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 ++ 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25910E-16 1.25909E-16 1.25909E-16 1.25909E-16 1.25909E-16 ++ 1.25909E-16 1.25909E-16 1.25909E-16 1.25909E-16 1.25909E-16 1.25909E-16 1.25909E-16 1.25909E-16 1.25909E-16 1.25909E-16 ++ 1.25909E-16 1.25908E-16 1.25908E-16 1.25908E-16 1.25908E-16 1.25908E-16 1.25908E-16 1.25908E-16 1.25908E-16 1.25908E-16 ++ 1.25908E-16 1.25908E-16 1.25908E-16 1.25908E-16 1.25908E-16 1.25908E-16 1.25908E-16 1.25908E-16 1.25907E-16 1.25907E-16 ++ 9.79565E-17 9.79566E-17 9.79566E-17 9.79567E-17 9.79567E-17 9.79568E-17 9.79568E-17 9.79569E-17 9.79569E-17 9.79570E-17 ++ 9.79570E-17 9.79571E-17 9.79571E-17 9.79572E-17 9.79572E-17 9.79573E-17 9.79573E-17 9.79574E-17 9.79574E-17 9.79575E-17 ++ 9.79575E-17 9.79576E-17 9.79576E-17 9.79577E-17 9.79577E-17 9.79578E-17 9.79578E-17 9.79579E-17 9.79579E-17 9.79580E-17 ++ 9.79580E-17 9.79581E-17 9.79582E-17 9.79582E-17 9.79583E-17 9.79583E-17 9.79583E-17 9.79583E-17 9.79583E-17 9.79583E-17 ++ 9.79583E-17 9.79583E-17 9.79583E-17 9.79583E-17 9.79583E-17 9.79583E-17 9.79583E-17 9.79584E-17 9.79584E-17 9.79584E-17 ++ 9.79584E-17 9.79584E-17 9.79584E-17 9.79584E-17 9.79584E-17 9.79584E-17 9.79584E-17 9.79584E-17 9.79585E-17 9.79585E-17 ++ 9.79585E-17 9.79585E-17 9.79585E-17 9.79585E-17 9.79585E-17 9.79585E-17 9.79585E-17 9.79585E-17 9.79585E-17 9.79585E-17 ++ 9.79585E-17 9.79585E-17 9.79585E-17 9.79585E-17 9.79585E-17 9.79585E-17 9.79585E-17 9.79585E-17 9.79585E-17 9.79585E-17 ++ 9.79585E-17 9.79585E-17 9.79585E-17 9.79585E-17 9.79585E-17 9.79585E-17 9.79585E-17 9.79585E-17 9.79585E-17 9.79585E-17 ++ 9.79585E-17 9.79585E-17 9.79584E-17 9.79584E-17 9.79584E-17 9.79584E-17 9.79584E-17 9.79584E-17 9.79584E-17 9.79584E-17 ++ 9.79584E-17 9.79584E-17 9.79584E-17 9.79583E-17 9.79583E-17 9.79583E-17 9.79583E-17 9.79583E-17 9.79583E-17 9.79583E-17 ++ 9.79583E-17 9.79583E-17 9.79583E-17 9.79583E-17 9.79583E-17 9.79583E-17 9.79582E-17 9.79582E-17 9.79581E-17 9.79580E-17 ++ 9.79580E-17 9.79579E-17 9.79579E-17 9.79578E-17 9.79578E-17 9.79577E-17 9.79577E-17 9.79576E-17 9.79576E-17 9.79575E-17 ++ 9.79575E-17 9.79574E-17 9.79574E-17 9.79573E-17 9.79573E-17 9.79572E-17 9.79572E-17 9.79571E-17 9.79571E-17 9.79570E-17 ++ 9.79570E-17 9.79569E-17 9.79569E-17 9.79568E-17 9.79568E-17 9.79567E-17 9.79567E-17 9.79566E-17 9.79566E-17 9.79565E-17 ++ 7.59370E-17 7.59370E-17 7.59371E-17 7.59371E-17 7.59372E-17 7.59372E-17 7.59373E-17 7.59373E-17 7.59373E-17 7.59374E-17 ++ 7.59374E-17 7.59375E-17 7.59375E-17 7.59375E-17 7.59376E-17 7.59376E-17 7.59377E-17 7.59377E-17 7.59377E-17 7.59378E-17 ++ 7.59378E-17 7.59379E-17 7.59379E-17 7.59379E-17 7.59380E-17 7.59380E-17 7.59381E-17 7.59381E-17 7.59381E-17 7.59382E-17 ++ 7.59382E-17 7.59383E-17 7.59383E-17 7.59384E-17 7.59384E-17 7.59384E-17 7.59384E-17 7.59384E-17 7.59384E-17 7.59384E-17 ++ 7.59384E-17 7.59384E-17 7.59385E-17 7.59385E-17 7.59385E-17 7.59385E-17 7.59385E-17 7.59385E-17 7.59385E-17 7.59385E-17 ++ 7.59385E-17 7.59385E-17 7.59385E-17 7.59385E-17 7.59385E-17 7.59385E-17 7.59385E-17 7.59385E-17 7.59386E-17 7.59386E-17 ++ 7.59386E-17 7.59386E-17 7.59386E-17 7.59386E-17 7.59386E-17 7.59386E-17 7.59386E-17 7.59386E-17 7.59386E-17 7.59386E-17 ++ 7.59386E-17 7.59386E-17 7.59386E-17 7.59386E-17 7.59386E-17 7.59386E-17 7.59386E-17 7.59386E-17 7.59386E-17 7.59386E-17 ++ 7.59386E-17 7.59386E-17 7.59386E-17 7.59386E-17 7.59386E-17 7.59386E-17 7.59386E-17 7.59386E-17 7.59386E-17 7.59386E-17 ++ 7.59386E-17 7.59386E-17 7.59385E-17 7.59385E-17 7.59385E-17 7.59385E-17 7.59385E-17 7.59385E-17 7.59385E-17 7.59385E-17 ++ 7.59385E-17 7.59385E-17 7.59385E-17 7.59385E-17 7.59385E-17 7.59385E-17 7.59385E-17 7.59385E-17 7.59384E-17 7.59384E-17 ++ 7.59384E-17 7.59384E-17 7.59384E-17 7.59384E-17 7.59384E-17 7.59384E-17 7.59384E-17 7.59383E-17 7.59383E-17 7.59382E-17 ++ 7.59382E-17 7.59381E-17 7.59381E-17 7.59381E-17 7.59380E-17 7.59380E-17 7.59379E-17 7.59379E-17 7.59379E-17 7.59378E-17 ++ 7.59378E-17 7.59377E-17 7.59377E-17 7.59377E-17 7.59376E-17 7.59376E-17 7.59375E-17 7.59375E-17 7.59375E-17 7.59374E-17 ++ 7.59374E-17 7.59373E-17 7.59373E-17 7.59373E-17 7.59372E-17 7.59372E-17 7.59371E-17 7.59371E-17 7.59370E-17 7.59370E-17 ++ 5.86559E-17 5.86559E-17 5.86560E-17 5.86560E-17 5.86560E-17 5.86561E-17 5.86561E-17 5.86561E-17 5.86561E-17 5.86562E-17 ++ 5.86562E-17 5.86562E-17 5.86563E-17 5.86563E-17 5.86563E-17 5.86564E-17 5.86564E-17 5.86564E-17 5.86565E-17 5.86565E-17 ++ 5.86565E-17 5.86566E-17 5.86566E-17 5.86566E-17 5.86567E-17 5.86567E-17 5.86567E-17 5.86568E-17 5.86568E-17 5.86568E-17 ++ 5.86569E-17 5.86569E-17 5.86569E-17 5.86570E-17 5.86570E-17 5.86570E-17 5.86570E-17 5.86570E-17 5.86570E-17 5.86570E-17 ++ 5.86570E-17 5.86570E-17 5.86570E-17 5.86571E-17 5.86571E-17 5.86571E-17 5.86571E-17 5.86571E-17 5.86571E-17 5.86571E-17 ++ 5.86571E-17 5.86571E-17 5.86571E-17 5.86571E-17 5.86571E-17 5.86571E-17 5.86571E-17 5.86571E-17 5.86571E-17 5.86571E-17 ++ 5.86571E-17 5.86571E-17 5.86572E-17 5.86572E-17 5.86572E-17 5.86572E-17 5.86572E-17 5.86572E-17 5.86572E-17 5.86572E-17 ++ 5.86572E-17 5.86572E-17 5.86572E-17 5.86572E-17 5.86572E-17 5.86572E-17 5.86572E-17 5.86572E-17 5.86572E-17 5.86572E-17 ++ 5.86572E-17 5.86572E-17 5.86572E-17 5.86572E-17 5.86572E-17 5.86572E-17 5.86572E-17 5.86572E-17 5.86571E-17 5.86571E-17 ++ 5.86571E-17 5.86571E-17 5.86571E-17 5.86571E-17 5.86571E-17 5.86571E-17 5.86571E-17 5.86571E-17 5.86571E-17 5.86571E-17 ++ 5.86571E-17 5.86571E-17 5.86571E-17 5.86571E-17 5.86571E-17 5.86571E-17 5.86571E-17 5.86570E-17 5.86570E-17 5.86570E-17 ++ 5.86570E-17 5.86570E-17 5.86570E-17 5.86570E-17 5.86570E-17 5.86570E-17 5.86570E-17 5.86569E-17 5.86569E-17 5.86569E-17 ++ 5.86568E-17 5.86568E-17 5.86568E-17 5.86567E-17 5.86567E-17 5.86567E-17 5.86566E-17 5.86566E-17 5.86566E-17 5.86565E-17 ++ 5.86565E-17 5.86565E-17 5.86564E-17 5.86564E-17 5.86564E-17 5.86563E-17 5.86563E-17 5.86563E-17 5.86562E-17 5.86562E-17 ++ 5.86562E-17 5.86561E-17 5.86561E-17 5.86561E-17 5.86561E-17 5.86560E-17 5.86560E-17 5.86560E-17 5.86559E-17 5.86559E-17 ++ 4.51448E-17 4.51449E-17 4.51449E-17 4.51449E-17 4.51449E-17 4.51450E-17 4.51450E-17 4.51450E-17 4.51450E-17 4.51451E-17 ++ 4.51451E-17 4.51451E-17 4.51452E-17 4.51452E-17 4.51452E-17 4.51452E-17 4.51453E-17 4.51453E-17 4.51453E-17 4.51453E-17 ++ 4.51454E-17 4.51454E-17 4.51454E-17 4.51454E-17 4.51455E-17 4.51455E-17 4.51455E-17 4.51455E-17 4.51456E-17 4.51456E-17 ++ 4.51456E-17 4.51457E-17 4.51457E-17 4.51457E-17 4.51457E-17 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 ++ 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 ++ 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 ++ 4.51458E-17 4.51458E-17 4.51459E-17 4.51459E-17 4.51459E-17 4.51459E-17 4.51459E-17 4.51459E-17 4.51459E-17 4.51459E-17 ++ 4.51459E-17 4.51459E-17 4.51459E-17 4.51459E-17 4.51459E-17 4.51459E-17 4.51459E-17 4.51459E-17 4.51459E-17 4.51459E-17 ++ 4.51459E-17 4.51459E-17 4.51459E-17 4.51459E-17 4.51459E-17 4.51459E-17 4.51459E-17 4.51459E-17 4.51458E-17 4.51458E-17 ++ 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 ++ 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 ++ 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 4.51458E-17 4.51457E-17 4.51457E-17 4.51457E-17 4.51457E-17 4.51456E-17 ++ 4.51456E-17 4.51456E-17 4.51455E-17 4.51455E-17 4.51455E-17 4.51455E-17 4.51454E-17 4.51454E-17 4.51454E-17 4.51454E-17 ++ 4.51453E-17 4.51453E-17 4.51453E-17 4.51453E-17 4.51452E-17 4.51452E-17 4.51452E-17 4.51452E-17 4.51451E-17 4.51451E-17 ++ 4.51451E-17 4.51450E-17 4.51450E-17 4.51450E-17 4.51450E-17 4.51449E-17 4.51449E-17 4.51449E-17 4.51449E-17 4.51448E-17 ++ 3.46213E-17 3.46213E-17 3.46213E-17 3.46213E-17 3.46214E-17 3.46214E-17 3.46214E-17 3.46214E-17 3.46215E-17 3.46215E-17 ++ 3.46215E-17 3.46215E-17 3.46215E-17 3.46216E-17 3.46216E-17 3.46216E-17 3.46216E-17 3.46216E-17 3.46217E-17 3.46217E-17 ++ 3.46217E-17 3.46217E-17 3.46217E-17 3.46218E-17 3.46218E-17 3.46218E-17 3.46218E-17 3.46218E-17 3.46219E-17 3.46219E-17 ++ 3.46219E-17 3.46219E-17 3.46220E-17 3.46220E-17 3.46220E-17 3.46220E-17 3.46220E-17 3.46220E-17 3.46220E-17 3.46220E-17 ++ 3.46220E-17 3.46220E-17 3.46220E-17 3.46220E-17 3.46220E-17 3.46220E-17 3.46220E-17 3.46220E-17 3.46220E-17 3.46220E-17 ++ 3.46220E-17 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 ++ 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 ++ 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 ++ 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 ++ 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 3.46221E-17 3.46220E-17 ++ 3.46220E-17 3.46220E-17 3.46220E-17 3.46220E-17 3.46220E-17 3.46220E-17 3.46220E-17 3.46220E-17 3.46220E-17 3.46220E-17 ++ 3.46220E-17 3.46220E-17 3.46220E-17 3.46220E-17 3.46220E-17 3.46220E-17 3.46220E-17 3.46220E-17 3.46219E-17 3.46219E-17 ++ 3.46219E-17 3.46219E-17 3.46218E-17 3.46218E-17 3.46218E-17 3.46218E-17 3.46218E-17 3.46217E-17 3.46217E-17 3.46217E-17 ++ 3.46217E-17 3.46217E-17 3.46216E-17 3.46216E-17 3.46216E-17 3.46216E-17 3.46216E-17 3.46215E-17 3.46215E-17 3.46215E-17 ++ 3.46215E-17 3.46215E-17 3.46214E-17 3.46214E-17 3.46214E-17 3.46214E-17 3.46213E-17 3.46213E-17 3.46213E-17 3.46213E-17 ++ 2.64556E-17 2.64556E-17 2.64556E-17 2.64556E-17 2.64556E-17 2.64556E-17 2.64557E-17 2.64557E-17 2.64557E-17 2.64557E-17 ++ 2.64557E-17 2.64557E-17 2.64558E-17 2.64558E-17 2.64558E-17 2.64558E-17 2.64558E-17 2.64558E-17 2.64559E-17 2.64559E-17 ++ 2.64559E-17 2.64559E-17 2.64559E-17 2.64559E-17 2.64560E-17 2.64560E-17 2.64560E-17 2.64560E-17 2.64560E-17 2.64560E-17 ++ 2.64561E-17 2.64561E-17 2.64561E-17 2.64561E-17 2.64561E-17 2.64561E-17 2.64561E-17 2.64561E-17 2.64561E-17 2.64561E-17 ++ 2.64561E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 ++ 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 ++ 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 ++ 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 ++ 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 ++ 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 ++ 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64562E-17 2.64561E-17 ++ 2.64561E-17 2.64561E-17 2.64561E-17 2.64561E-17 2.64561E-17 2.64561E-17 2.64561E-17 2.64561E-17 2.64561E-17 2.64561E-17 ++ 2.64560E-17 2.64560E-17 2.64560E-17 2.64560E-17 2.64560E-17 2.64560E-17 2.64559E-17 2.64559E-17 2.64559E-17 2.64559E-17 ++ 2.64559E-17 2.64559E-17 2.64558E-17 2.64558E-17 2.64558E-17 2.64558E-17 2.64558E-17 2.64558E-17 2.64557E-17 2.64557E-17 ++ 2.64557E-17 2.64557E-17 2.64557E-17 2.64557E-17 2.64556E-17 2.64556E-17 2.64556E-17 2.64556E-17 2.64556E-17 2.64556E-17 ++ 2.01433E-17 2.01433E-17 2.01433E-17 2.01433E-17 2.01433E-17 2.01433E-17 2.01433E-17 2.01434E-17 2.01434E-17 2.01434E-17 ++ 2.01434E-17 2.01434E-17 2.01434E-17 2.01434E-17 2.01435E-17 2.01435E-17 2.01435E-17 2.01435E-17 2.01435E-17 2.01435E-17 ++ 2.01435E-17 2.01435E-17 2.01436E-17 2.01436E-17 2.01436E-17 2.01436E-17 2.01436E-17 2.01436E-17 2.01436E-17 2.01436E-17 ++ 2.01437E-17 2.01437E-17 2.01437E-17 2.01437E-17 2.01437E-17 2.01437E-17 2.01437E-17 2.01437E-17 2.01437E-17 2.01437E-17 ++ 2.01437E-17 2.01437E-17 2.01437E-17 2.01437E-17 2.01437E-17 2.01437E-17 2.01437E-17 2.01437E-17 2.01437E-17 2.01437E-17 ++ 2.01437E-17 2.01437E-17 2.01438E-17 2.01438E-17 2.01438E-17 2.01438E-17 2.01438E-17 2.01438E-17 2.01438E-17 2.01438E-17 ++ 2.01438E-17 2.01438E-17 2.01438E-17 2.01438E-17 2.01438E-17 2.01438E-17 2.01438E-17 2.01438E-17 2.01438E-17 2.01438E-17 ++ 2.01438E-17 2.01438E-17 2.01438E-17 2.01438E-17 2.01438E-17 2.01438E-17 2.01438E-17 2.01438E-17 2.01438E-17 2.01438E-17 ++ 2.01438E-17 2.01438E-17 2.01438E-17 2.01438E-17 2.01438E-17 2.01438E-17 2.01438E-17 2.01438E-17 2.01438E-17 2.01438E-17 ++ 2.01438E-17 2.01438E-17 2.01438E-17 2.01438E-17 2.01438E-17 2.01438E-17 2.01438E-17 2.01438E-17 2.01437E-17 2.01437E-17 ++ 2.01437E-17 2.01437E-17 2.01437E-17 2.01437E-17 2.01437E-17 2.01437E-17 2.01437E-17 2.01437E-17 2.01437E-17 2.01437E-17 ++ 2.01437E-17 2.01437E-17 2.01437E-17 2.01437E-17 2.01437E-17 2.01437E-17 2.01437E-17 2.01437E-17 2.01437E-17 2.01437E-17 ++ 2.01436E-17 2.01436E-17 2.01436E-17 2.01436E-17 2.01436E-17 2.01436E-17 2.01436E-17 2.01436E-17 2.01435E-17 2.01435E-17 ++ 2.01435E-17 2.01435E-17 2.01435E-17 2.01435E-17 2.01435E-17 2.01435E-17 2.01434E-17 2.01434E-17 2.01434E-17 2.01434E-17 ++ 2.01434E-17 2.01434E-17 2.01434E-17 2.01433E-17 2.01433E-17 2.01433E-17 2.01433E-17 2.01433E-17 2.01433E-17 2.01433E-17 ++ 1.52821E-17 1.52821E-17 1.52821E-17 1.52821E-17 1.52821E-17 1.52821E-17 1.52821E-17 1.52821E-17 1.52822E-17 1.52822E-17 ++ 1.52822E-17 1.52822E-17 1.52822E-17 1.52822E-17 1.52822E-17 1.52822E-17 1.52822E-17 1.52822E-17 1.52823E-17 1.52823E-17 ++ 1.52823E-17 1.52823E-17 1.52823E-17 1.52823E-17 1.52823E-17 1.52823E-17 1.52823E-17 1.52823E-17 1.52824E-17 1.52824E-17 ++ 1.52824E-17 1.52824E-17 1.52824E-17 1.52824E-17 1.52824E-17 1.52824E-17 1.52824E-17 1.52824E-17 1.52824E-17 1.52824E-17 ++ 1.52824E-17 1.52824E-17 1.52824E-17 1.52824E-17 1.52824E-17 1.52824E-17 1.52824E-17 1.52824E-17 1.52824E-17 1.52824E-17 ++ 1.52824E-17 1.52824E-17 1.52824E-17 1.52824E-17 1.52825E-17 1.52825E-17 1.52825E-17 1.52825E-17 1.52825E-17 1.52825E-17 ++ 1.52825E-17 1.52825E-17 1.52825E-17 1.52825E-17 1.52825E-17 1.52825E-17 1.52825E-17 1.52825E-17 1.52825E-17 1.52825E-17 ++ 1.52825E-17 1.52825E-17 1.52825E-17 1.52825E-17 1.52825E-17 1.52825E-17 1.52825E-17 1.52825E-17 1.52825E-17 1.52825E-17 ++ 1.52825E-17 1.52825E-17 1.52825E-17 1.52825E-17 1.52825E-17 1.52825E-17 1.52825E-17 1.52825E-17 1.52825E-17 1.52825E-17 ++ 1.52825E-17 1.52825E-17 1.52825E-17 1.52825E-17 1.52825E-17 1.52825E-17 1.52824E-17 1.52824E-17 1.52824E-17 1.52824E-17 ++ 1.52824E-17 1.52824E-17 1.52824E-17 1.52824E-17 1.52824E-17 1.52824E-17 1.52824E-17 1.52824E-17 1.52824E-17 1.52824E-17 ++ 1.52824E-17 1.52824E-17 1.52824E-17 1.52824E-17 1.52824E-17 1.52824E-17 1.52824E-17 1.52824E-17 1.52824E-17 1.52824E-17 ++ 1.52824E-17 1.52824E-17 1.52823E-17 1.52823E-17 1.52823E-17 1.52823E-17 1.52823E-17 1.52823E-17 1.52823E-17 1.52823E-17 ++ 1.52823E-17 1.52823E-17 1.52822E-17 1.52822E-17 1.52822E-17 1.52822E-17 1.52822E-17 1.52822E-17 1.52822E-17 1.52822E-17 ++ 1.52822E-17 1.52822E-17 1.52821E-17 1.52821E-17 1.52821E-17 1.52821E-17 1.52821E-17 1.52821E-17 1.52821E-17 1.52821E-17 ++ 1.15524E-17 1.15525E-17 1.15525E-17 1.15525E-17 1.15525E-17 1.15525E-17 1.15525E-17 1.15525E-17 1.15525E-17 1.15525E-17 ++ 1.15525E-17 1.15525E-17 1.15525E-17 1.15525E-17 1.15526E-17 1.15526E-17 1.15526E-17 1.15526E-17 1.15526E-17 1.15526E-17 ++ 1.15526E-17 1.15526E-17 1.15526E-17 1.15526E-17 1.15526E-17 1.15526E-17 1.15526E-17 1.15527E-17 1.15527E-17 1.15527E-17 ++ 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 ++ 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 ++ 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 ++ 1.15527E-17 1.15528E-17 1.15528E-17 1.15528E-17 1.15528E-17 1.15528E-17 1.15528E-17 1.15528E-17 1.15528E-17 1.15528E-17 ++ 1.15528E-17 1.15528E-17 1.15528E-17 1.15528E-17 1.15528E-17 1.15528E-17 1.15528E-17 1.15528E-17 1.15528E-17 1.15528E-17 ++ 1.15528E-17 1.15528E-17 1.15528E-17 1.15528E-17 1.15528E-17 1.15528E-17 1.15528E-17 1.15528E-17 1.15528E-17 1.15527E-17 ++ 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 ++ 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 ++ 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 1.15527E-17 ++ 1.15527E-17 1.15527E-17 1.15527E-17 1.15526E-17 1.15526E-17 1.15526E-17 1.15526E-17 1.15526E-17 1.15526E-17 1.15526E-17 ++ 1.15526E-17 1.15526E-17 1.15526E-17 1.15526E-17 1.15526E-17 1.15526E-17 1.15525E-17 1.15525E-17 1.15525E-17 1.15525E-17 ++ 1.15525E-17 1.15525E-17 1.15525E-17 1.15525E-17 1.15525E-17 1.15525E-17 1.15525E-17 1.15525E-17 1.15525E-17 1.15524E-17 ++ 8.70172E-18 8.70173E-18 8.70173E-18 8.70174E-18 8.70175E-18 8.70175E-18 8.70176E-18 8.70176E-18 8.70177E-18 8.70178E-18 ++ 8.70178E-18 8.70179E-18 8.70179E-18 8.70180E-18 8.70181E-18 8.70181E-18 8.70182E-18 8.70183E-18 8.70183E-18 8.70184E-18 ++ 8.70184E-18 8.70185E-18 8.70186E-18 8.70186E-18 8.70187E-18 8.70188E-18 8.70188E-18 8.70189E-18 8.70189E-18 8.70190E-18 ++ 8.70191E-18 8.70191E-18 8.70192E-18 8.70193E-18 8.70193E-18 8.70194E-18 8.70194E-18 8.70194E-18 8.70194E-18 8.70194E-18 ++ 8.70194E-18 8.70194E-18 8.70194E-18 8.70194E-18 8.70194E-18 8.70194E-18 8.70194E-18 8.70195E-18 8.70195E-18 8.70195E-18 ++ 8.70195E-18 8.70195E-18 8.70195E-18 8.70195E-18 8.70195E-18 8.70195E-18 8.70196E-18 8.70196E-18 8.70196E-18 8.70196E-18 ++ 8.70196E-18 8.70196E-18 8.70196E-18 8.70196E-18 8.70196E-18 8.70196E-18 8.70197E-18 8.70197E-18 8.70197E-18 8.70197E-18 ++ 8.70197E-18 8.70197E-18 8.70197E-18 8.70197E-18 8.70197E-18 8.70197E-18 8.70197E-18 8.70197E-18 8.70197E-18 8.70197E-18 ++ 8.70197E-18 8.70197E-18 8.70197E-18 8.70197E-18 8.70196E-18 8.70196E-18 8.70196E-18 8.70196E-18 8.70196E-18 8.70196E-18 ++ 8.70196E-18 8.70196E-18 8.70196E-18 8.70196E-18 8.70195E-18 8.70195E-18 8.70195E-18 8.70195E-18 8.70195E-18 8.70195E-18 ++ 8.70195E-18 8.70195E-18 8.70195E-18 8.70194E-18 8.70194E-18 8.70194E-18 8.70194E-18 8.70194E-18 8.70194E-18 8.70194E-18 ++ 8.70194E-18 8.70194E-18 8.70194E-18 8.70194E-18 8.70194E-18 8.70193E-18 8.70193E-18 8.70192E-18 8.70191E-18 8.70191E-18 ++ 8.70190E-18 8.70189E-18 8.70189E-18 8.70188E-18 8.70188E-18 8.70187E-18 8.70186E-18 8.70186E-18 8.70185E-18 8.70184E-18 ++ 8.70184E-18 8.70183E-18 8.70183E-18 8.70182E-18 8.70181E-18 8.70181E-18 8.70180E-18 8.70179E-18 8.70179E-18 8.70178E-18 ++ 8.70178E-18 8.70177E-18 8.70176E-18 8.70176E-18 8.70175E-18 8.70175E-18 8.70174E-18 8.70173E-18 8.70173E-18 8.70172E-18 ++ 6.53095E-18 6.53096E-18 6.53096E-18 6.53097E-18 6.53097E-18 6.53097E-18 6.53098E-18 6.53098E-18 6.53099E-18 6.53099E-18 ++ 6.53100E-18 6.53100E-18 6.53101E-18 6.53101E-18 6.53102E-18 6.53102E-18 6.53103E-18 6.53103E-18 6.53104E-18 6.53104E-18 ++ 6.53105E-18 6.53105E-18 6.53106E-18 6.53106E-18 6.53107E-18 6.53107E-18 6.53108E-18 6.53108E-18 6.53109E-18 6.53109E-18 ++ 6.53110E-18 6.53110E-18 6.53111E-18 6.53111E-18 6.53112E-18 6.53112E-18 6.53112E-18 6.53112E-18 6.53112E-18 6.53112E-18 ++ 6.53112E-18 6.53112E-18 6.53112E-18 6.53112E-18 6.53112E-18 6.53112E-18 6.53112E-18 6.53112E-18 6.53113E-18 6.53113E-18 ++ 6.53113E-18 6.53113E-18 6.53113E-18 6.53113E-18 6.53113E-18 6.53113E-18 6.53113E-18 6.53113E-18 6.53113E-18 6.53113E-18 ++ 6.53114E-18 6.53114E-18 6.53114E-18 6.53114E-18 6.53114E-18 6.53114E-18 6.53114E-18 6.53114E-18 6.53114E-18 6.53114E-18 ++ 6.53114E-18 6.53114E-18 6.53114E-18 6.53114E-18 6.53114E-18 6.53114E-18 6.53114E-18 6.53114E-18 6.53114E-18 6.53114E-18 ++ 6.53114E-18 6.53114E-18 6.53114E-18 6.53114E-18 6.53114E-18 6.53114E-18 6.53114E-18 6.53114E-18 6.53114E-18 6.53114E-18 ++ 6.53113E-18 6.53113E-18 6.53113E-18 6.53113E-18 6.53113E-18 6.53113E-18 6.53113E-18 6.53113E-18 6.53113E-18 6.53113E-18 ++ 6.53113E-18 6.53113E-18 6.53112E-18 6.53112E-18 6.53112E-18 6.53112E-18 6.53112E-18 6.53112E-18 6.53112E-18 6.53112E-18 ++ 6.53112E-18 6.53112E-18 6.53112E-18 6.53112E-18 6.53112E-18 6.53112E-18 6.53111E-18 6.53111E-18 6.53110E-18 6.53110E-18 ++ 6.53109E-18 6.53109E-18 6.53108E-18 6.53108E-18 6.53107E-18 6.53107E-18 6.53106E-18 6.53106E-18 6.53105E-18 6.53105E-18 ++ 6.53104E-18 6.53104E-18 6.53103E-18 6.53103E-18 6.53102E-18 6.53102E-18 6.53101E-18 6.53101E-18 6.53100E-18 6.53100E-18 ++ 6.53099E-18 6.53099E-18 6.53098E-18 6.53098E-18 6.53097E-18 6.53097E-18 6.53097E-18 6.53096E-18 6.53096E-18 6.53095E-18 ++ 4.88414E-18 4.88414E-18 4.88414E-18 4.88415E-18 4.88415E-18 4.88415E-18 4.88416E-18 4.88416E-18 4.88417E-18 4.88417E-18 ++ 4.88417E-18 4.88418E-18 4.88418E-18 4.88418E-18 4.88419E-18 4.88419E-18 4.88419E-18 4.88420E-18 4.88420E-18 4.88421E-18 ++ 4.88421E-18 4.88421E-18 4.88422E-18 4.88422E-18 4.88422E-18 4.88423E-18 4.88423E-18 4.88424E-18 4.88424E-18 4.88424E-18 ++ 4.88425E-18 4.88425E-18 4.88426E-18 4.88426E-18 4.88426E-18 4.88427E-18 4.88427E-18 4.88427E-18 4.88427E-18 4.88427E-18 ++ 4.88427E-18 4.88427E-18 4.88427E-18 4.88427E-18 4.88427E-18 4.88427E-18 4.88427E-18 4.88427E-18 4.88427E-18 4.88427E-18 ++ 4.88427E-18 4.88427E-18 4.88427E-18 4.88427E-18 4.88428E-18 4.88428E-18 4.88428E-18 4.88428E-18 4.88428E-18 4.88428E-18 ++ 4.88428E-18 4.88428E-18 4.88428E-18 4.88428E-18 4.88428E-18 4.88428E-18 4.88428E-18 4.88428E-18 4.88428E-18 4.88428E-18 ++ 4.88428E-18 4.88428E-18 4.88428E-18 4.88428E-18 4.88428E-18 4.88428E-18 4.88428E-18 4.88428E-18 4.88428E-18 4.88428E-18 ++ 4.88428E-18 4.88428E-18 4.88428E-18 4.88428E-18 4.88428E-18 4.88428E-18 4.88428E-18 4.88428E-18 4.88428E-18 4.88428E-18 ++ 4.88428E-18 4.88428E-18 4.88428E-18 4.88428E-18 4.88428E-18 4.88428E-18 4.88427E-18 4.88427E-18 4.88427E-18 4.88427E-18 ++ 4.88427E-18 4.88427E-18 4.88427E-18 4.88427E-18 4.88427E-18 4.88427E-18 4.88427E-18 4.88427E-18 4.88427E-18 4.88427E-18 ++ 4.88427E-18 4.88427E-18 4.88427E-18 4.88427E-18 4.88427E-18 4.88426E-18 4.88426E-18 4.88426E-18 4.88425E-18 4.88425E-18 ++ 4.88424E-18 4.88424E-18 4.88424E-18 4.88423E-18 4.88423E-18 4.88422E-18 4.88422E-18 4.88422E-18 4.88421E-18 4.88421E-18 ++ 4.88421E-18 4.88420E-18 4.88420E-18 4.88419E-18 4.88419E-18 4.88419E-18 4.88418E-18 4.88418E-18 4.88418E-18 4.88417E-18 ++ 4.88417E-18 4.88417E-18 4.88416E-18 4.88416E-18 4.88415E-18 4.88415E-18 4.88415E-18 4.88414E-18 4.88414E-18 4.88414E-18 ++ 3.63948E-18 3.63948E-18 3.63949E-18 3.63949E-18 3.63949E-18 3.63950E-18 3.63950E-18 3.63950E-18 3.63950E-18 3.63951E-18 ++ 3.63951E-18 3.63951E-18 3.63951E-18 3.63952E-18 3.63952E-18 3.63952E-18 3.63953E-18 3.63953E-18 3.63953E-18 3.63953E-18 ++ 3.63954E-18 3.63954E-18 3.63954E-18 3.63955E-18 3.63955E-18 3.63955E-18 3.63956E-18 3.63956E-18 3.63956E-18 3.63956E-18 ++ 3.63957E-18 3.63957E-18 3.63957E-18 3.63958E-18 3.63958E-18 3.63958E-18 3.63958E-18 3.63958E-18 3.63958E-18 3.63958E-18 ++ 3.63958E-18 3.63958E-18 3.63958E-18 3.63958E-18 3.63958E-18 3.63958E-18 3.63958E-18 3.63958E-18 3.63958E-18 3.63959E-18 ++ 3.63959E-18 3.63959E-18 3.63959E-18 3.63959E-18 3.63959E-18 3.63959E-18 3.63959E-18 3.63959E-18 3.63959E-18 3.63959E-18 ++ 3.63959E-18 3.63959E-18 3.63959E-18 3.63959E-18 3.63959E-18 3.63959E-18 3.63959E-18 3.63959E-18 3.63959E-18 3.63959E-18 ++ 3.63959E-18 3.63959E-18 3.63959E-18 3.63960E-18 3.63960E-18 3.63960E-18 3.63960E-18 3.63959E-18 3.63959E-18 3.63959E-18 ++ 3.63959E-18 3.63959E-18 3.63959E-18 3.63959E-18 3.63959E-18 3.63959E-18 3.63959E-18 3.63959E-18 3.63959E-18 3.63959E-18 ++ 3.63959E-18 3.63959E-18 3.63959E-18 3.63959E-18 3.63959E-18 3.63959E-18 3.63959E-18 3.63959E-18 3.63959E-18 3.63959E-18 ++ 3.63959E-18 3.63958E-18 3.63958E-18 3.63958E-18 3.63958E-18 3.63958E-18 3.63958E-18 3.63958E-18 3.63958E-18 3.63958E-18 ++ 3.63958E-18 3.63958E-18 3.63958E-18 3.63958E-18 3.63958E-18 3.63958E-18 3.63958E-18 3.63957E-18 3.63957E-18 3.63957E-18 ++ 3.63956E-18 3.63956E-18 3.63956E-18 3.63956E-18 3.63955E-18 3.63955E-18 3.63955E-18 3.63954E-18 3.63954E-18 3.63954E-18 ++ 3.63953E-18 3.63953E-18 3.63953E-18 3.63953E-18 3.63952E-18 3.63952E-18 3.63952E-18 3.63951E-18 3.63951E-18 3.63951E-18 ++ 3.63951E-18 3.63950E-18 3.63950E-18 3.63950E-18 3.63950E-18 3.63949E-18 3.63949E-18 3.63949E-18 3.63948E-18 3.63948E-18 ++ 2.70229E-18 2.70229E-18 2.70229E-18 2.70230E-18 2.70230E-18 2.70230E-18 2.70230E-18 2.70230E-18 2.70231E-18 2.70231E-18 ++ 2.70231E-18 2.70231E-18 2.70231E-18 2.70232E-18 2.70232E-18 2.70232E-18 2.70232E-18 2.70233E-18 2.70233E-18 2.70233E-18 ++ 2.70233E-18 2.70233E-18 2.70234E-18 2.70234E-18 2.70234E-18 2.70234E-18 2.70235E-18 2.70235E-18 2.70235E-18 2.70235E-18 ++ 2.70235E-18 2.70236E-18 2.70236E-18 2.70236E-18 2.70236E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 ++ 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 ++ 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 ++ 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70238E-18 2.70238E-18 2.70238E-18 ++ 2.70238E-18 2.70238E-18 2.70238E-18 2.70238E-18 2.70238E-18 2.70238E-18 2.70238E-18 2.70238E-18 2.70238E-18 2.70238E-18 ++ 2.70238E-18 2.70238E-18 2.70238E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 ++ 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 ++ 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 ++ 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70237E-18 2.70236E-18 2.70236E-18 2.70236E-18 2.70236E-18 2.70235E-18 ++ 2.70235E-18 2.70235E-18 2.70235E-18 2.70235E-18 2.70234E-18 2.70234E-18 2.70234E-18 2.70234E-18 2.70233E-18 2.70233E-18 ++ 2.70233E-18 2.70233E-18 2.70233E-18 2.70232E-18 2.70232E-18 2.70232E-18 2.70232E-18 2.70231E-18 2.70231E-18 2.70231E-18 ++ 2.70231E-18 2.70231E-18 2.70230E-18 2.70230E-18 2.70230E-18 2.70230E-18 2.70230E-18 2.70229E-18 2.70229E-18 2.70229E-18 ++ 1.99924E-18 1.99924E-18 1.99924E-18 1.99924E-18 1.99925E-18 1.99925E-18 1.99925E-18 1.99925E-18 1.99925E-18 1.99925E-18 ++ 1.99926E-18 1.99926E-18 1.99926E-18 1.99926E-18 1.99926E-18 1.99926E-18 1.99927E-18 1.99927E-18 1.99927E-18 1.99927E-18 ++ 1.99927E-18 1.99927E-18 1.99928E-18 1.99928E-18 1.99928E-18 1.99928E-18 1.99928E-18 1.99928E-18 1.99929E-18 1.99929E-18 ++ 1.99929E-18 1.99929E-18 1.99929E-18 1.99929E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 ++ 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 ++ 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 ++ 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99931E-18 1.99931E-18 1.99931E-18 1.99931E-18 ++ 1.99931E-18 1.99931E-18 1.99931E-18 1.99931E-18 1.99931E-18 1.99931E-18 1.99931E-18 1.99931E-18 1.99931E-18 1.99931E-18 ++ 1.99931E-18 1.99931E-18 1.99931E-18 1.99931E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 ++ 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 ++ 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 ++ 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99930E-18 1.99929E-18 1.99929E-18 1.99929E-18 1.99929E-18 ++ 1.99929E-18 1.99929E-18 1.99928E-18 1.99928E-18 1.99928E-18 1.99928E-18 1.99928E-18 1.99928E-18 1.99927E-18 1.99927E-18 ++ 1.99927E-18 1.99927E-18 1.99927E-18 1.99927E-18 1.99926E-18 1.99926E-18 1.99926E-18 1.99926E-18 1.99926E-18 1.99926E-18 ++ 1.99925E-18 1.99925E-18 1.99925E-18 1.99925E-18 1.99925E-18 1.99925E-18 1.99924E-18 1.99924E-18 1.99924E-18 1.99924E-18 ++ 1.47380E-18 1.47380E-18 1.47380E-18 1.47380E-18 1.47381E-18 1.47381E-18 1.47381E-18 1.47381E-18 1.47381E-18 1.47381E-18 ++ 1.47381E-18 1.47381E-18 1.47382E-18 1.47382E-18 1.47382E-18 1.47382E-18 1.47382E-18 1.47382E-18 1.47382E-18 1.47382E-18 ++ 1.47383E-18 1.47383E-18 1.47383E-18 1.47383E-18 1.47383E-18 1.47383E-18 1.47383E-18 1.47384E-18 1.47384E-18 1.47384E-18 ++ 1.47384E-18 1.47384E-18 1.47384E-18 1.47384E-18 1.47384E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 ++ 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 ++ 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 ++ 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 ++ 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 ++ 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 ++ 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 ++ 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 ++ 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47385E-18 1.47384E-18 1.47384E-18 1.47384E-18 1.47384E-18 1.47384E-18 ++ 1.47384E-18 1.47384E-18 1.47384E-18 1.47383E-18 1.47383E-18 1.47383E-18 1.47383E-18 1.47383E-18 1.47383E-18 1.47383E-18 ++ 1.47382E-18 1.47382E-18 1.47382E-18 1.47382E-18 1.47382E-18 1.47382E-18 1.47382E-18 1.47382E-18 1.47381E-18 1.47381E-18 ++ 1.47381E-18 1.47381E-18 1.47381E-18 1.47381E-18 1.47381E-18 1.47381E-18 1.47380E-18 1.47380E-18 1.47380E-18 1.47380E-18 ++ 1.08257E-18 1.08257E-18 1.08257E-18 1.08257E-18 1.08257E-18 1.08257E-18 1.08257E-18 1.08257E-18 1.08257E-18 1.08257E-18 ++ 1.08257E-18 1.08258E-18 1.08258E-18 1.08258E-18 1.08258E-18 1.08258E-18 1.08258E-18 1.08258E-18 1.08258E-18 1.08258E-18 ++ 1.08258E-18 1.08259E-18 1.08259E-18 1.08259E-18 1.08259E-18 1.08259E-18 1.08259E-18 1.08259E-18 1.08259E-18 1.08259E-18 ++ 1.08259E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 ++ 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 ++ 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 ++ 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 ++ 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 ++ 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 ++ 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 ++ 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 ++ 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08260E-18 1.08259E-18 ++ 1.08259E-18 1.08259E-18 1.08259E-18 1.08259E-18 1.08259E-18 1.08259E-18 1.08259E-18 1.08259E-18 1.08259E-18 1.08258E-18 ++ 1.08258E-18 1.08258E-18 1.08258E-18 1.08258E-18 1.08258E-18 1.08258E-18 1.08258E-18 1.08258E-18 1.08258E-18 1.08257E-18 ++ 1.08257E-18 1.08257E-18 1.08257E-18 1.08257E-18 1.08257E-18 1.08257E-18 1.08257E-18 1.08257E-18 1.08257E-18 1.08257E-18 ++ 7.92339E-19 7.92340E-19 7.92341E-19 7.92341E-19 7.92342E-19 7.92343E-19 7.92343E-19 7.92344E-19 7.92345E-19 7.92345E-19 ++ 7.92346E-19 7.92347E-19 7.92348E-19 7.92348E-19 7.92349E-19 7.92350E-19 7.92350E-19 7.92351E-19 7.92352E-19 7.92353E-19 ++ 7.92353E-19 7.92354E-19 7.92355E-19 7.92355E-19 7.92356E-19 7.92357E-19 7.92358E-19 7.92358E-19 7.92359E-19 7.92360E-19 ++ 7.92361E-19 7.92361E-19 7.92362E-19 7.92363E-19 7.92364E-19 7.92364E-19 7.92364E-19 7.92364E-19 7.92364E-19 7.92364E-19 ++ 7.92365E-19 7.92365E-19 7.92365E-19 7.92365E-19 7.92365E-19 7.92365E-19 7.92365E-19 7.92365E-19 7.92365E-19 7.92365E-19 ++ 7.92365E-19 7.92366E-19 7.92366E-19 7.92366E-19 7.92366E-19 7.92366E-19 7.92366E-19 7.92366E-19 7.92367E-19 7.92367E-19 ++ 7.92367E-19 7.92367E-19 7.92367E-19 7.92367E-19 7.92367E-19 7.92367E-19 7.92367E-19 7.92368E-19 7.92368E-19 7.92368E-19 ++ 7.92368E-19 7.92368E-19 7.92368E-19 7.92368E-19 7.92368E-19 7.92368E-19 7.92368E-19 7.92368E-19 7.92368E-19 7.92368E-19 ++ 7.92368E-19 7.92368E-19 7.92368E-19 7.92367E-19 7.92367E-19 7.92367E-19 7.92367E-19 7.92367E-19 7.92367E-19 7.92367E-19 ++ 7.92367E-19 7.92367E-19 7.92366E-19 7.92366E-19 7.92366E-19 7.92366E-19 7.92366E-19 7.92366E-19 7.92366E-19 7.92365E-19 ++ 7.92365E-19 7.92365E-19 7.92365E-19 7.92365E-19 7.92365E-19 7.92365E-19 7.92365E-19 7.92365E-19 7.92365E-19 7.92365E-19 ++ 7.92364E-19 7.92364E-19 7.92364E-19 7.92364E-19 7.92364E-19 7.92364E-19 7.92363E-19 7.92362E-19 7.92361E-19 7.92361E-19 ++ 7.92360E-19 7.92359E-19 7.92358E-19 7.92358E-19 7.92357E-19 7.92356E-19 7.92355E-19 7.92355E-19 7.92354E-19 7.92353E-19 ++ 7.92353E-19 7.92352E-19 7.92351E-19 7.92350E-19 7.92350E-19 7.92349E-19 7.92348E-19 7.92348E-19 7.92347E-19 7.92346E-19 ++ 7.92345E-19 7.92345E-19 7.92344E-19 7.92343E-19 7.92343E-19 7.92342E-19 7.92341E-19 7.92341E-19 7.92340E-19 7.92339E-19 ++ 5.77843E-19 5.77843E-19 5.77844E-19 5.77844E-19 5.77845E-19 5.77845E-19 5.77846E-19 5.77846E-19 5.77847E-19 5.77847E-19 ++ 5.77848E-19 5.77849E-19 5.77849E-19 5.77850E-19 5.77850E-19 5.77851E-19 5.77851E-19 5.77852E-19 5.77852E-19 5.77853E-19 ++ 5.77853E-19 5.77854E-19 5.77854E-19 5.77855E-19 5.77856E-19 5.77856E-19 5.77857E-19 5.77857E-19 5.77858E-19 5.77858E-19 ++ 5.77859E-19 5.77859E-19 5.77860E-19 5.77861E-19 5.77861E-19 5.77862E-19 5.77862E-19 5.77862E-19 5.77862E-19 5.77862E-19 ++ 5.77862E-19 5.77862E-19 5.77862E-19 5.77862E-19 5.77862E-19 5.77862E-19 5.77862E-19 5.77862E-19 5.77862E-19 5.77862E-19 ++ 5.77863E-19 5.77863E-19 5.77863E-19 5.77863E-19 5.77863E-19 5.77863E-19 5.77863E-19 5.77863E-19 5.77863E-19 5.77863E-19 ++ 5.77864E-19 5.77864E-19 5.77864E-19 5.77864E-19 5.77864E-19 5.77864E-19 5.77864E-19 5.77864E-19 5.77864E-19 5.77864E-19 ++ 5.77864E-19 5.77864E-19 5.77864E-19 5.77864E-19 5.77864E-19 5.77864E-19 5.77864E-19 5.77864E-19 5.77864E-19 5.77864E-19 ++ 5.77864E-19 5.77864E-19 5.77864E-19 5.77864E-19 5.77864E-19 5.77864E-19 5.77864E-19 5.77864E-19 5.77864E-19 5.77864E-19 ++ 5.77863E-19 5.77863E-19 5.77863E-19 5.77863E-19 5.77863E-19 5.77863E-19 5.77863E-19 5.77863E-19 5.77863E-19 5.77863E-19 ++ 5.77862E-19 5.77862E-19 5.77862E-19 5.77862E-19 5.77862E-19 5.77862E-19 5.77862E-19 5.77862E-19 5.77862E-19 5.77862E-19 ++ 5.77862E-19 5.77862E-19 5.77862E-19 5.77862E-19 5.77862E-19 5.77861E-19 5.77861E-19 5.77860E-19 5.77859E-19 5.77859E-19 ++ 5.77858E-19 5.77858E-19 5.77857E-19 5.77857E-19 5.77856E-19 5.77856E-19 5.77855E-19 5.77854E-19 5.77854E-19 5.77853E-19 ++ 5.77853E-19 5.77852E-19 5.77852E-19 5.77851E-19 5.77851E-19 5.77850E-19 5.77850E-19 5.77849E-19 5.77849E-19 5.77848E-19 ++ 5.77847E-19 5.77847E-19 5.77846E-19 5.77846E-19 5.77845E-19 5.77845E-19 5.77844E-19 5.77844E-19 5.77843E-19 5.77843E-19 ++ 4.19904E-19 4.19905E-19 4.19905E-19 4.19905E-19 4.19906E-19 4.19906E-19 4.19907E-19 4.19907E-19 4.19907E-19 4.19908E-19 ++ 4.19908E-19 4.19909E-19 4.19909E-19 4.19909E-19 4.19910E-19 4.19910E-19 4.19911E-19 4.19911E-19 4.19911E-19 4.19912E-19 ++ 4.19912E-19 4.19913E-19 4.19913E-19 4.19913E-19 4.19914E-19 4.19914E-19 4.19915E-19 4.19915E-19 4.19915E-19 4.19916E-19 ++ 4.19916E-19 4.19917E-19 4.19917E-19 4.19918E-19 4.19918E-19 4.19918E-19 4.19918E-19 4.19918E-19 4.19918E-19 4.19918E-19 ++ 4.19918E-19 4.19919E-19 4.19919E-19 4.19919E-19 4.19919E-19 4.19919E-19 4.19919E-19 4.19919E-19 4.19919E-19 4.19919E-19 ++ 4.19919E-19 4.19919E-19 4.19919E-19 4.19919E-19 4.19919E-19 4.19919E-19 4.19919E-19 4.19920E-19 4.19920E-19 4.19920E-19 ++ 4.19920E-19 4.19920E-19 4.19920E-19 4.19920E-19 4.19920E-19 4.19920E-19 4.19920E-19 4.19920E-19 4.19920E-19 4.19920E-19 ++ 4.19920E-19 4.19920E-19 4.19920E-19 4.19920E-19 4.19920E-19 4.19920E-19 4.19920E-19 4.19920E-19 4.19920E-19 4.19920E-19 ++ 4.19920E-19 4.19920E-19 4.19920E-19 4.19920E-19 4.19920E-19 4.19920E-19 4.19920E-19 4.19920E-19 4.19920E-19 4.19920E-19 ++ 4.19920E-19 4.19920E-19 4.19920E-19 4.19919E-19 4.19919E-19 4.19919E-19 4.19919E-19 4.19919E-19 4.19919E-19 4.19919E-19 ++ 4.19919E-19 4.19919E-19 4.19919E-19 4.19919E-19 4.19919E-19 4.19919E-19 4.19919E-19 4.19919E-19 4.19919E-19 4.19918E-19 ++ 4.19918E-19 4.19918E-19 4.19918E-19 4.19918E-19 4.19918E-19 4.19918E-19 4.19918E-19 4.19917E-19 4.19917E-19 4.19916E-19 ++ 4.19916E-19 4.19915E-19 4.19915E-19 4.19915E-19 4.19914E-19 4.19914E-19 4.19913E-19 4.19913E-19 4.19913E-19 4.19912E-19 ++ 4.19912E-19 4.19911E-19 4.19911E-19 4.19911E-19 4.19910E-19 4.19910E-19 4.19909E-19 4.19909E-19 4.19909E-19 4.19908E-19 ++ 4.19908E-19 4.19907E-19 4.19907E-19 4.19907E-19 4.19906E-19 4.19906E-19 4.19905E-19 4.19905E-19 4.19905E-19 4.19904E-19 ++ 3.04042E-19 3.04042E-19 3.04042E-19 3.04043E-19 3.04043E-19 3.04043E-19 3.04043E-19 3.04044E-19 3.04044E-19 3.04044E-19 ++ 3.04045E-19 3.04045E-19 3.04045E-19 3.04045E-19 3.04046E-19 3.04046E-19 3.04046E-19 3.04047E-19 3.04047E-19 3.04047E-19 ++ 3.04048E-19 3.04048E-19 3.04048E-19 3.04048E-19 3.04049E-19 3.04049E-19 3.04049E-19 3.04050E-19 3.04050E-19 3.04050E-19 ++ 3.04051E-19 3.04051E-19 3.04051E-19 3.04052E-19 3.04052E-19 3.04052E-19 3.04052E-19 3.04052E-19 3.04052E-19 3.04052E-19 ++ 3.04052E-19 3.04052E-19 3.04052E-19 3.04052E-19 3.04052E-19 3.04052E-19 3.04052E-19 3.04053E-19 3.04053E-19 3.04053E-19 ++ 3.04053E-19 3.04053E-19 3.04053E-19 3.04053E-19 3.04053E-19 3.04053E-19 3.04053E-19 3.04053E-19 3.04053E-19 3.04053E-19 ++ 3.04053E-19 3.04053E-19 3.04053E-19 3.04053E-19 3.04053E-19 3.04053E-19 3.04053E-19 3.04054E-19 3.04054E-19 3.04054E-19 ++ 3.04054E-19 3.04054E-19 3.04054E-19 3.04054E-19 3.04054E-19 3.04054E-19 3.04054E-19 3.04054E-19 3.04054E-19 3.04054E-19 ++ 3.04054E-19 3.04054E-19 3.04054E-19 3.04053E-19 3.04053E-19 3.04053E-19 3.04053E-19 3.04053E-19 3.04053E-19 3.04053E-19 ++ 3.04053E-19 3.04053E-19 3.04053E-19 3.04053E-19 3.04053E-19 3.04053E-19 3.04053E-19 3.04053E-19 3.04053E-19 3.04053E-19 ++ 3.04053E-19 3.04053E-19 3.04053E-19 3.04052E-19 3.04052E-19 3.04052E-19 3.04052E-19 3.04052E-19 3.04052E-19 3.04052E-19 ++ 3.04052E-19 3.04052E-19 3.04052E-19 3.04052E-19 3.04052E-19 3.04052E-19 3.04052E-19 3.04051E-19 3.04051E-19 3.04051E-19 ++ 3.04050E-19 3.04050E-19 3.04050E-19 3.04049E-19 3.04049E-19 3.04049E-19 3.04048E-19 3.04048E-19 3.04048E-19 3.04048E-19 ++ 3.04047E-19 3.04047E-19 3.04047E-19 3.04046E-19 3.04046E-19 3.04046E-19 3.04045E-19 3.04045E-19 3.04045E-19 3.04045E-19 ++ 3.04044E-19 3.04044E-19 3.04044E-19 3.04043E-19 3.04043E-19 3.04043E-19 3.04043E-19 3.04042E-19 3.04042E-19 3.04042E-19 ++ 2.19361E-19 2.19361E-19 2.19361E-19 2.19361E-19 2.19361E-19 2.19362E-19 2.19362E-19 2.19362E-19 2.19362E-19 2.19362E-19 ++ 2.19363E-19 2.19363E-19 2.19363E-19 2.19363E-19 2.19364E-19 2.19364E-19 2.19364E-19 2.19364E-19 2.19364E-19 2.19365E-19 ++ 2.19365E-19 2.19365E-19 2.19365E-19 2.19366E-19 2.19366E-19 2.19366E-19 2.19366E-19 2.19366E-19 2.19367E-19 2.19367E-19 ++ 2.19367E-19 2.19367E-19 2.19368E-19 2.19368E-19 2.19368E-19 2.19368E-19 2.19368E-19 2.19368E-19 2.19368E-19 2.19368E-19 ++ 2.19368E-19 2.19368E-19 2.19368E-19 2.19368E-19 2.19368E-19 2.19368E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 ++ 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 ++ 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 ++ 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 ++ 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 ++ 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 ++ 2.19369E-19 2.19369E-19 2.19369E-19 2.19369E-19 2.19368E-19 2.19368E-19 2.19368E-19 2.19368E-19 2.19368E-19 2.19368E-19 ++ 2.19368E-19 2.19368E-19 2.19368E-19 2.19368E-19 2.19368E-19 2.19368E-19 2.19368E-19 2.19368E-19 2.19367E-19 2.19367E-19 ++ 2.19367E-19 2.19367E-19 2.19366E-19 2.19366E-19 2.19366E-19 2.19366E-19 2.19366E-19 2.19365E-19 2.19365E-19 2.19365E-19 ++ 2.19365E-19 2.19364E-19 2.19364E-19 2.19364E-19 2.19364E-19 2.19364E-19 2.19363E-19 2.19363E-19 2.19363E-19 2.19363E-19 ++ 2.19362E-19 2.19362E-19 2.19362E-19 2.19362E-19 2.19362E-19 2.19361E-19 2.19361E-19 2.19361E-19 2.19361E-19 2.19361E-19 ++ 1.57698E-19 1.57698E-19 1.57699E-19 1.57699E-19 1.57699E-19 1.57699E-19 1.57699E-19 1.57699E-19 1.57699E-19 1.57700E-19 ++ 1.57700E-19 1.57700E-19 1.57700E-19 1.57700E-19 1.57700E-19 1.57701E-19 1.57701E-19 1.57701E-19 1.57701E-19 1.57701E-19 ++ 1.57701E-19 1.57702E-19 1.57702E-19 1.57702E-19 1.57702E-19 1.57702E-19 1.57702E-19 1.57703E-19 1.57703E-19 1.57703E-19 ++ 1.57703E-19 1.57703E-19 1.57703E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 ++ 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 ++ 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 ++ 1.57704E-19 1.57704E-19 1.57705E-19 1.57705E-19 1.57705E-19 1.57705E-19 1.57705E-19 1.57705E-19 1.57705E-19 1.57705E-19 ++ 1.57705E-19 1.57705E-19 1.57705E-19 1.57705E-19 1.57705E-19 1.57705E-19 1.57705E-19 1.57705E-19 1.57705E-19 1.57705E-19 ++ 1.57705E-19 1.57705E-19 1.57705E-19 1.57705E-19 1.57705E-19 1.57705E-19 1.57705E-19 1.57705E-19 1.57704E-19 1.57704E-19 ++ 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 ++ 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 ++ 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57704E-19 1.57703E-19 1.57703E-19 1.57703E-19 ++ 1.57703E-19 1.57703E-19 1.57703E-19 1.57702E-19 1.57702E-19 1.57702E-19 1.57702E-19 1.57702E-19 1.57702E-19 1.57701E-19 ++ 1.57701E-19 1.57701E-19 1.57701E-19 1.57701E-19 1.57701E-19 1.57700E-19 1.57700E-19 1.57700E-19 1.57700E-19 1.57700E-19 ++ 1.57700E-19 1.57699E-19 1.57699E-19 1.57699E-19 1.57699E-19 1.57699E-19 1.57699E-19 1.57699E-19 1.57698E-19 1.57698E-19 ++ 1.12963E-19 1.12964E-19 1.12964E-19 1.12964E-19 1.12964E-19 1.12964E-19 1.12964E-19 1.12964E-19 1.12964E-19 1.12964E-19 ++ 1.12965E-19 1.12965E-19 1.12965E-19 1.12965E-19 1.12965E-19 1.12965E-19 1.12965E-19 1.12965E-19 1.12966E-19 1.12966E-19 ++ 1.12966E-19 1.12966E-19 1.12966E-19 1.12966E-19 1.12966E-19 1.12966E-19 1.12967E-19 1.12967E-19 1.12967E-19 1.12967E-19 ++ 1.12967E-19 1.12967E-19 1.12967E-19 1.12967E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 ++ 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 ++ 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 ++ 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 ++ 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 ++ 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 ++ 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 ++ 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 ++ 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12968E-19 1.12967E-19 1.12967E-19 1.12967E-19 1.12967E-19 ++ 1.12967E-19 1.12967E-19 1.12967E-19 1.12967E-19 1.12966E-19 1.12966E-19 1.12966E-19 1.12966E-19 1.12966E-19 1.12966E-19 ++ 1.12966E-19 1.12966E-19 1.12965E-19 1.12965E-19 1.12965E-19 1.12965E-19 1.12965E-19 1.12965E-19 1.12965E-19 1.12965E-19 ++ 1.12964E-19 1.12964E-19 1.12964E-19 1.12964E-19 1.12964E-19 1.12964E-19 1.12964E-19 1.12964E-19 1.12964E-19 1.12963E-19 ++ 8.06293E-20 8.06293E-20 8.06294E-20 8.06295E-20 8.06296E-20 8.06297E-20 8.06298E-20 8.06298E-20 8.06299E-20 8.06300E-20 ++ 8.06301E-20 8.06302E-20 8.06303E-20 8.06303E-20 8.06304E-20 8.06305E-20 8.06306E-20 8.06307E-20 8.06308E-20 8.06309E-20 ++ 8.06310E-20 8.06310E-20 8.06311E-20 8.06312E-20 8.06313E-20 8.06314E-20 8.06315E-20 8.06316E-20 8.06317E-20 8.06318E-20 ++ 8.06319E-20 8.06320E-20 8.06320E-20 8.06321E-20 8.06322E-20 8.06323E-20 8.06323E-20 8.06323E-20 8.06323E-20 8.06323E-20 ++ 8.06323E-20 8.06324E-20 8.06324E-20 8.06324E-20 8.06324E-20 8.06324E-20 8.06324E-20 8.06324E-20 8.06324E-20 8.06324E-20 ++ 8.06325E-20 8.06325E-20 8.06325E-20 8.06325E-20 8.06325E-20 8.06325E-20 8.06326E-20 8.06326E-20 8.06326E-20 8.06326E-20 ++ 8.06326E-20 8.06326E-20 8.06327E-20 8.06327E-20 8.06327E-20 8.06327E-20 8.06327E-20 8.06327E-20 8.06327E-20 8.06327E-20 ++ 8.06327E-20 8.06327E-20 8.06327E-20 8.06327E-20 8.06328E-20 8.06328E-20 8.06327E-20 8.06327E-20 8.06327E-20 8.06327E-20 ++ 8.06327E-20 8.06327E-20 8.06327E-20 8.06327E-20 8.06327E-20 8.06327E-20 8.06327E-20 8.06327E-20 8.06326E-20 8.06326E-20 ++ 8.06326E-20 8.06326E-20 8.06326E-20 8.06326E-20 8.06325E-20 8.06325E-20 8.06325E-20 8.06325E-20 8.06325E-20 8.06325E-20 ++ 8.06324E-20 8.06324E-20 8.06324E-20 8.06324E-20 8.06324E-20 8.06324E-20 8.06324E-20 8.06324E-20 8.06324E-20 8.06323E-20 ++ 8.06323E-20 8.06323E-20 8.06323E-20 8.06323E-20 8.06323E-20 8.06322E-20 8.06321E-20 8.06320E-20 8.06320E-20 8.06319E-20 ++ 8.06318E-20 8.06317E-20 8.06316E-20 8.06315E-20 8.06314E-20 8.06313E-20 8.06312E-20 8.06311E-20 8.06310E-20 8.06310E-20 ++ 8.06309E-20 8.06308E-20 8.06307E-20 8.06306E-20 8.06305E-20 8.06304E-20 8.06303E-20 8.06303E-20 8.06302E-20 8.06301E-20 ++ 8.06300E-20 8.06299E-20 8.06298E-20 8.06298E-20 8.06297E-20 8.06296E-20 8.06295E-20 8.06294E-20 8.06293E-20 8.06293E-20 ++ 5.73444E-20 5.73444E-20 5.73445E-20 5.73446E-20 5.73446E-20 5.73447E-20 5.73448E-20 5.73448E-20 5.73449E-20 5.73449E-20 ++ 5.73450E-20 5.73451E-20 5.73451E-20 5.73452E-20 5.73452E-20 5.73453E-20 5.73454E-20 5.73454E-20 5.73455E-20 5.73456E-20 ++ 5.73456E-20 5.73457E-20 5.73458E-20 5.73458E-20 5.73459E-20 5.73460E-20 5.73460E-20 5.73461E-20 5.73462E-20 5.73462E-20 ++ 5.73463E-20 5.73464E-20 5.73464E-20 5.73465E-20 5.73466E-20 5.73466E-20 5.73466E-20 5.73466E-20 5.73466E-20 5.73466E-20 ++ 5.73466E-20 5.73466E-20 5.73467E-20 5.73467E-20 5.73467E-20 5.73467E-20 5.73467E-20 5.73467E-20 5.73467E-20 5.73467E-20 ++ 5.73467E-20 5.73467E-20 5.73467E-20 5.73468E-20 5.73468E-20 5.73468E-20 5.73468E-20 5.73468E-20 5.73468E-20 5.73468E-20 ++ 5.73468E-20 5.73469E-20 5.73469E-20 5.73469E-20 5.73469E-20 5.73469E-20 5.73469E-20 5.73469E-20 5.73469E-20 5.73469E-20 ++ 5.73469E-20 5.73469E-20 5.73469E-20 5.73469E-20 5.73469E-20 5.73469E-20 5.73469E-20 5.73469E-20 5.73469E-20 5.73469E-20 ++ 5.73469E-20 5.73469E-20 5.73469E-20 5.73469E-20 5.73469E-20 5.73469E-20 5.73469E-20 5.73469E-20 5.73469E-20 5.73468E-20 ++ 5.73468E-20 5.73468E-20 5.73468E-20 5.73468E-20 5.73468E-20 5.73468E-20 5.73468E-20 5.73467E-20 5.73467E-20 5.73467E-20 ++ 5.73467E-20 5.73467E-20 5.73467E-20 5.73467E-20 5.73467E-20 5.73467E-20 5.73467E-20 5.73467E-20 5.73466E-20 5.73466E-20 ++ 5.73466E-20 5.73466E-20 5.73466E-20 5.73466E-20 5.73466E-20 5.73466E-20 5.73465E-20 5.73464E-20 5.73464E-20 5.73463E-20 ++ 5.73462E-20 5.73462E-20 5.73461E-20 5.73460E-20 5.73460E-20 5.73459E-20 5.73458E-20 5.73458E-20 5.73457E-20 5.73456E-20 ++ 5.73456E-20 5.73455E-20 5.73454E-20 5.73454E-20 5.73453E-20 5.73452E-20 5.73452E-20 5.73451E-20 5.73451E-20 5.73450E-20 ++ 5.73449E-20 5.73449E-20 5.73448E-20 5.73448E-20 5.73447E-20 5.73446E-20 5.73446E-20 5.73445E-20 5.73444E-20 5.73444E-20 ++ 4.06381E-20 4.06381E-20 4.06382E-20 4.06382E-20 4.06383E-20 4.06383E-20 4.06383E-20 4.06384E-20 4.06384E-20 4.06385E-20 ++ 4.06385E-20 4.06386E-20 4.06386E-20 4.06387E-20 4.06387E-20 4.06387E-20 4.06388E-20 4.06388E-20 4.06389E-20 4.06389E-20 ++ 4.06390E-20 4.06390E-20 4.06391E-20 4.06391E-20 4.06392E-20 4.06392E-20 4.06393E-20 4.06393E-20 4.06394E-20 4.06394E-20 ++ 4.06395E-20 4.06395E-20 4.06396E-20 4.06396E-20 4.06397E-20 4.06397E-20 4.06397E-20 4.06397E-20 4.06397E-20 4.06397E-20 ++ 4.06397E-20 4.06397E-20 4.06397E-20 4.06397E-20 4.06397E-20 4.06397E-20 4.06397E-20 4.06397E-20 4.06398E-20 4.06398E-20 ++ 4.06398E-20 4.06398E-20 4.06398E-20 4.06398E-20 4.06398E-20 4.06398E-20 4.06398E-20 4.06398E-20 4.06398E-20 4.06398E-20 ++ 4.06399E-20 4.06399E-20 4.06399E-20 4.06399E-20 4.06399E-20 4.06399E-20 4.06399E-20 4.06399E-20 4.06399E-20 4.06399E-20 ++ 4.06399E-20 4.06399E-20 4.06399E-20 4.06399E-20 4.06399E-20 4.06399E-20 4.06399E-20 4.06399E-20 4.06399E-20 4.06399E-20 ++ 4.06399E-20 4.06399E-20 4.06399E-20 4.06399E-20 4.06399E-20 4.06399E-20 4.06399E-20 4.06399E-20 4.06399E-20 4.06399E-20 ++ 4.06398E-20 4.06398E-20 4.06398E-20 4.06398E-20 4.06398E-20 4.06398E-20 4.06398E-20 4.06398E-20 4.06398E-20 4.06398E-20 ++ 4.06398E-20 4.06398E-20 4.06397E-20 4.06397E-20 4.06397E-20 4.06397E-20 4.06397E-20 4.06397E-20 4.06397E-20 4.06397E-20 ++ 4.06397E-20 4.06397E-20 4.06397E-20 4.06397E-20 4.06397E-20 4.06397E-20 4.06396E-20 4.06396E-20 4.06395E-20 4.06395E-20 ++ 4.06394E-20 4.06394E-20 4.06393E-20 4.06393E-20 4.06392E-20 4.06392E-20 4.06391E-20 4.06391E-20 4.06390E-20 4.06390E-20 ++ 4.06389E-20 4.06389E-20 4.06388E-20 4.06388E-20 4.06387E-20 4.06387E-20 4.06387E-20 4.06386E-20 4.06386E-20 4.06385E-20 ++ 4.06385E-20 4.06384E-20 4.06384E-20 4.06383E-20 4.06383E-20 4.06383E-20 4.06382E-20 4.06382E-20 4.06381E-20 4.06381E-20 ++ 2.86959E-20 2.86959E-20 2.86959E-20 2.86960E-20 2.86960E-20 2.86960E-20 2.86961E-20 2.86961E-20 2.86961E-20 2.86962E-20 ++ 2.86962E-20 2.86962E-20 2.86963E-20 2.86963E-20 2.86963E-20 2.86964E-20 2.86964E-20 2.86964E-20 2.86965E-20 2.86965E-20 ++ 2.86965E-20 2.86966E-20 2.86966E-20 2.86966E-20 2.86967E-20 2.86967E-20 2.86967E-20 2.86968E-20 2.86968E-20 2.86968E-20 ++ 2.86969E-20 2.86969E-20 2.86970E-20 2.86970E-20 2.86970E-20 2.86971E-20 2.86971E-20 2.86971E-20 2.86971E-20 2.86971E-20 ++ 2.86971E-20 2.86971E-20 2.86971E-20 2.86971E-20 2.86971E-20 2.86971E-20 2.86971E-20 2.86971E-20 2.86971E-20 2.86971E-20 ++ 2.86971E-20 2.86971E-20 2.86971E-20 2.86971E-20 2.86971E-20 2.86971E-20 2.86971E-20 2.86972E-20 2.86972E-20 2.86972E-20 ++ 2.86972E-20 2.86972E-20 2.86972E-20 2.86972E-20 2.86972E-20 2.86972E-20 2.86972E-20 2.86972E-20 2.86972E-20 2.86972E-20 ++ 2.86972E-20 2.86972E-20 2.86972E-20 2.86972E-20 2.86972E-20 2.86972E-20 2.86972E-20 2.86972E-20 2.86972E-20 2.86972E-20 ++ 2.86972E-20 2.86972E-20 2.86972E-20 2.86972E-20 2.86972E-20 2.86972E-20 2.86972E-20 2.86972E-20 2.86972E-20 2.86972E-20 ++ 2.86972E-20 2.86972E-20 2.86972E-20 2.86971E-20 2.86971E-20 2.86971E-20 2.86971E-20 2.86971E-20 2.86971E-20 2.86971E-20 ++ 2.86971E-20 2.86971E-20 2.86971E-20 2.86971E-20 2.86971E-20 2.86971E-20 2.86971E-20 2.86971E-20 2.86971E-20 2.86971E-20 ++ 2.86971E-20 2.86971E-20 2.86971E-20 2.86971E-20 2.86971E-20 2.86970E-20 2.86970E-20 2.86970E-20 2.86969E-20 2.86969E-20 ++ 2.86968E-20 2.86968E-20 2.86968E-20 2.86967E-20 2.86967E-20 2.86967E-20 2.86966E-20 2.86966E-20 2.86966E-20 2.86965E-20 ++ 2.86965E-20 2.86965E-20 2.86964E-20 2.86964E-20 2.86964E-20 2.86963E-20 2.86963E-20 2.86963E-20 2.86962E-20 2.86962E-20 ++ 2.86962E-20 2.86961E-20 2.86961E-20 2.86961E-20 2.86960E-20 2.86960E-20 2.86960E-20 2.86959E-20 2.86959E-20 2.86959E-20 ++ 2.01907E-20 2.01907E-20 2.01907E-20 2.01907E-20 2.01908E-20 2.01908E-20 2.01908E-20 2.01908E-20 2.01909E-20 2.01909E-20 ++ 2.01909E-20 2.01909E-20 2.01909E-20 2.01910E-20 2.01910E-20 2.01910E-20 2.01910E-20 2.01911E-20 2.01911E-20 2.01911E-20 ++ 2.01911E-20 2.01912E-20 2.01912E-20 2.01912E-20 2.01912E-20 2.01913E-20 2.01913E-20 2.01913E-20 2.01913E-20 2.01914E-20 ++ 2.01914E-20 2.01914E-20 2.01914E-20 2.01915E-20 2.01915E-20 2.01915E-20 2.01915E-20 2.01915E-20 2.01915E-20 2.01915E-20 ++ 2.01915E-20 2.01915E-20 2.01915E-20 2.01915E-20 2.01915E-20 2.01915E-20 2.01915E-20 2.01915E-20 2.01915E-20 2.01915E-20 ++ 2.01915E-20 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 ++ 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 ++ 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 ++ 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 ++ 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 2.01916E-20 2.01915E-20 ++ 2.01915E-20 2.01915E-20 2.01915E-20 2.01915E-20 2.01915E-20 2.01915E-20 2.01915E-20 2.01915E-20 2.01915E-20 2.01915E-20 ++ 2.01915E-20 2.01915E-20 2.01915E-20 2.01915E-20 2.01915E-20 2.01915E-20 2.01915E-20 2.01914E-20 2.01914E-20 2.01914E-20 ++ 2.01914E-20 2.01913E-20 2.01913E-20 2.01913E-20 2.01913E-20 2.01912E-20 2.01912E-20 2.01912E-20 2.01912E-20 2.01911E-20 ++ 2.01911E-20 2.01911E-20 2.01911E-20 2.01910E-20 2.01910E-20 2.01910E-20 2.01910E-20 2.01909E-20 2.01909E-20 2.01909E-20 ++ 2.01909E-20 2.01909E-20 2.01908E-20 2.01908E-20 2.01908E-20 2.01908E-20 2.01907E-20 2.01907E-20 2.01907E-20 2.01907E-20 ++ 1.41555E-20 1.41556E-20 1.41556E-20 1.41556E-20 1.41556E-20 1.41556E-20 1.41556E-20 1.41557E-20 1.41557E-20 1.41557E-20 ++ 1.41557E-20 1.41557E-20 1.41557E-20 1.41558E-20 1.41558E-20 1.41558E-20 1.41558E-20 1.41558E-20 1.41558E-20 1.41559E-20 ++ 1.41559E-20 1.41559E-20 1.41559E-20 1.41559E-20 1.41559E-20 1.41560E-20 1.41560E-20 1.41560E-20 1.41560E-20 1.41560E-20 ++ 1.41561E-20 1.41561E-20 1.41561E-20 1.41561E-20 1.41561E-20 1.41561E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 ++ 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 ++ 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 ++ 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 ++ 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 ++ 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 ++ 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 ++ 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 ++ 1.41562E-20 1.41562E-20 1.41562E-20 1.41562E-20 1.41561E-20 1.41561E-20 1.41561E-20 1.41561E-20 1.41561E-20 1.41561E-20 ++ 1.41560E-20 1.41560E-20 1.41560E-20 1.41560E-20 1.41560E-20 1.41559E-20 1.41559E-20 1.41559E-20 1.41559E-20 1.41559E-20 ++ 1.41559E-20 1.41558E-20 1.41558E-20 1.41558E-20 1.41558E-20 1.41558E-20 1.41558E-20 1.41557E-20 1.41557E-20 1.41557E-20 ++ 1.41557E-20 1.41557E-20 1.41557E-20 1.41556E-20 1.41556E-20 1.41556E-20 1.41556E-20 1.41556E-20 1.41556E-20 1.41555E-20 ++ 9.88889E-21 9.88890E-21 9.88892E-21 9.88893E-21 9.88894E-21 9.88895E-21 9.88896E-21 9.88897E-21 9.88899E-21 9.88900E-21 ++ 9.88901E-21 9.88902E-21 9.88903E-21 9.88905E-21 9.88906E-21 9.88907E-21 9.88908E-21 9.88909E-21 9.88911E-21 9.88912E-21 ++ 9.88913E-21 9.88914E-21 9.88916E-21 9.88917E-21 9.88918E-21 9.88919E-21 9.88921E-21 9.88922E-21 9.88923E-21 9.88925E-21 ++ 9.88926E-21 9.88927E-21 9.88928E-21 9.88930E-21 9.88931E-21 9.88932E-21 9.88933E-21 9.88933E-21 9.88933E-21 9.88933E-21 ++ 9.88933E-21 9.88933E-21 9.88933E-21 9.88933E-21 9.88933E-21 9.88933E-21 9.88934E-21 9.88934E-21 9.88934E-21 9.88934E-21 ++ 9.88934E-21 9.88935E-21 9.88935E-21 9.88935E-21 9.88935E-21 9.88936E-21 9.88936E-21 9.88936E-21 9.88936E-21 9.88936E-21 ++ 9.88937E-21 9.88937E-21 9.88937E-21 9.88937E-21 9.88937E-21 9.88938E-21 9.88938E-21 9.88938E-21 9.88938E-21 9.88938E-21 ++ 9.88938E-21 9.88938E-21 9.88938E-21 9.88939E-21 9.88939E-21 9.88939E-21 9.88939E-21 9.88938E-21 9.88938E-21 9.88938E-21 ++ 9.88938E-21 9.88938E-21 9.88938E-21 9.88938E-21 9.88938E-21 9.88937E-21 9.88937E-21 9.88937E-21 9.88937E-21 9.88937E-21 ++ 9.88936E-21 9.88936E-21 9.88936E-21 9.88936E-21 9.88936E-21 9.88935E-21 9.88935E-21 9.88935E-21 9.88935E-21 9.88934E-21 ++ 9.88934E-21 9.88934E-21 9.88934E-21 9.88934E-21 9.88933E-21 9.88933E-21 9.88933E-21 9.88933E-21 9.88933E-21 9.88933E-21 ++ 9.88933E-21 9.88933E-21 9.88933E-21 9.88933E-21 9.88932E-21 9.88931E-21 9.88930E-21 9.88928E-21 9.88927E-21 9.88926E-21 ++ 9.88925E-21 9.88923E-21 9.88922E-21 9.88921E-21 9.88919E-21 9.88918E-21 9.88917E-21 9.88916E-21 9.88914E-21 9.88913E-21 ++ 9.88912E-21 9.88911E-21 9.88909E-21 9.88908E-21 9.88907E-21 9.88906E-21 9.88905E-21 9.88903E-21 9.88902E-21 9.88901E-21 ++ 9.88900E-21 9.88899E-21 9.88897E-21 9.88896E-21 9.88895E-21 9.88894E-21 9.88893E-21 9.88892E-21 9.88890E-21 9.88889E-21 ++ 6.88358E-21 6.88359E-21 6.88360E-21 6.88360E-21 6.88361E-21 6.88362E-21 6.88363E-21 6.88364E-21 6.88364E-21 6.88365E-21 ++ 6.88366E-21 6.88367E-21 6.88368E-21 6.88369E-21 6.88370E-21 6.88370E-21 6.88371E-21 6.88372E-21 6.88373E-21 6.88374E-21 ++ 6.88375E-21 6.88376E-21 6.88377E-21 6.88377E-21 6.88378E-21 6.88379E-21 6.88380E-21 6.88381E-21 6.88382E-21 6.88383E-21 ++ 6.88384E-21 6.88385E-21 6.88386E-21 6.88387E-21 6.88388E-21 6.88389E-21 6.88389E-21 6.88389E-21 6.88389E-21 6.88389E-21 ++ 6.88389E-21 6.88389E-21 6.88389E-21 6.88389E-21 6.88389E-21 6.88389E-21 6.88389E-21 6.88389E-21 6.88390E-21 6.88390E-21 ++ 6.88390E-21 6.88390E-21 6.88390E-21 6.88390E-21 6.88391E-21 6.88391E-21 6.88391E-21 6.88391E-21 6.88391E-21 6.88391E-21 ++ 6.88392E-21 6.88392E-21 6.88392E-21 6.88392E-21 6.88392E-21 6.88392E-21 6.88392E-21 6.88392E-21 6.88393E-21 6.88393E-21 ++ 6.88393E-21 6.88393E-21 6.88393E-21 6.88393E-21 6.88393E-21 6.88393E-21 6.88393E-21 6.88393E-21 6.88393E-21 6.88393E-21 ++ 6.88393E-21 6.88393E-21 6.88392E-21 6.88392E-21 6.88392E-21 6.88392E-21 6.88392E-21 6.88392E-21 6.88392E-21 6.88392E-21 ++ 6.88391E-21 6.88391E-21 6.88391E-21 6.88391E-21 6.88391E-21 6.88391E-21 6.88390E-21 6.88390E-21 6.88390E-21 6.88390E-21 ++ 6.88390E-21 6.88390E-21 6.88389E-21 6.88389E-21 6.88389E-21 6.88389E-21 6.88389E-21 6.88389E-21 6.88389E-21 6.88389E-21 ++ 6.88389E-21 6.88389E-21 6.88389E-21 6.88389E-21 6.88389E-21 6.88388E-21 6.88387E-21 6.88386E-21 6.88385E-21 6.88384E-21 ++ 6.88383E-21 6.88382E-21 6.88381E-21 6.88380E-21 6.88379E-21 6.88378E-21 6.88377E-21 6.88377E-21 6.88376E-21 6.88375E-21 ++ 6.88374E-21 6.88373E-21 6.88372E-21 6.88371E-21 6.88370E-21 6.88370E-21 6.88369E-21 6.88368E-21 6.88367E-21 6.88366E-21 ++ 6.88365E-21 6.88364E-21 6.88364E-21 6.88363E-21 6.88362E-21 6.88361E-21 6.88360E-21 6.88360E-21 6.88359E-21 6.88358E-21 ++ 4.77449E-21 4.77449E-21 4.77450E-21 4.77450E-21 4.77451E-21 4.77452E-21 4.77452E-21 4.77453E-21 4.77453E-21 4.77454E-21 ++ 4.77455E-21 4.77455E-21 4.77456E-21 4.77456E-21 4.77457E-21 4.77458E-21 4.77458E-21 4.77459E-21 4.77459E-21 4.77460E-21 ++ 4.77461E-21 4.77461E-21 4.77462E-21 4.77463E-21 4.77463E-21 4.77464E-21 4.77464E-21 4.77465E-21 4.77466E-21 4.77466E-21 ++ 4.77467E-21 4.77468E-21 4.77468E-21 4.77469E-21 4.77470E-21 4.77470E-21 4.77470E-21 4.77470E-21 4.77470E-21 4.77470E-21 ++ 4.77471E-21 4.77471E-21 4.77471E-21 4.77471E-21 4.77471E-21 4.77471E-21 4.77471E-21 4.77471E-21 4.77471E-21 4.77471E-21 ++ 4.77471E-21 4.77471E-21 4.77472E-21 4.77472E-21 4.77472E-21 4.77472E-21 4.77472E-21 4.77472E-21 4.77472E-21 4.77472E-21 ++ 4.77473E-21 4.77473E-21 4.77473E-21 4.77473E-21 4.77473E-21 4.77473E-21 4.77473E-21 4.77473E-21 4.77473E-21 4.77473E-21 ++ 4.77473E-21 4.77473E-21 4.77473E-21 4.77473E-21 4.77473E-21 4.77473E-21 4.77473E-21 4.77473E-21 4.77473E-21 4.77473E-21 ++ 4.77473E-21 4.77473E-21 4.77473E-21 4.77473E-21 4.77473E-21 4.77473E-21 4.77473E-21 4.77473E-21 4.77473E-21 4.77473E-21 ++ 4.77472E-21 4.77472E-21 4.77472E-21 4.77472E-21 4.77472E-21 4.77472E-21 4.77472E-21 4.77472E-21 4.77471E-21 4.77471E-21 ++ 4.77471E-21 4.77471E-21 4.77471E-21 4.77471E-21 4.77471E-21 4.77471E-21 4.77471E-21 4.77471E-21 4.77471E-21 4.77471E-21 ++ 4.77470E-21 4.77470E-21 4.77470E-21 4.77470E-21 4.77470E-21 4.77470E-21 4.77469E-21 4.77468E-21 4.77468E-21 4.77467E-21 ++ 4.77466E-21 4.77466E-21 4.77465E-21 4.77464E-21 4.77464E-21 4.77463E-21 4.77463E-21 4.77462E-21 4.77461E-21 4.77461E-21 ++ 4.77460E-21 4.77459E-21 4.77459E-21 4.77458E-21 4.77458E-21 4.77457E-21 4.77456E-21 4.77456E-21 4.77455E-21 4.77455E-21 ++ 4.77454E-21 4.77453E-21 4.77453E-21 4.77452E-21 4.77452E-21 4.77451E-21 4.77450E-21 4.77450E-21 4.77449E-21 4.77449E-21 ++ 3.29978E-21 3.29979E-21 3.29979E-21 3.29979E-21 3.29980E-21 3.29980E-21 3.29981E-21 3.29981E-21 3.29981E-21 3.29982E-21 ++ 3.29982E-21 3.29983E-21 3.29983E-21 3.29984E-21 3.29984E-21 3.29984E-21 3.29985E-21 3.29985E-21 3.29986E-21 3.29986E-21 ++ 3.29987E-21 3.29987E-21 3.29988E-21 3.29988E-21 3.29988E-21 3.29989E-21 3.29989E-21 3.29990E-21 3.29990E-21 3.29991E-21 ++ 3.29991E-21 3.29992E-21 3.29992E-21 3.29993E-21 3.29993E-21 3.29994E-21 3.29994E-21 3.29994E-21 3.29994E-21 3.29994E-21 ++ 3.29994E-21 3.29994E-21 3.29994E-21 3.29994E-21 3.29994E-21 3.29994E-21 3.29994E-21 3.29994E-21 3.29994E-21 3.29994E-21 ++ 3.29994E-21 3.29994E-21 3.29994E-21 3.29994E-21 3.29995E-21 3.29995E-21 3.29995E-21 3.29995E-21 3.29995E-21 3.29995E-21 ++ 3.29995E-21 3.29995E-21 3.29995E-21 3.29995E-21 3.29995E-21 3.29995E-21 3.29995E-21 3.29995E-21 3.29996E-21 3.29996E-21 ++ 3.29996E-21 3.29996E-21 3.29996E-21 3.29996E-21 3.29996E-21 3.29996E-21 3.29996E-21 3.29996E-21 3.29996E-21 3.29996E-21 ++ 3.29996E-21 3.29996E-21 3.29995E-21 3.29995E-21 3.29995E-21 3.29995E-21 3.29995E-21 3.29995E-21 3.29995E-21 3.29995E-21 ++ 3.29995E-21 3.29995E-21 3.29995E-21 3.29995E-21 3.29995E-21 3.29995E-21 3.29994E-21 3.29994E-21 3.29994E-21 3.29994E-21 ++ 3.29994E-21 3.29994E-21 3.29994E-21 3.29994E-21 3.29994E-21 3.29994E-21 3.29994E-21 3.29994E-21 3.29994E-21 3.29994E-21 ++ 3.29994E-21 3.29994E-21 3.29994E-21 3.29994E-21 3.29994E-21 3.29993E-21 3.29993E-21 3.29992E-21 3.29992E-21 3.29991E-21 ++ 3.29991E-21 3.29990E-21 3.29990E-21 3.29989E-21 3.29989E-21 3.29988E-21 3.29988E-21 3.29988E-21 3.29987E-21 3.29987E-21 ++ 3.29986E-21 3.29986E-21 3.29985E-21 3.29985E-21 3.29984E-21 3.29984E-21 3.29984E-21 3.29983E-21 3.29983E-21 3.29982E-21 ++ 3.29982E-21 3.29981E-21 3.29981E-21 3.29981E-21 3.29980E-21 3.29980E-21 3.29979E-21 3.29979E-21 3.29979E-21 3.29978E-21 ++ 2.27243E-21 2.27243E-21 2.27243E-21 2.27244E-21 2.27244E-21 2.27244E-21 2.27245E-21 2.27245E-21 2.27245E-21 2.27245E-21 ++ 2.27246E-21 2.27246E-21 2.27246E-21 2.27247E-21 2.27247E-21 2.27247E-21 2.27248E-21 2.27248E-21 2.27248E-21 2.27248E-21 ++ 2.27249E-21 2.27249E-21 2.27249E-21 2.27250E-21 2.27250E-21 2.27250E-21 2.27251E-21 2.27251E-21 2.27251E-21 2.27252E-21 ++ 2.27252E-21 2.27252E-21 2.27253E-21 2.27253E-21 2.27253E-21 2.27254E-21 2.27254E-21 2.27254E-21 2.27254E-21 2.27254E-21 ++ 2.27254E-21 2.27254E-21 2.27254E-21 2.27254E-21 2.27254E-21 2.27254E-21 2.27254E-21 2.27254E-21 2.27254E-21 2.27254E-21 ++ 2.27254E-21 2.27254E-21 2.27254E-21 2.27254E-21 2.27254E-21 2.27254E-21 2.27254E-21 2.27255E-21 2.27255E-21 2.27255E-21 ++ 2.27255E-21 2.27255E-21 2.27255E-21 2.27255E-21 2.27255E-21 2.27255E-21 2.27255E-21 2.27255E-21 2.27255E-21 2.27255E-21 ++ 2.27255E-21 2.27255E-21 2.27255E-21 2.27255E-21 2.27255E-21 2.27255E-21 2.27255E-21 2.27255E-21 2.27255E-21 2.27255E-21 ++ 2.27255E-21 2.27255E-21 2.27255E-21 2.27255E-21 2.27255E-21 2.27255E-21 2.27255E-21 2.27255E-21 2.27255E-21 2.27255E-21 ++ 2.27255E-21 2.27255E-21 2.27255E-21 2.27254E-21 2.27254E-21 2.27254E-21 2.27254E-21 2.27254E-21 2.27254E-21 2.27254E-21 ++ 2.27254E-21 2.27254E-21 2.27254E-21 2.27254E-21 2.27254E-21 2.27254E-21 2.27254E-21 2.27254E-21 2.27254E-21 2.27254E-21 ++ 2.27254E-21 2.27254E-21 2.27254E-21 2.27254E-21 2.27254E-21 2.27253E-21 2.27253E-21 2.27253E-21 2.27252E-21 2.27252E-21 ++ 2.27252E-21 2.27251E-21 2.27251E-21 2.27251E-21 2.27250E-21 2.27250E-21 2.27250E-21 2.27249E-21 2.27249E-21 2.27249E-21 ++ 2.27248E-21 2.27248E-21 2.27248E-21 2.27248E-21 2.27247E-21 2.27247E-21 2.27247E-21 2.27246E-21 2.27246E-21 2.27246E-21 ++ 2.27245E-21 2.27245E-21 2.27245E-21 2.27245E-21 2.27244E-21 2.27244E-21 2.27244E-21 2.27243E-21 2.27243E-21 2.27243E-21 ++ 1.55934E-21 1.55935E-21 1.55935E-21 1.55935E-21 1.55935E-21 1.55935E-21 1.55936E-21 1.55936E-21 1.55936E-21 1.55936E-21 ++ 1.55936E-21 1.55937E-21 1.55937E-21 1.55937E-21 1.55937E-21 1.55938E-21 1.55938E-21 1.55938E-21 1.55938E-21 1.55938E-21 ++ 1.55939E-21 1.55939E-21 1.55939E-21 1.55939E-21 1.55939E-21 1.55940E-21 1.55940E-21 1.55940E-21 1.55940E-21 1.55941E-21 ++ 1.55941E-21 1.55941E-21 1.55941E-21 1.55942E-21 1.55942E-21 1.55942E-21 1.55942E-21 1.55942E-21 1.55942E-21 1.55942E-21 ++ 1.55942E-21 1.55942E-21 1.55942E-21 1.55942E-21 1.55942E-21 1.55942E-21 1.55942E-21 1.55942E-21 1.55942E-21 1.55942E-21 ++ 1.55942E-21 1.55942E-21 1.55942E-21 1.55942E-21 1.55943E-21 1.55943E-21 1.55943E-21 1.55943E-21 1.55943E-21 1.55943E-21 ++ 1.55943E-21 1.55943E-21 1.55943E-21 1.55943E-21 1.55943E-21 1.55943E-21 1.55943E-21 1.55943E-21 1.55943E-21 1.55943E-21 ++ 1.55943E-21 1.55943E-21 1.55943E-21 1.55943E-21 1.55943E-21 1.55943E-21 1.55943E-21 1.55943E-21 1.55943E-21 1.55943E-21 ++ 1.55943E-21 1.55943E-21 1.55943E-21 1.55943E-21 1.55943E-21 1.55943E-21 1.55943E-21 1.55943E-21 1.55943E-21 1.55943E-21 ++ 1.55943E-21 1.55943E-21 1.55943E-21 1.55943E-21 1.55943E-21 1.55943E-21 1.55942E-21 1.55942E-21 1.55942E-21 1.55942E-21 ++ 1.55942E-21 1.55942E-21 1.55942E-21 1.55942E-21 1.55942E-21 1.55942E-21 1.55942E-21 1.55942E-21 1.55942E-21 1.55942E-21 ++ 1.55942E-21 1.55942E-21 1.55942E-21 1.55942E-21 1.55942E-21 1.55942E-21 1.55942E-21 1.55941E-21 1.55941E-21 1.55941E-21 ++ 1.55941E-21 1.55940E-21 1.55940E-21 1.55940E-21 1.55940E-21 1.55939E-21 1.55939E-21 1.55939E-21 1.55939E-21 1.55939E-21 ++ 1.55938E-21 1.55938E-21 1.55938E-21 1.55938E-21 1.55938E-21 1.55937E-21 1.55937E-21 1.55937E-21 1.55937E-21 1.55936E-21 ++ 1.55936E-21 1.55936E-21 1.55936E-21 1.55936E-21 1.55935E-21 1.55935E-21 1.55935E-21 1.55935E-21 1.55935E-21 1.55934E-21 ++ 1.06621E-21 1.06621E-21 1.06621E-21 1.06621E-21 1.06621E-21 1.06621E-21 1.06621E-21 1.06622E-21 1.06622E-21 1.06622E-21 ++ 1.06622E-21 1.06622E-21 1.06622E-21 1.06622E-21 1.06623E-21 1.06623E-21 1.06623E-21 1.06623E-21 1.06623E-21 1.06623E-21 ++ 1.06623E-21 1.06624E-21 1.06624E-21 1.06624E-21 1.06624E-21 1.06624E-21 1.06624E-21 1.06625E-21 1.06625E-21 1.06625E-21 ++ 1.06625E-21 1.06625E-21 1.06625E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 ++ 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 ++ 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 ++ 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06627E-21 1.06627E-21 1.06627E-21 1.06627E-21 1.06627E-21 ++ 1.06627E-21 1.06627E-21 1.06627E-21 1.06627E-21 1.06627E-21 1.06627E-21 1.06627E-21 1.06627E-21 1.06627E-21 1.06627E-21 ++ 1.06627E-21 1.06627E-21 1.06627E-21 1.06627E-21 1.06627E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 ++ 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 ++ 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 ++ 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06626E-21 1.06625E-21 1.06625E-21 1.06625E-21 ++ 1.06625E-21 1.06625E-21 1.06625E-21 1.06624E-21 1.06624E-21 1.06624E-21 1.06624E-21 1.06624E-21 1.06624E-21 1.06623E-21 ++ 1.06623E-21 1.06623E-21 1.06623E-21 1.06623E-21 1.06623E-21 1.06623E-21 1.06622E-21 1.06622E-21 1.06622E-21 1.06622E-21 ++ 1.06622E-21 1.06622E-21 1.06622E-21 1.06621E-21 1.06621E-21 1.06621E-21 1.06621E-21 1.06621E-21 1.06621E-21 1.06621E-21 ++ 7.26420E-22 7.26421E-22 7.26422E-22 7.26423E-22 7.26424E-22 7.26425E-22 7.26426E-22 7.26427E-22 7.26428E-22 7.26429E-22 ++ 7.26430E-22 7.26431E-22 7.26432E-22 7.26433E-22 7.26434E-22 7.26435E-22 7.26436E-22 7.26437E-22 7.26438E-22 7.26439E-22 ++ 7.26440E-22 7.26441E-22 7.26442E-22 7.26443E-22 7.26444E-22 7.26445E-22 7.26446E-22 7.26447E-22 7.26448E-22 7.26450E-22 ++ 7.26451E-22 7.26452E-22 7.26453E-22 7.26454E-22 7.26455E-22 7.26456E-22 7.26456E-22 7.26456E-22 7.26456E-22 7.26457E-22 ++ 7.26457E-22 7.26457E-22 7.26457E-22 7.26457E-22 7.26457E-22 7.26457E-22 7.26457E-22 7.26457E-22 7.26458E-22 7.26458E-22 ++ 7.26458E-22 7.26458E-22 7.26458E-22 7.26459E-22 7.26459E-22 7.26459E-22 7.26459E-22 7.26459E-22 7.26460E-22 7.26460E-22 ++ 7.26460E-22 7.26460E-22 7.26460E-22 7.26461E-22 7.26461E-22 7.26461E-22 7.26461E-22 7.26461E-22 7.26461E-22 7.26461E-22 ++ 7.26461E-22 7.26461E-22 7.26462E-22 7.26462E-22 7.26462E-22 7.26462E-22 7.26462E-22 7.26462E-22 7.26461E-22 7.26461E-22 ++ 7.26461E-22 7.26461E-22 7.26461E-22 7.26461E-22 7.26461E-22 7.26461E-22 7.26461E-22 7.26460E-22 7.26460E-22 7.26460E-22 ++ 7.26460E-22 7.26460E-22 7.26459E-22 7.26459E-22 7.26459E-22 7.26459E-22 7.26459E-22 7.26458E-22 7.26458E-22 7.26458E-22 ++ 7.26458E-22 7.26458E-22 7.26457E-22 7.26457E-22 7.26457E-22 7.26457E-22 7.26457E-22 7.26457E-22 7.26457E-22 7.26457E-22 ++ 7.26457E-22 7.26456E-22 7.26456E-22 7.26456E-22 7.26456E-22 7.26455E-22 7.26454E-22 7.26453E-22 7.26452E-22 7.26451E-22 ++ 7.26450E-22 7.26448E-22 7.26447E-22 7.26446E-22 7.26445E-22 7.26444E-22 7.26443E-22 7.26442E-22 7.26441E-22 7.26440E-22 ++ 7.26439E-22 7.26438E-22 7.26437E-22 7.26436E-22 7.26435E-22 7.26434E-22 7.26433E-22 7.26432E-22 7.26431E-22 7.26430E-22 ++ 7.26429E-22 7.26428E-22 7.26427E-22 7.26426E-22 7.26425E-22 7.26424E-22 7.26423E-22 7.26422E-22 7.26421E-22 7.26420E-22 ++ 4.93154E-22 4.93154E-22 4.93155E-22 4.93155E-22 4.93156E-22 4.93157E-22 4.93157E-22 4.93158E-22 4.93159E-22 4.93160E-22 ++ 4.93160E-22 4.93161E-22 4.93162E-22 4.93162E-22 4.93163E-22 4.93164E-22 4.93164E-22 4.93165E-22 4.93166E-22 4.93167E-22 ++ 4.93167E-22 4.93168E-22 4.93169E-22 4.93169E-22 4.93170E-22 4.93171E-22 4.93172E-22 4.93172E-22 4.93173E-22 4.93174E-22 ++ 4.93175E-22 4.93176E-22 4.93176E-22 4.93177E-22 4.93178E-22 4.93179E-22 4.93179E-22 4.93179E-22 4.93179E-22 4.93179E-22 ++ 4.93179E-22 4.93179E-22 4.93179E-22 4.93179E-22 4.93179E-22 4.93179E-22 4.93179E-22 4.93179E-22 4.93180E-22 4.93180E-22 ++ 4.93180E-22 4.93180E-22 4.93180E-22 4.93180E-22 4.93180E-22 4.93181E-22 4.93181E-22 4.93181E-22 4.93181E-22 4.93181E-22 ++ 4.93181E-22 4.93181E-22 4.93181E-22 4.93182E-22 4.93182E-22 4.93182E-22 4.93182E-22 4.93182E-22 4.93182E-22 4.93182E-22 ++ 4.93182E-22 4.93182E-22 4.93182E-22 4.93182E-22 4.93182E-22 4.93182E-22 4.93182E-22 4.93182E-22 4.93182E-22 4.93182E-22 ++ 4.93182E-22 4.93182E-22 4.93182E-22 4.93182E-22 4.93182E-22 4.93182E-22 4.93182E-22 4.93181E-22 4.93181E-22 4.93181E-22 ++ 4.93181E-22 4.93181E-22 4.93181E-22 4.93181E-22 4.93181E-22 4.93180E-22 4.93180E-22 4.93180E-22 4.93180E-22 4.93180E-22 ++ 4.93180E-22 4.93180E-22 4.93179E-22 4.93179E-22 4.93179E-22 4.93179E-22 4.93179E-22 4.93179E-22 4.93179E-22 4.93179E-22 ++ 4.93179E-22 4.93179E-22 4.93179E-22 4.93179E-22 4.93179E-22 4.93178E-22 4.93177E-22 4.93176E-22 4.93176E-22 4.93175E-22 ++ 4.93174E-22 4.93173E-22 4.93172E-22 4.93172E-22 4.93171E-22 4.93170E-22 4.93169E-22 4.93169E-22 4.93168E-22 4.93167E-22 ++ 4.93167E-22 4.93166E-22 4.93165E-22 4.93164E-22 4.93164E-22 4.93163E-22 4.93162E-22 4.93162E-22 4.93161E-22 4.93160E-22 ++ 4.93160E-22 4.93159E-22 4.93158E-22 4.93157E-22 4.93157E-22 4.93156E-22 4.93155E-22 4.93155E-22 4.93154E-22 4.93154E-22 ++ 3.33599E-22 3.33599E-22 3.33600E-22 3.33600E-22 3.33601E-22 3.33601E-22 3.33602E-22 3.33602E-22 3.33603E-22 3.33603E-22 ++ 3.33604E-22 3.33604E-22 3.33605E-22 3.33605E-22 3.33605E-22 3.33606E-22 3.33606E-22 3.33607E-22 3.33607E-22 3.33608E-22 ++ 3.33608E-22 3.33609E-22 3.33609E-22 3.33610E-22 3.33610E-22 3.33611E-22 3.33612E-22 3.33612E-22 3.33613E-22 3.33613E-22 ++ 3.33614E-22 3.33614E-22 3.33615E-22 3.33615E-22 3.33616E-22 3.33616E-22 3.33616E-22 3.33616E-22 3.33616E-22 3.33616E-22 ++ 3.33616E-22 3.33616E-22 3.33617E-22 3.33617E-22 3.33617E-22 3.33617E-22 3.33617E-22 3.33617E-22 3.33617E-22 3.33617E-22 ++ 3.33617E-22 3.33617E-22 3.33617E-22 3.33617E-22 3.33617E-22 3.33618E-22 3.33618E-22 3.33618E-22 3.33618E-22 3.33618E-22 ++ 3.33618E-22 3.33618E-22 3.33618E-22 3.33618E-22 3.33618E-22 3.33618E-22 3.33619E-22 3.33619E-22 3.33619E-22 3.33619E-22 ++ 3.33619E-22 3.33619E-22 3.33619E-22 3.33619E-22 3.33619E-22 3.33619E-22 3.33619E-22 3.33619E-22 3.33619E-22 3.33619E-22 ++ 3.33619E-22 3.33619E-22 3.33619E-22 3.33619E-22 3.33618E-22 3.33618E-22 3.33618E-22 3.33618E-22 3.33618E-22 3.33618E-22 ++ 3.33618E-22 3.33618E-22 3.33618E-22 3.33618E-22 3.33618E-22 3.33617E-22 3.33617E-22 3.33617E-22 3.33617E-22 3.33617E-22 ++ 3.33617E-22 3.33617E-22 3.33617E-22 3.33617E-22 3.33617E-22 3.33617E-22 3.33617E-22 3.33617E-22 3.33616E-22 3.33616E-22 ++ 3.33616E-22 3.33616E-22 3.33616E-22 3.33616E-22 3.33616E-22 3.33616E-22 3.33615E-22 3.33615E-22 3.33614E-22 3.33614E-22 ++ 3.33613E-22 3.33613E-22 3.33612E-22 3.33612E-22 3.33611E-22 3.33610E-22 3.33610E-22 3.33609E-22 3.33609E-22 3.33608E-22 ++ 3.33608E-22 3.33607E-22 3.33607E-22 3.33606E-22 3.33606E-22 3.33605E-22 3.33605E-22 3.33605E-22 3.33604E-22 3.33604E-22 ++ 3.33603E-22 3.33603E-22 3.33602E-22 3.33602E-22 3.33601E-22 3.33601E-22 3.33600E-22 3.33600E-22 3.33599E-22 3.33599E-22 ++ 2.24862E-22 2.24862E-22 2.24862E-22 2.24863E-22 2.24863E-22 2.24863E-22 2.24864E-22 2.24864E-22 2.24864E-22 2.24865E-22 ++ 2.24865E-22 2.24865E-22 2.24866E-22 2.24866E-22 2.24866E-22 2.24867E-22 2.24867E-22 2.24867E-22 2.24868E-22 2.24868E-22 ++ 2.24868E-22 2.24869E-22 2.24869E-22 2.24869E-22 2.24870E-22 2.24870E-22 2.24870E-22 2.24871E-22 2.24871E-22 2.24872E-22 ++ 2.24872E-22 2.24872E-22 2.24873E-22 2.24873E-22 2.24873E-22 2.24874E-22 2.24874E-22 2.24874E-22 2.24874E-22 2.24874E-22 ++ 2.24874E-22 2.24874E-22 2.24874E-22 2.24874E-22 2.24874E-22 2.24874E-22 2.24874E-22 2.24874E-22 2.24874E-22 2.24874E-22 ++ 2.24874E-22 2.24874E-22 2.24874E-22 2.24875E-22 2.24875E-22 2.24875E-22 2.24875E-22 2.24875E-22 2.24875E-22 2.24875E-22 ++ 2.24875E-22 2.24875E-22 2.24875E-22 2.24875E-22 2.24875E-22 2.24875E-22 2.24875E-22 2.24875E-22 2.24875E-22 2.24875E-22 ++ 2.24875E-22 2.24875E-22 2.24876E-22 2.24876E-22 2.24876E-22 2.24876E-22 2.24876E-22 2.24876E-22 2.24875E-22 2.24875E-22 ++ 2.24875E-22 2.24875E-22 2.24875E-22 2.24875E-22 2.24875E-22 2.24875E-22 2.24875E-22 2.24875E-22 2.24875E-22 2.24875E-22 ++ 2.24875E-22 2.24875E-22 2.24875E-22 2.24875E-22 2.24875E-22 2.24875E-22 2.24875E-22 2.24874E-22 2.24874E-22 2.24874E-22 ++ 2.24874E-22 2.24874E-22 2.24874E-22 2.24874E-22 2.24874E-22 2.24874E-22 2.24874E-22 2.24874E-22 2.24874E-22 2.24874E-22 ++ 2.24874E-22 2.24874E-22 2.24874E-22 2.24874E-22 2.24874E-22 2.24873E-22 2.24873E-22 2.24873E-22 2.24872E-22 2.24872E-22 ++ 2.24872E-22 2.24871E-22 2.24871E-22 2.24870E-22 2.24870E-22 2.24870E-22 2.24869E-22 2.24869E-22 2.24869E-22 2.24868E-22 ++ 2.24868E-22 2.24868E-22 2.24867E-22 2.24867E-22 2.24867E-22 2.24866E-22 2.24866E-22 2.24866E-22 2.24865E-22 2.24865E-22 ++ 2.24865E-22 2.24864E-22 2.24864E-22 2.24864E-22 2.24863E-22 2.24863E-22 2.24863E-22 2.24862E-22 2.24862E-22 2.24862E-22 ++ 1.51027E-22 1.51028E-22 1.51028E-22 1.51028E-22 1.51028E-22 1.51029E-22 1.51029E-22 1.51029E-22 1.51029E-22 1.51029E-22 ++ 1.51030E-22 1.51030E-22 1.51030E-22 1.51030E-22 1.51030E-22 1.51031E-22 1.51031E-22 1.51031E-22 1.51031E-22 1.51032E-22 ++ 1.51032E-22 1.51032E-22 1.51032E-22 1.51033E-22 1.51033E-22 1.51033E-22 1.51033E-22 1.51034E-22 1.51034E-22 1.51034E-22 ++ 1.51034E-22 1.51035E-22 1.51035E-22 1.51035E-22 1.51035E-22 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 ++ 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 ++ 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 ++ 1.51036E-22 1.51036E-22 1.51036E-22 1.51037E-22 1.51037E-22 1.51037E-22 1.51037E-22 1.51037E-22 1.51037E-22 1.51037E-22 ++ 1.51037E-22 1.51037E-22 1.51037E-22 1.51037E-22 1.51037E-22 1.51037E-22 1.51037E-22 1.51037E-22 1.51037E-22 1.51037E-22 ++ 1.51037E-22 1.51037E-22 1.51037E-22 1.51037E-22 1.51037E-22 1.51037E-22 1.51037E-22 1.51036E-22 1.51036E-22 1.51036E-22 ++ 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 ++ 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 ++ 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 1.51036E-22 1.51035E-22 1.51035E-22 1.51035E-22 1.51035E-22 1.51034E-22 ++ 1.51034E-22 1.51034E-22 1.51034E-22 1.51033E-22 1.51033E-22 1.51033E-22 1.51033E-22 1.51032E-22 1.51032E-22 1.51032E-22 ++ 1.51032E-22 1.51031E-22 1.51031E-22 1.51031E-22 1.51031E-22 1.51030E-22 1.51030E-22 1.51030E-22 1.51030E-22 1.51030E-22 ++ 1.51029E-22 1.51029E-22 1.51029E-22 1.51029E-22 1.51029E-22 1.51028E-22 1.51028E-22 1.51028E-22 1.51028E-22 1.51027E-22 ++ 1.01075E-22 1.01075E-22 1.01076E-22 1.01076E-22 1.01076E-22 1.01076E-22 1.01076E-22 1.01076E-22 1.01076E-22 1.01077E-22 ++ 1.01077E-22 1.01077E-22 1.01077E-22 1.01077E-22 1.01077E-22 1.01078E-22 1.01078E-22 1.01078E-22 1.01078E-22 1.01078E-22 ++ 1.01078E-22 1.01079E-22 1.01079E-22 1.01079E-22 1.01079E-22 1.01079E-22 1.01079E-22 1.01079E-22 1.01080E-22 1.01080E-22 ++ 1.01080E-22 1.01080E-22 1.01080E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 ++ 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 ++ 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 ++ 1.01081E-22 1.01081E-22 1.01081E-22 1.01082E-22 1.01082E-22 1.01082E-22 1.01082E-22 1.01082E-22 1.01082E-22 1.01082E-22 ++ 1.01082E-22 1.01082E-22 1.01082E-22 1.01082E-22 1.01082E-22 1.01082E-22 1.01082E-22 1.01082E-22 1.01082E-22 1.01082E-22 ++ 1.01082E-22 1.01082E-22 1.01082E-22 1.01082E-22 1.01082E-22 1.01082E-22 1.01082E-22 1.01081E-22 1.01081E-22 1.01081E-22 ++ 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 ++ 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 ++ 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01081E-22 1.01080E-22 1.01080E-22 1.01080E-22 ++ 1.01080E-22 1.01080E-22 1.01079E-22 1.01079E-22 1.01079E-22 1.01079E-22 1.01079E-22 1.01079E-22 1.01079E-22 1.01078E-22 ++ 1.01078E-22 1.01078E-22 1.01078E-22 1.01078E-22 1.01078E-22 1.01077E-22 1.01077E-22 1.01077E-22 1.01077E-22 1.01077E-22 ++ 1.01077E-22 1.01076E-22 1.01076E-22 1.01076E-22 1.01076E-22 1.01076E-22 1.01076E-22 1.01076E-22 1.01075E-22 1.01075E-22 ++ 6.74038E-23 6.74039E-23 6.74040E-23 6.74041E-23 6.74041E-23 6.74042E-23 6.74043E-23 6.74044E-23 6.74045E-23 6.74046E-23 ++ 6.74047E-23 6.74048E-23 6.74050E-23 6.74051E-23 6.74052E-23 6.74053E-23 6.74054E-23 6.74055E-23 6.74056E-23 6.74057E-23 ++ 6.74058E-23 6.74059E-23 6.74060E-23 6.74061E-23 6.74062E-23 6.74064E-23 6.74065E-23 6.74066E-23 6.74067E-23 6.74068E-23 ++ 6.74069E-23 6.74070E-23 6.74072E-23 6.74073E-23 6.74074E-23 6.74075E-23 6.74075E-23 6.74075E-23 6.74075E-23 6.74075E-23 ++ 6.74075E-23 6.74076E-23 6.74076E-23 6.74076E-23 6.74076E-23 6.74076E-23 6.74076E-23 6.74076E-23 6.74077E-23 6.74077E-23 ++ 6.74077E-23 6.74077E-23 6.74077E-23 6.74078E-23 6.74078E-23 6.74078E-23 6.74078E-23 6.74078E-23 6.74079E-23 6.74079E-23 ++ 6.74079E-23 6.74079E-23 6.74079E-23 6.74080E-23 6.74080E-23 6.74080E-23 6.74080E-23 6.74080E-23 6.74080E-23 6.74080E-23 ++ 6.74081E-23 6.74081E-23 6.74081E-23 6.74081E-23 6.74081E-23 6.74081E-23 6.74081E-23 6.74081E-23 6.74081E-23 6.74081E-23 ++ 6.74080E-23 6.74080E-23 6.74080E-23 6.74080E-23 6.74080E-23 6.74080E-23 6.74080E-23 6.74079E-23 6.74079E-23 6.74079E-23 ++ 6.74079E-23 6.74079E-23 6.74078E-23 6.74078E-23 6.74078E-23 6.74078E-23 6.74078E-23 6.74077E-23 6.74077E-23 6.74077E-23 ++ 6.74077E-23 6.74077E-23 6.74076E-23 6.74076E-23 6.74076E-23 6.74076E-23 6.74076E-23 6.74076E-23 6.74076E-23 6.74075E-23 ++ 6.74075E-23 6.74075E-23 6.74075E-23 6.74075E-23 6.74075E-23 6.74074E-23 6.74073E-23 6.74072E-23 6.74070E-23 6.74069E-23 ++ 6.74068E-23 6.74067E-23 6.74066E-23 6.74065E-23 6.74064E-23 6.74062E-23 6.74061E-23 6.74060E-23 6.74059E-23 6.74058E-23 ++ 6.74057E-23 6.74056E-23 6.74055E-23 6.74054E-23 6.74053E-23 6.74052E-23 6.74051E-23 6.74050E-23 6.74048E-23 6.74047E-23 ++ 6.74046E-23 6.74045E-23 6.74044E-23 6.74043E-23 6.74042E-23 6.74041E-23 6.74041E-23 6.74040E-23 6.74039E-23 6.74038E-23 ++ 4.47892E-23 4.47892E-23 4.47893E-23 4.47894E-23 4.47894E-23 4.47895E-23 4.47896E-23 4.47896E-23 4.47897E-23 4.47898E-23 ++ 4.47898E-23 4.47899E-23 4.47900E-23 4.47900E-23 4.47901E-23 4.47902E-23 4.47903E-23 4.47903E-23 4.47904E-23 4.47905E-23 ++ 4.47905E-23 4.47906E-23 4.47907E-23 4.47908E-23 4.47908E-23 4.47909E-23 4.47910E-23 4.47911E-23 4.47912E-23 4.47912E-23 ++ 4.47913E-23 4.47914E-23 4.47915E-23 4.47916E-23 4.47916E-23 4.47917E-23 4.47917E-23 4.47917E-23 4.47917E-23 4.47917E-23 ++ 4.47917E-23 4.47917E-23 4.47917E-23 4.47918E-23 4.47918E-23 4.47918E-23 4.47918E-23 4.47918E-23 4.47918E-23 4.47918E-23 ++ 4.47918E-23 4.47918E-23 4.47919E-23 4.47919E-23 4.47919E-23 4.47919E-23 4.47919E-23 4.47919E-23 4.47919E-23 4.47920E-23 ++ 4.47920E-23 4.47920E-23 4.47920E-23 4.47920E-23 4.47920E-23 4.47920E-23 4.47920E-23 4.47921E-23 4.47921E-23 4.47921E-23 ++ 4.47921E-23 4.47921E-23 4.47921E-23 4.47921E-23 4.47921E-23 4.47921E-23 4.47921E-23 4.47921E-23 4.47921E-23 4.47921E-23 ++ 4.47921E-23 4.47921E-23 4.47921E-23 4.47920E-23 4.47920E-23 4.47920E-23 4.47920E-23 4.47920E-23 4.47920E-23 4.47920E-23 ++ 4.47920E-23 4.47919E-23 4.47919E-23 4.47919E-23 4.47919E-23 4.47919E-23 4.47919E-23 4.47919E-23 4.47918E-23 4.47918E-23 ++ 4.47918E-23 4.47918E-23 4.47918E-23 4.47918E-23 4.47918E-23 4.47918E-23 4.47918E-23 4.47917E-23 4.47917E-23 4.47917E-23 ++ 4.47917E-23 4.47917E-23 4.47917E-23 4.47917E-23 4.47917E-23 4.47916E-23 4.47916E-23 4.47915E-23 4.47914E-23 4.47913E-23 ++ 4.47912E-23 4.47912E-23 4.47911E-23 4.47910E-23 4.47909E-23 4.47908E-23 4.47908E-23 4.47907E-23 4.47906E-23 4.47905E-23 ++ 4.47905E-23 4.47904E-23 4.47903E-23 4.47903E-23 4.47902E-23 4.47901E-23 4.47900E-23 4.47900E-23 4.47899E-23 4.47898E-23 ++ 4.47898E-23 4.47897E-23 4.47896E-23 4.47896E-23 4.47895E-23 4.47894E-23 4.47894E-23 4.47893E-23 4.47892E-23 4.47892E-23 ++ 2.96560E-23 2.96560E-23 2.96561E-23 2.96561E-23 2.96562E-23 2.96562E-23 2.96563E-23 2.96563E-23 2.96563E-23 2.96564E-23 ++ 2.96564E-23 2.96565E-23 2.96565E-23 2.96566E-23 2.96566E-23 2.96567E-23 2.96567E-23 2.96568E-23 2.96568E-23 2.96569E-23 ++ 2.96569E-23 2.96570E-23 2.96570E-23 2.96571E-23 2.96571E-23 2.96572E-23 2.96572E-23 2.96573E-23 2.96573E-23 2.96574E-23 ++ 2.96574E-23 2.96575E-23 2.96575E-23 2.96576E-23 2.96576E-23 2.96577E-23 2.96577E-23 2.96577E-23 2.96577E-23 2.96577E-23 ++ 2.96577E-23 2.96577E-23 2.96577E-23 2.96577E-23 2.96577E-23 2.96577E-23 2.96577E-23 2.96578E-23 2.96578E-23 2.96578E-23 ++ 2.96578E-23 2.96578E-23 2.96578E-23 2.96578E-23 2.96578E-23 2.96578E-23 2.96578E-23 2.96578E-23 2.96579E-23 2.96579E-23 ++ 2.96579E-23 2.96579E-23 2.96579E-23 2.96579E-23 2.96579E-23 2.96579E-23 2.96579E-23 2.96579E-23 2.96579E-23 2.96579E-23 ++ 2.96579E-23 2.96579E-23 2.96579E-23 2.96579E-23 2.96579E-23 2.96579E-23 2.96579E-23 2.96579E-23 2.96579E-23 2.96579E-23 ++ 2.96579E-23 2.96579E-23 2.96579E-23 2.96579E-23 2.96579E-23 2.96579E-23 2.96579E-23 2.96579E-23 2.96579E-23 2.96579E-23 ++ 2.96579E-23 2.96579E-23 2.96578E-23 2.96578E-23 2.96578E-23 2.96578E-23 2.96578E-23 2.96578E-23 2.96578E-23 2.96578E-23 ++ 2.96578E-23 2.96578E-23 2.96578E-23 2.96577E-23 2.96577E-23 2.96577E-23 2.96577E-23 2.96577E-23 2.96577E-23 2.96577E-23 ++ 2.96577E-23 2.96577E-23 2.96577E-23 2.96577E-23 2.96577E-23 2.96576E-23 2.96576E-23 2.96575E-23 2.96575E-23 2.96574E-23 ++ 2.96574E-23 2.96573E-23 2.96573E-23 2.96572E-23 2.96572E-23 2.96571E-23 2.96571E-23 2.96570E-23 2.96570E-23 2.96569E-23 ++ 2.96569E-23 2.96568E-23 2.96568E-23 2.96567E-23 2.96567E-23 2.96566E-23 2.96566E-23 2.96565E-23 2.96565E-23 2.96564E-23 ++ 2.96564E-23 2.96563E-23 2.96563E-23 2.96563E-23 2.96562E-23 2.96562E-23 2.96561E-23 2.96561E-23 2.96560E-23 2.96560E-23 ++ 1.95660E-23 1.95660E-23 1.95661E-23 1.95661E-23 1.95661E-23 1.95662E-23 1.95662E-23 1.95662E-23 1.95663E-23 1.95663E-23 ++ 1.95663E-23 1.95663E-23 1.95664E-23 1.95664E-23 1.95664E-23 1.95665E-23 1.95665E-23 1.95665E-23 1.95666E-23 1.95666E-23 ++ 1.95666E-23 1.95667E-23 1.95667E-23 1.95667E-23 1.95668E-23 1.95668E-23 1.95668E-23 1.95669E-23 1.95669E-23 1.95669E-23 ++ 1.95670E-23 1.95670E-23 1.95671E-23 1.95671E-23 1.95671E-23 1.95672E-23 1.95672E-23 1.95672E-23 1.95672E-23 1.95672E-23 ++ 1.95672E-23 1.95672E-23 1.95672E-23 1.95672E-23 1.95672E-23 1.95672E-23 1.95672E-23 1.95672E-23 1.95672E-23 1.95672E-23 ++ 1.95672E-23 1.95672E-23 1.95672E-23 1.95672E-23 1.95672E-23 1.95672E-23 1.95673E-23 1.95673E-23 1.95673E-23 1.95673E-23 ++ 1.95673E-23 1.95673E-23 1.95673E-23 1.95673E-23 1.95673E-23 1.95673E-23 1.95673E-23 1.95673E-23 1.95673E-23 1.95673E-23 ++ 1.95673E-23 1.95673E-23 1.95673E-23 1.95673E-23 1.95673E-23 1.95673E-23 1.95673E-23 1.95673E-23 1.95673E-23 1.95673E-23 ++ 1.95673E-23 1.95673E-23 1.95673E-23 1.95673E-23 1.95673E-23 1.95673E-23 1.95673E-23 1.95673E-23 1.95673E-23 1.95673E-23 ++ 1.95673E-23 1.95673E-23 1.95673E-23 1.95673E-23 1.95672E-23 1.95672E-23 1.95672E-23 1.95672E-23 1.95672E-23 1.95672E-23 ++ 1.95672E-23 1.95672E-23 1.95672E-23 1.95672E-23 1.95672E-23 1.95672E-23 1.95672E-23 1.95672E-23 1.95672E-23 1.95672E-23 ++ 1.95672E-23 1.95672E-23 1.95672E-23 1.95672E-23 1.95672E-23 1.95671E-23 1.95671E-23 1.95671E-23 1.95670E-23 1.95670E-23 ++ 1.95669E-23 1.95669E-23 1.95669E-23 1.95668E-23 1.95668E-23 1.95668E-23 1.95667E-23 1.95667E-23 1.95667E-23 1.95666E-23 ++ 1.95666E-23 1.95666E-23 1.95665E-23 1.95665E-23 1.95665E-23 1.95664E-23 1.95664E-23 1.95664E-23 1.95663E-23 1.95663E-23 ++ 1.95663E-23 1.95663E-23 1.95662E-23 1.95662E-23 1.95662E-23 1.95661E-23 1.95661E-23 1.95661E-23 1.95660E-23 1.95660E-23 ++ 1.28630E-23 1.28631E-23 1.28631E-23 1.28631E-23 1.28631E-23 1.28631E-23 1.28632E-23 1.28632E-23 1.28632E-23 1.28632E-23 ++ 1.28632E-23 1.28633E-23 1.28633E-23 1.28633E-23 1.28633E-23 1.28633E-23 1.28634E-23 1.28634E-23 1.28634E-23 1.28634E-23 ++ 1.28635E-23 1.28635E-23 1.28635E-23 1.28635E-23 1.28635E-23 1.28636E-23 1.28636E-23 1.28636E-23 1.28636E-23 1.28637E-23 ++ 1.28637E-23 1.28637E-23 1.28637E-23 1.28638E-23 1.28638E-23 1.28638E-23 1.28638E-23 1.28638E-23 1.28638E-23 1.28638E-23 ++ 1.28638E-23 1.28638E-23 1.28638E-23 1.28638E-23 1.28638E-23 1.28638E-23 1.28638E-23 1.28638E-23 1.28638E-23 1.28638E-23 ++ 1.28638E-23 1.28638E-23 1.28638E-23 1.28639E-23 1.28639E-23 1.28639E-23 1.28639E-23 1.28639E-23 1.28639E-23 1.28639E-23 ++ 1.28639E-23 1.28639E-23 1.28639E-23 1.28639E-23 1.28639E-23 1.28639E-23 1.28639E-23 1.28639E-23 1.28639E-23 1.28639E-23 ++ 1.28639E-23 1.28639E-23 1.28639E-23 1.28639E-23 1.28639E-23 1.28639E-23 1.28639E-23 1.28639E-23 1.28639E-23 1.28639E-23 ++ 1.28639E-23 1.28639E-23 1.28639E-23 1.28639E-23 1.28639E-23 1.28639E-23 1.28639E-23 1.28639E-23 1.28639E-23 1.28639E-23 ++ 1.28639E-23 1.28639E-23 1.28639E-23 1.28639E-23 1.28639E-23 1.28639E-23 1.28639E-23 1.28638E-23 1.28638E-23 1.28638E-23 ++ 1.28638E-23 1.28638E-23 1.28638E-23 1.28638E-23 1.28638E-23 1.28638E-23 1.28638E-23 1.28638E-23 1.28638E-23 1.28638E-23 ++ 1.28638E-23 1.28638E-23 1.28638E-23 1.28638E-23 1.28638E-23 1.28638E-23 1.28638E-23 1.28637E-23 1.28637E-23 1.28637E-23 ++ 1.28637E-23 1.28636E-23 1.28636E-23 1.28636E-23 1.28636E-23 1.28635E-23 1.28635E-23 1.28635E-23 1.28635E-23 1.28635E-23 ++ 1.28634E-23 1.28634E-23 1.28634E-23 1.28634E-23 1.28633E-23 1.28633E-23 1.28633E-23 1.28633E-23 1.28633E-23 1.28632E-23 ++ 1.28632E-23 1.28632E-23 1.28632E-23 1.28632E-23 1.28631E-23 1.28631E-23 1.28631E-23 1.28631E-23 1.28631E-23 1.28630E-23 ++ 8.42629E-24 8.42630E-24 8.42631E-24 8.42633E-24 8.42634E-24 8.42635E-24 8.42636E-24 8.42638E-24 8.42639E-24 8.42641E-24 ++ 8.42642E-24 8.42643E-24 8.42645E-24 8.42646E-24 8.42647E-24 8.42649E-24 8.42650E-24 8.42652E-24 8.42653E-24 8.42655E-24 ++ 8.42656E-24 8.42658E-24 8.42659E-24 8.42661E-24 8.42662E-24 8.42664E-24 8.42665E-24 8.42667E-24 8.42668E-24 8.42670E-24 ++ 8.42672E-24 8.42673E-24 8.42675E-24 8.42676E-24 8.42678E-24 8.42680E-24 8.42680E-24 8.42680E-24 8.42680E-24 8.42680E-24 ++ 8.42680E-24 8.42680E-24 8.42680E-24 8.42680E-24 8.42681E-24 8.42681E-24 8.42681E-24 8.42681E-24 8.42682E-24 8.42682E-24 ++ 8.42682E-24 8.42682E-24 8.42683E-24 8.42683E-24 8.42683E-24 8.42683E-24 8.42684E-24 8.42684E-24 8.42684E-24 8.42685E-24 ++ 8.42685E-24 8.42685E-24 8.42685E-24 8.42686E-24 8.42686E-24 8.42686E-24 8.42686E-24 8.42687E-24 8.42687E-24 8.42687E-24 ++ 8.42687E-24 8.42687E-24 8.42687E-24 8.42687E-24 8.42687E-24 8.42687E-24 8.42687E-24 8.42687E-24 8.42687E-24 8.42687E-24 ++ 8.42687E-24 8.42687E-24 8.42687E-24 8.42686E-24 8.42686E-24 8.42686E-24 8.42686E-24 8.42685E-24 8.42685E-24 8.42685E-24 ++ 8.42685E-24 8.42684E-24 8.42684E-24 8.42684E-24 8.42683E-24 8.42683E-24 8.42683E-24 8.42683E-24 8.42682E-24 8.42682E-24 ++ 8.42682E-24 8.42682E-24 8.42681E-24 8.42681E-24 8.42681E-24 8.42681E-24 8.42680E-24 8.42680E-24 8.42680E-24 8.42680E-24 ++ 8.42680E-24 8.42680E-24 8.42680E-24 8.42680E-24 8.42680E-24 8.42678E-24 8.42676E-24 8.42675E-24 8.42673E-24 8.42672E-24 ++ 8.42670E-24 8.42668E-24 8.42667E-24 8.42665E-24 8.42664E-24 8.42662E-24 8.42661E-24 8.42659E-24 8.42658E-24 8.42656E-24 ++ 8.42655E-24 8.42653E-24 8.42652E-24 8.42650E-24 8.42649E-24 8.42647E-24 8.42646E-24 8.42645E-24 8.42643E-24 8.42642E-24 ++ 8.42641E-24 8.42639E-24 8.42638E-24 8.42636E-24 8.42635E-24 8.42634E-24 8.42633E-24 8.42631E-24 8.42630E-24 8.42629E-24 ++ 5.50023E-24 5.50024E-24 5.50025E-24 5.50025E-24 5.50026E-24 5.50027E-24 5.50028E-24 5.50029E-24 5.50030E-24 5.50031E-24 ++ 5.50032E-24 5.50033E-24 5.50033E-24 5.50034E-24 5.50035E-24 5.50036E-24 5.50037E-24 5.50038E-24 5.50039E-24 5.50040E-24 ++ 5.50041E-24 5.50042E-24 5.50043E-24 5.50044E-24 5.50045E-24 5.50046E-24 5.50047E-24 5.50048E-24 5.50049E-24 5.50050E-24 ++ 5.50051E-24 5.50052E-24 5.50053E-24 5.50055E-24 5.50056E-24 5.50057E-24 5.50057E-24 5.50057E-24 5.50057E-24 5.50057E-24 ++ 5.50057E-24 5.50057E-24 5.50057E-24 5.50057E-24 5.50057E-24 5.50057E-24 5.50058E-24 5.50058E-24 5.50058E-24 5.50058E-24 ++ 5.50058E-24 5.50058E-24 5.50059E-24 5.50059E-24 5.50059E-24 5.50059E-24 5.50059E-24 5.50060E-24 5.50060E-24 5.50060E-24 ++ 5.50060E-24 5.50060E-24 5.50061E-24 5.50061E-24 5.50061E-24 5.50061E-24 5.50061E-24 5.50061E-24 5.50061E-24 5.50062E-24 ++ 5.50062E-24 5.50062E-24 5.50062E-24 5.50062E-24 5.50062E-24 5.50062E-24 5.50062E-24 5.50062E-24 5.50062E-24 5.50062E-24 ++ 5.50062E-24 5.50061E-24 5.50061E-24 5.50061E-24 5.50061E-24 5.50061E-24 5.50061E-24 5.50061E-24 5.50060E-24 5.50060E-24 ++ 5.50060E-24 5.50060E-24 5.50060E-24 5.50059E-24 5.50059E-24 5.50059E-24 5.50059E-24 5.50059E-24 5.50058E-24 5.50058E-24 ++ 5.50058E-24 5.50058E-24 5.50058E-24 5.50058E-24 5.50057E-24 5.50057E-24 5.50057E-24 5.50057E-24 5.50057E-24 5.50057E-24 ++ 5.50057E-24 5.50057E-24 5.50057E-24 5.50057E-24 5.50057E-24 5.50056E-24 5.50055E-24 5.50053E-24 5.50052E-24 5.50051E-24 ++ 5.50050E-24 5.50049E-24 5.50048E-24 5.50047E-24 5.50046E-24 5.50045E-24 5.50044E-24 5.50043E-24 5.50042E-24 5.50041E-24 ++ 5.50040E-24 5.50039E-24 5.50038E-24 5.50037E-24 5.50036E-24 5.50035E-24 5.50034E-24 5.50033E-24 5.50033E-24 5.50032E-24 ++ 5.50031E-24 5.50030E-24 5.50029E-24 5.50028E-24 5.50027E-24 5.50026E-24 5.50025E-24 5.50025E-24 5.50024E-24 5.50023E-24 ++ 3.57748E-24 3.57749E-24 3.57749E-24 3.57750E-24 3.57751E-24 3.57751E-24 3.57752E-24 3.57752E-24 3.57753E-24 3.57753E-24 ++ 3.57754E-24 3.57755E-24 3.57755E-24 3.57756E-24 3.57756E-24 3.57757E-24 3.57758E-24 3.57758E-24 3.57759E-24 3.57760E-24 ++ 3.57760E-24 3.57761E-24 3.57762E-24 3.57762E-24 3.57763E-24 3.57764E-24 3.57764E-24 3.57765E-24 3.57766E-24 3.57766E-24 ++ 3.57767E-24 3.57768E-24 3.57768E-24 3.57769E-24 3.57770E-24 3.57771E-24 3.57771E-24 3.57771E-24 3.57771E-24 3.57771E-24 ++ 3.57771E-24 3.57771E-24 3.57771E-24 3.57771E-24 3.57771E-24 3.57771E-24 3.57771E-24 3.57771E-24 3.57771E-24 3.57772E-24 ++ 3.57772E-24 3.57772E-24 3.57772E-24 3.57772E-24 3.57772E-24 3.57772E-24 3.57772E-24 3.57773E-24 3.57773E-24 3.57773E-24 ++ 3.57773E-24 3.57773E-24 3.57773E-24 3.57773E-24 3.57773E-24 3.57773E-24 3.57774E-24 3.57774E-24 3.57774E-24 3.57774E-24 ++ 3.57774E-24 3.57774E-24 3.57774E-24 3.57774E-24 3.57774E-24 3.57774E-24 3.57774E-24 3.57774E-24 3.57774E-24 3.57774E-24 ++ 3.57774E-24 3.57774E-24 3.57774E-24 3.57774E-24 3.57773E-24 3.57773E-24 3.57773E-24 3.57773E-24 3.57773E-24 3.57773E-24 ++ 3.57773E-24 3.57773E-24 3.57773E-24 3.57772E-24 3.57772E-24 3.57772E-24 3.57772E-24 3.57772E-24 3.57772E-24 3.57772E-24 ++ 3.57772E-24 3.57771E-24 3.57771E-24 3.57771E-24 3.57771E-24 3.57771E-24 3.57771E-24 3.57771E-24 3.57771E-24 3.57771E-24 ++ 3.57771E-24 3.57771E-24 3.57771E-24 3.57771E-24 3.57771E-24 3.57770E-24 3.57769E-24 3.57768E-24 3.57768E-24 3.57767E-24 ++ 3.57766E-24 3.57766E-24 3.57765E-24 3.57764E-24 3.57764E-24 3.57763E-24 3.57762E-24 3.57762E-24 3.57761E-24 3.57760E-24 ++ 3.57760E-24 3.57759E-24 3.57758E-24 3.57758E-24 3.57757E-24 3.57756E-24 3.57756E-24 3.57755E-24 3.57755E-24 3.57754E-24 ++ 3.57753E-24 3.57753E-24 3.57752E-24 3.57752E-24 3.57751E-24 3.57751E-24 3.57750E-24 3.57749E-24 3.57749E-24 3.57748E-24 ++ 2.31861E-24 2.31861E-24 2.31861E-24 2.31862E-24 2.31862E-24 2.31862E-24 2.31863E-24 2.31863E-24 2.31864E-24 2.31864E-24 ++ 2.31864E-24 2.31865E-24 2.31865E-24 2.31866E-24 2.31866E-24 2.31866E-24 2.31867E-24 2.31867E-24 2.31868E-24 2.31868E-24 ++ 2.31869E-24 2.31869E-24 2.31869E-24 2.31870E-24 2.31870E-24 2.31871E-24 2.31871E-24 2.31872E-24 2.31872E-24 2.31873E-24 ++ 2.31873E-24 2.31873E-24 2.31874E-24 2.31874E-24 2.31875E-24 2.31875E-24 2.31875E-24 2.31875E-24 2.31875E-24 2.31875E-24 ++ 2.31875E-24 2.31875E-24 2.31876E-24 2.31876E-24 2.31876E-24 2.31876E-24 2.31876E-24 2.31876E-24 2.31876E-24 2.31876E-24 ++ 2.31876E-24 2.31876E-24 2.31876E-24 2.31876E-24 2.31876E-24 2.31876E-24 2.31877E-24 2.31877E-24 2.31877E-24 2.31877E-24 ++ 2.31877E-24 2.31877E-24 2.31877E-24 2.31877E-24 2.31877E-24 2.31877E-24 2.31877E-24 2.31877E-24 2.31877E-24 2.31877E-24 ++ 2.31877E-24 2.31877E-24 2.31878E-24 2.31878E-24 2.31878E-24 2.31878E-24 2.31878E-24 2.31878E-24 2.31877E-24 2.31877E-24 ++ 2.31877E-24 2.31877E-24 2.31877E-24 2.31877E-24 2.31877E-24 2.31877E-24 2.31877E-24 2.31877E-24 2.31877E-24 2.31877E-24 ++ 2.31877E-24 2.31877E-24 2.31877E-24 2.31877E-24 2.31876E-24 2.31876E-24 2.31876E-24 2.31876E-24 2.31876E-24 2.31876E-24 ++ 2.31876E-24 2.31876E-24 2.31876E-24 2.31876E-24 2.31876E-24 2.31876E-24 2.31876E-24 2.31876E-24 2.31875E-24 2.31875E-24 ++ 2.31875E-24 2.31875E-24 2.31875E-24 2.31875E-24 2.31875E-24 2.31875E-24 2.31874E-24 2.31874E-24 2.31873E-24 2.31873E-24 ++ 2.31873E-24 2.31872E-24 2.31872E-24 2.31871E-24 2.31871E-24 2.31870E-24 2.31870E-24 2.31869E-24 2.31869E-24 2.31869E-24 ++ 2.31868E-24 2.31868E-24 2.31867E-24 2.31867E-24 2.31866E-24 2.31866E-24 2.31866E-24 2.31865E-24 2.31865E-24 2.31864E-24 ++ 2.31864E-24 2.31864E-24 2.31863E-24 2.31863E-24 2.31862E-24 2.31862E-24 2.31862E-24 2.31861E-24 2.31861E-24 2.31861E-24 ++ 1.49737E-24 1.49737E-24 1.49738E-24 1.49738E-24 1.49738E-24 1.49738E-24 1.49739E-24 1.49739E-24 1.49739E-24 1.49739E-24 ++ 1.49740E-24 1.49740E-24 1.49740E-24 1.49740E-24 1.49741E-24 1.49741E-24 1.49741E-24 1.49741E-24 1.49742E-24 1.49742E-24 ++ 1.49742E-24 1.49743E-24 1.49743E-24 1.49743E-24 1.49743E-24 1.49744E-24 1.49744E-24 1.49744E-24 1.49745E-24 1.49745E-24 ++ 1.49745E-24 1.49746E-24 1.49746E-24 1.49746E-24 1.49746E-24 1.49747E-24 1.49747E-24 1.49747E-24 1.49747E-24 1.49747E-24 ++ 1.49747E-24 1.49747E-24 1.49747E-24 1.49747E-24 1.49747E-24 1.49747E-24 1.49747E-24 1.49747E-24 1.49747E-24 1.49747E-24 ++ 1.49747E-24 1.49747E-24 1.49747E-24 1.49747E-24 1.49747E-24 1.49747E-24 1.49748E-24 1.49748E-24 1.49748E-24 1.49748E-24 ++ 1.49748E-24 1.49748E-24 1.49748E-24 1.49748E-24 1.49748E-24 1.49748E-24 1.49748E-24 1.49748E-24 1.49748E-24 1.49748E-24 ++ 1.49748E-24 1.49748E-24 1.49748E-24 1.49748E-24 1.49748E-24 1.49748E-24 1.49748E-24 1.49748E-24 1.49748E-24 1.49748E-24 ++ 1.49748E-24 1.49748E-24 1.49748E-24 1.49748E-24 1.49748E-24 1.49748E-24 1.49748E-24 1.49748E-24 1.49748E-24 1.49748E-24 ++ 1.49748E-24 1.49748E-24 1.49748E-24 1.49748E-24 1.49747E-24 1.49747E-24 1.49747E-24 1.49747E-24 1.49747E-24 1.49747E-24 ++ 1.49747E-24 1.49747E-24 1.49747E-24 1.49747E-24 1.49747E-24 1.49747E-24 1.49747E-24 1.49747E-24 1.49747E-24 1.49747E-24 ++ 1.49747E-24 1.49747E-24 1.49747E-24 1.49747E-24 1.49747E-24 1.49746E-24 1.49746E-24 1.49746E-24 1.49746E-24 1.49745E-24 ++ 1.49745E-24 1.49745E-24 1.49744E-24 1.49744E-24 1.49744E-24 1.49743E-24 1.49743E-24 1.49743E-24 1.49743E-24 1.49742E-24 ++ 1.49742E-24 1.49742E-24 1.49741E-24 1.49741E-24 1.49741E-24 1.49741E-24 1.49740E-24 1.49740E-24 1.49740E-24 1.49740E-24 ++ 1.49739E-24 1.49739E-24 1.49739E-24 1.49739E-24 1.49738E-24 1.49738E-24 1.49738E-24 1.49738E-24 1.49737E-24 1.49737E-24 ++ 9.63575E-25 9.63576E-25 9.63578E-25 9.63579E-25 9.63581E-25 9.63583E-25 9.63584E-25 9.63586E-25 9.63588E-25 9.63589E-25 ++ 9.63591E-25 9.63593E-25 9.63594E-25 9.63596E-25 9.63598E-25 9.63599E-25 9.63601E-25 9.63603E-25 9.63605E-25 9.63607E-25 ++ 9.63608E-25 9.63610E-25 9.63612E-25 9.63614E-25 9.63616E-25 9.63618E-25 9.63620E-25 9.63622E-25 9.63624E-25 9.63626E-25 ++ 9.63628E-25 9.63630E-25 9.63632E-25 9.63634E-25 9.63636E-25 9.63638E-25 9.63638E-25 9.63638E-25 9.63638E-25 9.63638E-25 ++ 9.63638E-25 9.63638E-25 9.63638E-25 9.63639E-25 9.63639E-25 9.63639E-25 9.63639E-25 9.63640E-25 9.63640E-25 9.63640E-25 ++ 9.63641E-25 9.63641E-25 9.63641E-25 9.63642E-25 9.63642E-25 9.63642E-25 9.63643E-25 9.63643E-25 9.63644E-25 9.63644E-25 ++ 9.63644E-25 9.63645E-25 9.63645E-25 9.63645E-25 9.63646E-25 9.63646E-25 9.63646E-25 9.63646E-25 9.63647E-25 9.63647E-25 ++ 9.63647E-25 9.63647E-25 9.63647E-25 9.63647E-25 9.63647E-25 9.63647E-25 9.63647E-25 9.63647E-25 9.63647E-25 9.63647E-25 ++ 9.63647E-25 9.63647E-25 9.63646E-25 9.63646E-25 9.63646E-25 9.63646E-25 9.63645E-25 9.63645E-25 9.63645E-25 9.63644E-25 ++ 9.63644E-25 9.63644E-25 9.63643E-25 9.63643E-25 9.63642E-25 9.63642E-25 9.63642E-25 9.63641E-25 9.63641E-25 9.63641E-25 ++ 9.63640E-25 9.63640E-25 9.63640E-25 9.63639E-25 9.63639E-25 9.63639E-25 9.63639E-25 9.63638E-25 9.63638E-25 9.63638E-25 ++ 9.63638E-25 9.63638E-25 9.63638E-25 9.63638E-25 9.63638E-25 9.63636E-25 9.63634E-25 9.63632E-25 9.63630E-25 9.63628E-25 ++ 9.63626E-25 9.63624E-25 9.63622E-25 9.63620E-25 9.63618E-25 9.63616E-25 9.63614E-25 9.63612E-25 9.63610E-25 9.63608E-25 ++ 9.63607E-25 9.63605E-25 9.63603E-25 9.63601E-25 9.63599E-25 9.63598E-25 9.63596E-25 9.63594E-25 9.63593E-25 9.63591E-25 ++ 9.63589E-25 9.63588E-25 9.63586E-25 9.63584E-25 9.63583E-25 9.63581E-25 9.63579E-25 9.63578E-25 9.63576E-25 9.63575E-25 ++ 6.17867E-25 6.17868E-25 6.17869E-25 6.17870E-25 6.17871E-25 6.17872E-25 6.17873E-25 6.17875E-25 6.17876E-25 6.17877E-25 ++ 6.17878E-25 6.17879E-25 6.17880E-25 6.17881E-25 6.17882E-25 6.17883E-25 6.17884E-25 6.17886E-25 6.17887E-25 6.17888E-25 ++ 6.17889E-25 6.17890E-25 6.17892E-25 6.17893E-25 6.17894E-25 6.17895E-25 6.17896E-25 6.17898E-25 6.17899E-25 6.17900E-25 ++ 6.17902E-25 6.17903E-25 6.17904E-25 6.17906E-25 6.17907E-25 6.17908E-25 6.17908E-25 6.17908E-25 6.17908E-25 6.17908E-25 ++ 6.17908E-25 6.17909E-25 6.17909E-25 6.17909E-25 6.17909E-25 6.17909E-25 6.17909E-25 6.17910E-25 6.17910E-25 6.17910E-25 ++ 6.17910E-25 6.17910E-25 6.17911E-25 6.17911E-25 6.17911E-25 6.17911E-25 6.17912E-25 6.17912E-25 6.17912E-25 6.17912E-25 ++ 6.17913E-25 6.17913E-25 6.17913E-25 6.17913E-25 6.17913E-25 6.17914E-25 6.17914E-25 6.17914E-25 6.17914E-25 6.17914E-25 ++ 6.17914E-25 6.17914E-25 6.17914E-25 6.17914E-25 6.17914E-25 6.17914E-25 6.17914E-25 6.17914E-25 6.17914E-25 6.17914E-25 ++ 6.17914E-25 6.17914E-25 6.17914E-25 6.17914E-25 6.17914E-25 6.17913E-25 6.17913E-25 6.17913E-25 6.17913E-25 6.17913E-25 ++ 6.17912E-25 6.17912E-25 6.17912E-25 6.17912E-25 6.17911E-25 6.17911E-25 6.17911E-25 6.17911E-25 6.17910E-25 6.17910E-25 ++ 6.17910E-25 6.17910E-25 6.17910E-25 6.17909E-25 6.17909E-25 6.17909E-25 6.17909E-25 6.17909E-25 6.17909E-25 6.17908E-25 ++ 6.17908E-25 6.17908E-25 6.17908E-25 6.17908E-25 6.17908E-25 6.17907E-25 6.17906E-25 6.17904E-25 6.17903E-25 6.17902E-25 ++ 6.17900E-25 6.17899E-25 6.17898E-25 6.17896E-25 6.17895E-25 6.17894E-25 6.17893E-25 6.17892E-25 6.17890E-25 6.17889E-25 ++ 6.17888E-25 6.17887E-25 6.17886E-25 6.17884E-25 6.17883E-25 6.17882E-25 6.17881E-25 6.17880E-25 6.17879E-25 6.17878E-25 ++ 6.17877E-25 6.17876E-25 6.17875E-25 6.17873E-25 6.17872E-25 6.17871E-25 6.17870E-25 6.17869E-25 6.17868E-25 6.17867E-25 ++ 3.94784E-25 3.94784E-25 3.94785E-25 3.94786E-25 3.94786E-25 3.94787E-25 3.94788E-25 3.94788E-25 3.94789E-25 3.94790E-25 ++ 3.94790E-25 3.94791E-25 3.94792E-25 3.94793E-25 3.94793E-25 3.94794E-25 3.94795E-25 3.94796E-25 3.94796E-25 3.94797E-25 ++ 3.94798E-25 3.94799E-25 3.94799E-25 3.94800E-25 3.94801E-25 3.94802E-25 3.94803E-25 3.94803E-25 3.94804E-25 3.94805E-25 ++ 3.94806E-25 3.94807E-25 3.94808E-25 3.94808E-25 3.94809E-25 3.94810E-25 3.94810E-25 3.94810E-25 3.94810E-25 3.94810E-25 ++ 3.94810E-25 3.94810E-25 3.94811E-25 3.94811E-25 3.94811E-25 3.94811E-25 3.94811E-25 3.94811E-25 3.94811E-25 3.94811E-25 ++ 3.94811E-25 3.94812E-25 3.94812E-25 3.94812E-25 3.94812E-25 3.94812E-25 3.94812E-25 3.94813E-25 3.94813E-25 3.94813E-25 ++ 3.94813E-25 3.94813E-25 3.94813E-25 3.94813E-25 3.94814E-25 3.94814E-25 3.94814E-25 3.94814E-25 3.94814E-25 3.94814E-25 ++ 3.94814E-25 3.94814E-25 3.94814E-25 3.94814E-25 3.94814E-25 3.94814E-25 3.94814E-25 3.94814E-25 3.94814E-25 3.94814E-25 ++ 3.94814E-25 3.94814E-25 3.94814E-25 3.94814E-25 3.94814E-25 3.94814E-25 3.94813E-25 3.94813E-25 3.94813E-25 3.94813E-25 ++ 3.94813E-25 3.94813E-25 3.94813E-25 3.94812E-25 3.94812E-25 3.94812E-25 3.94812E-25 3.94812E-25 3.94812E-25 3.94811E-25 ++ 3.94811E-25 3.94811E-25 3.94811E-25 3.94811E-25 3.94811E-25 3.94811E-25 3.94811E-25 3.94811E-25 3.94810E-25 3.94810E-25 ++ 3.94810E-25 3.94810E-25 3.94810E-25 3.94810E-25 3.94810E-25 3.94809E-25 3.94808E-25 3.94808E-25 3.94807E-25 3.94806E-25 ++ 3.94805E-25 3.94804E-25 3.94803E-25 3.94803E-25 3.94802E-25 3.94801E-25 3.94800E-25 3.94799E-25 3.94799E-25 3.94798E-25 ++ 3.94797E-25 3.94796E-25 3.94796E-25 3.94795E-25 3.94794E-25 3.94793E-25 3.94793E-25 3.94792E-25 3.94791E-25 3.94790E-25 ++ 3.94790E-25 3.94789E-25 3.94788E-25 3.94788E-25 3.94787E-25 3.94786E-25 3.94786E-25 3.94785E-25 3.94784E-25 3.94784E-25 ++ 2.51349E-25 2.51350E-25 2.51350E-25 2.51351E-25 2.51351E-25 2.51352E-25 2.51352E-25 2.51352E-25 2.51353E-25 2.51353E-25 ++ 2.51354E-25 2.51354E-25 2.51355E-25 2.51355E-25 2.51356E-25 2.51356E-25 2.51357E-25 2.51357E-25 2.51358E-25 2.51358E-25 ++ 2.51359E-25 2.51359E-25 2.51360E-25 2.51360E-25 2.51361E-25 2.51361E-25 2.51362E-25 2.51362E-25 2.51363E-25 2.51363E-25 ++ 2.51364E-25 2.51364E-25 2.51365E-25 2.51365E-25 2.51366E-25 2.51367E-25 2.51367E-25 2.51367E-25 2.51367E-25 2.51367E-25 ++ 2.51367E-25 2.51367E-25 2.51367E-25 2.51367E-25 2.51367E-25 2.51367E-25 2.51367E-25 2.51367E-25 2.51367E-25 2.51367E-25 ++ 2.51367E-25 2.51367E-25 2.51368E-25 2.51368E-25 2.51368E-25 2.51368E-25 2.51368E-25 2.51368E-25 2.51368E-25 2.51368E-25 ++ 2.51368E-25 2.51368E-25 2.51369E-25 2.51369E-25 2.51369E-25 2.51369E-25 2.51369E-25 2.51369E-25 2.51369E-25 2.51369E-25 ++ 2.51369E-25 2.51369E-25 2.51369E-25 2.51369E-25 2.51369E-25 2.51369E-25 2.51369E-25 2.51369E-25 2.51369E-25 2.51369E-25 ++ 2.51369E-25 2.51369E-25 2.51369E-25 2.51369E-25 2.51369E-25 2.51369E-25 2.51369E-25 2.51369E-25 2.51368E-25 2.51368E-25 ++ 2.51368E-25 2.51368E-25 2.51368E-25 2.51368E-25 2.51368E-25 2.51368E-25 2.51368E-25 2.51368E-25 2.51367E-25 2.51367E-25 ++ 2.51367E-25 2.51367E-25 2.51367E-25 2.51367E-25 2.51367E-25 2.51367E-25 2.51367E-25 2.51367E-25 2.51367E-25 2.51367E-25 ++ 2.51367E-25 2.51367E-25 2.51367E-25 2.51367E-25 2.51367E-25 2.51366E-25 2.51365E-25 2.51365E-25 2.51364E-25 2.51364E-25 ++ 2.51363E-25 2.51363E-25 2.51362E-25 2.51362E-25 2.51361E-25 2.51361E-25 2.51360E-25 2.51360E-25 2.51359E-25 2.51359E-25 ++ 2.51358E-25 2.51358E-25 2.51357E-25 2.51357E-25 2.51356E-25 2.51356E-25 2.51355E-25 2.51355E-25 2.51354E-25 2.51354E-25 ++ 2.51353E-25 2.51353E-25 2.51352E-25 2.51352E-25 2.51352E-25 2.51351E-25 2.51351E-25 2.51350E-25 2.51350E-25 2.51349E-25 ++ 1.59460E-25 1.59460E-25 1.59460E-25 1.59461E-25 1.59461E-25 1.59461E-25 1.59462E-25 1.59462E-25 1.59462E-25 1.59462E-25 ++ 1.59463E-25 1.59463E-25 1.59463E-25 1.59464E-25 1.59464E-25 1.59464E-25 1.59465E-25 1.59465E-25 1.59465E-25 1.59465E-25 ++ 1.59466E-25 1.59466E-25 1.59466E-25 1.59467E-25 1.59467E-25 1.59467E-25 1.59468E-25 1.59468E-25 1.59468E-25 1.59469E-25 ++ 1.59469E-25 1.59469E-25 1.59470E-25 1.59470E-25 1.59471E-25 1.59471E-25 1.59471E-25 1.59471E-25 1.59471E-25 1.59471E-25 ++ 1.59471E-25 1.59471E-25 1.59471E-25 1.59471E-25 1.59471E-25 1.59471E-25 1.59471E-25 1.59471E-25 1.59471E-25 1.59471E-25 ++ 1.59471E-25 1.59472E-25 1.59472E-25 1.59472E-25 1.59472E-25 1.59472E-25 1.59472E-25 1.59472E-25 1.59472E-25 1.59472E-25 ++ 1.59472E-25 1.59472E-25 1.59472E-25 1.59472E-25 1.59472E-25 1.59472E-25 1.59472E-25 1.59472E-25 1.59473E-25 1.59473E-25 ++ 1.59473E-25 1.59473E-25 1.59473E-25 1.59473E-25 1.59473E-25 1.59473E-25 1.59473E-25 1.59473E-25 1.59473E-25 1.59473E-25 ++ 1.59473E-25 1.59473E-25 1.59472E-25 1.59472E-25 1.59472E-25 1.59472E-25 1.59472E-25 1.59472E-25 1.59472E-25 1.59472E-25 ++ 1.59472E-25 1.59472E-25 1.59472E-25 1.59472E-25 1.59472E-25 1.59472E-25 1.59472E-25 1.59472E-25 1.59472E-25 1.59471E-25 ++ 1.59471E-25 1.59471E-25 1.59471E-25 1.59471E-25 1.59471E-25 1.59471E-25 1.59471E-25 1.59471E-25 1.59471E-25 1.59471E-25 ++ 1.59471E-25 1.59471E-25 1.59471E-25 1.59471E-25 1.59471E-25 1.59471E-25 1.59470E-25 1.59470E-25 1.59469E-25 1.59469E-25 ++ 1.59469E-25 1.59468E-25 1.59468E-25 1.59468E-25 1.59467E-25 1.59467E-25 1.59467E-25 1.59466E-25 1.59466E-25 1.59466E-25 ++ 1.59465E-25 1.59465E-25 1.59465E-25 1.59465E-25 1.59464E-25 1.59464E-25 1.59464E-25 1.59463E-25 1.59463E-25 1.59463E-25 ++ 1.59462E-25 1.59462E-25 1.59462E-25 1.59462E-25 1.59461E-25 1.59461E-25 1.59461E-25 1.59460E-25 1.59460E-25 1.59460E-25 ++ 1.00805E-25 1.00805E-25 1.00805E-25 1.00805E-25 1.00805E-25 1.00806E-25 1.00806E-25 1.00806E-25 1.00806E-25 1.00806E-25 ++ 1.00806E-25 1.00807E-25 1.00807E-25 1.00807E-25 1.00807E-25 1.00807E-25 1.00808E-25 1.00808E-25 1.00808E-25 1.00808E-25 ++ 1.00808E-25 1.00809E-25 1.00809E-25 1.00809E-25 1.00809E-25 1.00809E-25 1.00810E-25 1.00810E-25 1.00810E-25 1.00810E-25 ++ 1.00811E-25 1.00811E-25 1.00811E-25 1.00811E-25 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 ++ 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 ++ 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 ++ 1.00812E-25 1.00813E-25 1.00813E-25 1.00813E-25 1.00813E-25 1.00813E-25 1.00813E-25 1.00813E-25 1.00813E-25 1.00813E-25 ++ 1.00813E-25 1.00813E-25 1.00813E-25 1.00813E-25 1.00813E-25 1.00813E-25 1.00813E-25 1.00813E-25 1.00813E-25 1.00813E-25 ++ 1.00813E-25 1.00813E-25 1.00813E-25 1.00813E-25 1.00813E-25 1.00813E-25 1.00813E-25 1.00813E-25 1.00813E-25 1.00812E-25 ++ 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 ++ 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 ++ 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 1.00812E-25 1.00811E-25 1.00811E-25 1.00811E-25 1.00811E-25 ++ 1.00810E-25 1.00810E-25 1.00810E-25 1.00810E-25 1.00809E-25 1.00809E-25 1.00809E-25 1.00809E-25 1.00809E-25 1.00808E-25 ++ 1.00808E-25 1.00808E-25 1.00808E-25 1.00808E-25 1.00807E-25 1.00807E-25 1.00807E-25 1.00807E-25 1.00807E-25 1.00806E-25 ++ 1.00806E-25 1.00806E-25 1.00806E-25 1.00806E-25 1.00806E-25 1.00805E-25 1.00805E-25 1.00805E-25 1.00805E-25 1.00805E-25 ++ 6.34988E-26 6.34989E-26 6.34990E-26 6.34992E-26 6.34993E-26 6.34994E-26 6.34995E-26 6.34996E-26 6.34997E-26 6.34998E-26 ++ 6.35000E-26 6.35001E-26 6.35002E-26 6.35003E-26 6.35004E-26 6.35006E-26 6.35007E-26 6.35008E-26 6.35010E-26 6.35011E-26 ++ 6.35012E-26 6.35013E-26 6.35015E-26 6.35016E-26 6.35017E-26 6.35019E-26 6.35020E-26 6.35022E-26 6.35023E-26 6.35025E-26 ++ 6.35026E-26 6.35027E-26 6.35029E-26 6.35030E-26 6.35032E-26 6.35033E-26 6.35033E-26 6.35033E-26 6.35034E-26 6.35034E-26 ++ 6.35034E-26 6.35034E-26 6.35034E-26 6.35034E-26 6.35034E-26 6.35034E-26 6.35035E-26 6.35035E-26 6.35035E-26 6.35035E-26 ++ 6.35036E-26 6.35036E-26 6.35036E-26 6.35036E-26 6.35037E-26 6.35037E-26 6.35037E-26 6.35037E-26 6.35038E-26 6.35038E-26 ++ 6.35038E-26 6.35038E-26 6.35039E-26 6.35039E-26 6.35039E-26 6.35039E-26 6.35039E-26 6.35040E-26 6.35040E-26 6.35040E-26 ++ 6.35040E-26 6.35040E-26 6.35040E-26 6.35040E-26 6.35040E-26 6.35040E-26 6.35040E-26 6.35040E-26 6.35040E-26 6.35040E-26 ++ 6.35040E-26 6.35040E-26 6.35040E-26 6.35039E-26 6.35039E-26 6.35039E-26 6.35039E-26 6.35039E-26 6.35038E-26 6.35038E-26 ++ 6.35038E-26 6.35038E-26 6.35037E-26 6.35037E-26 6.35037E-26 6.35037E-26 6.35036E-26 6.35036E-26 6.35036E-26 6.35036E-26 ++ 6.35035E-26 6.35035E-26 6.35035E-26 6.35035E-26 6.35034E-26 6.35034E-26 6.35034E-26 6.35034E-26 6.35034E-26 6.35034E-26 ++ 6.35034E-26 6.35034E-26 6.35033E-26 6.35033E-26 6.35033E-26 6.35032E-26 6.35030E-26 6.35029E-26 6.35027E-26 6.35026E-26 ++ 6.35025E-26 6.35023E-26 6.35022E-26 6.35020E-26 6.35019E-26 6.35017E-26 6.35016E-26 6.35015E-26 6.35013E-26 6.35012E-26 ++ 6.35011E-26 6.35010E-26 6.35008E-26 6.35007E-26 6.35006E-26 6.35004E-26 6.35003E-26 6.35002E-26 6.35001E-26 6.35000E-26 ++ 6.34998E-26 6.34997E-26 6.34996E-26 6.34995E-26 6.34994E-26 6.34993E-26 6.34992E-26 6.34990E-26 6.34989E-26 6.34988E-26 ++ 3.98572E-26 3.98573E-26 3.98574E-26 3.98574E-26 3.98575E-26 3.98576E-26 3.98576E-26 3.98577E-26 3.98578E-26 3.98579E-26 ++ 3.98579E-26 3.98580E-26 3.98581E-26 3.98582E-26 3.98582E-26 3.98583E-26 3.98584E-26 3.98585E-26 3.98586E-26 3.98587E-26 ++ 3.98587E-26 3.98588E-26 3.98589E-26 3.98590E-26 3.98591E-26 3.98592E-26 3.98593E-26 3.98593E-26 3.98594E-26 3.98595E-26 ++ 3.98596E-26 3.98597E-26 3.98598E-26 3.98599E-26 3.98600E-26 3.98601E-26 3.98601E-26 3.98601E-26 3.98601E-26 3.98601E-26 ++ 3.98601E-26 3.98601E-26 3.98601E-26 3.98601E-26 3.98601E-26 3.98602E-26 3.98602E-26 3.98602E-26 3.98602E-26 3.98602E-26 ++ 3.98602E-26 3.98602E-26 3.98603E-26 3.98603E-26 3.98603E-26 3.98603E-26 3.98603E-26 3.98603E-26 3.98604E-26 3.98604E-26 ++ 3.98604E-26 3.98604E-26 3.98604E-26 3.98604E-26 3.98605E-26 3.98605E-26 3.98605E-26 3.98605E-26 3.98605E-26 3.98605E-26 ++ 3.98605E-26 3.98605E-26 3.98605E-26 3.98605E-26 3.98605E-26 3.98605E-26 3.98605E-26 3.98605E-26 3.98605E-26 3.98605E-26 ++ 3.98605E-26 3.98605E-26 3.98605E-26 3.98605E-26 3.98605E-26 3.98605E-26 3.98604E-26 3.98604E-26 3.98604E-26 3.98604E-26 ++ 3.98604E-26 3.98604E-26 3.98603E-26 3.98603E-26 3.98603E-26 3.98603E-26 3.98603E-26 3.98603E-26 3.98602E-26 3.98602E-26 ++ 3.98602E-26 3.98602E-26 3.98602E-26 3.98602E-26 3.98602E-26 3.98601E-26 3.98601E-26 3.98601E-26 3.98601E-26 3.98601E-26 ++ 3.98601E-26 3.98601E-26 3.98601E-26 3.98601E-26 3.98601E-26 3.98600E-26 3.98599E-26 3.98598E-26 3.98597E-26 3.98596E-26 ++ 3.98595E-26 3.98594E-26 3.98593E-26 3.98593E-26 3.98592E-26 3.98591E-26 3.98590E-26 3.98589E-26 3.98588E-26 3.98587E-26 ++ 3.98587E-26 3.98586E-26 3.98585E-26 3.98584E-26 3.98583E-26 3.98582E-26 3.98582E-26 3.98581E-26 3.98580E-26 3.98579E-26 ++ 3.98579E-26 3.98578E-26 3.98577E-26 3.98576E-26 3.98576E-26 3.98575E-26 3.98574E-26 3.98574E-26 3.98573E-26 3.98572E-26 ++ 2.49290E-26 2.49290E-26 2.49291E-26 2.49291E-26 2.49292E-26 2.49292E-26 2.49293E-26 2.49293E-26 2.49294E-26 2.49294E-26 ++ 2.49295E-26 2.49295E-26 2.49296E-26 2.49296E-26 2.49297E-26 2.49297E-26 2.49298E-26 2.49298E-26 2.49299E-26 2.49299E-26 ++ 2.49300E-26 2.49300E-26 2.49301E-26 2.49301E-26 2.49302E-26 2.49302E-26 2.49303E-26 2.49304E-26 2.49304E-26 2.49305E-26 ++ 2.49305E-26 2.49306E-26 2.49306E-26 2.49307E-26 2.49308E-26 2.49308E-26 2.49308E-26 2.49308E-26 2.49308E-26 2.49308E-26 ++ 2.49308E-26 2.49308E-26 2.49308E-26 2.49309E-26 2.49309E-26 2.49309E-26 2.49309E-26 2.49309E-26 2.49309E-26 2.49309E-26 ++ 2.49309E-26 2.49309E-26 2.49309E-26 2.49309E-26 2.49310E-26 2.49310E-26 2.49310E-26 2.49310E-26 2.49310E-26 2.49310E-26 ++ 2.49310E-26 2.49310E-26 2.49310E-26 2.49311E-26 2.49311E-26 2.49311E-26 2.49311E-26 2.49311E-26 2.49311E-26 2.49311E-26 ++ 2.49311E-26 2.49311E-26 2.49311E-26 2.49311E-26 2.49311E-26 2.49311E-26 2.49311E-26 2.49311E-26 2.49311E-26 2.49311E-26 ++ 2.49311E-26 2.49311E-26 2.49311E-26 2.49311E-26 2.49311E-26 2.49311E-26 2.49311E-26 2.49310E-26 2.49310E-26 2.49310E-26 ++ 2.49310E-26 2.49310E-26 2.49310E-26 2.49310E-26 2.49310E-26 2.49310E-26 2.49309E-26 2.49309E-26 2.49309E-26 2.49309E-26 ++ 2.49309E-26 2.49309E-26 2.49309E-26 2.49309E-26 2.49309E-26 2.49309E-26 2.49309E-26 2.49308E-26 2.49308E-26 2.49308E-26 ++ 2.49308E-26 2.49308E-26 2.49308E-26 2.49308E-26 2.49308E-26 2.49308E-26 2.49307E-26 2.49306E-26 2.49306E-26 2.49305E-26 ++ 2.49305E-26 2.49304E-26 2.49304E-26 2.49303E-26 2.49302E-26 2.49302E-26 2.49301E-26 2.49301E-26 2.49300E-26 2.49300E-26 ++ 2.49299E-26 2.49299E-26 2.49298E-26 2.49298E-26 2.49297E-26 2.49297E-26 2.49296E-26 2.49296E-26 2.49295E-26 2.49295E-26 ++ 2.49294E-26 2.49294E-26 2.49293E-26 2.49293E-26 2.49292E-26 2.49292E-26 2.49291E-26 2.49291E-26 2.49290E-26 2.49290E-26 ++ 1.55367E-26 1.55368E-26 1.55368E-26 1.55368E-26 1.55369E-26 1.55369E-26 1.55369E-26 1.55369E-26 1.55370E-26 1.55370E-26 ++ 1.55370E-26 1.55371E-26 1.55371E-26 1.55371E-26 1.55372E-26 1.55372E-26 1.55372E-26 1.55373E-26 1.55373E-26 1.55373E-26 ++ 1.55374E-26 1.55374E-26 1.55374E-26 1.55375E-26 1.55375E-26 1.55375E-26 1.55376E-26 1.55376E-26 1.55376E-26 1.55377E-26 ++ 1.55377E-26 1.55377E-26 1.55378E-26 1.55378E-26 1.55379E-26 1.55379E-26 1.55379E-26 1.55379E-26 1.55379E-26 1.55379E-26 ++ 1.55379E-26 1.55379E-26 1.55379E-26 1.55379E-26 1.55379E-26 1.55379E-26 1.55379E-26 1.55379E-26 1.55379E-26 1.55379E-26 ++ 1.55380E-26 1.55380E-26 1.55380E-26 1.55380E-26 1.55380E-26 1.55380E-26 1.55380E-26 1.55380E-26 1.55380E-26 1.55380E-26 ++ 1.55380E-26 1.55380E-26 1.55380E-26 1.55380E-26 1.55380E-26 1.55381E-26 1.55381E-26 1.55381E-26 1.55381E-26 1.55381E-26 ++ 1.55381E-26 1.55381E-26 1.55381E-26 1.55381E-26 1.55381E-26 1.55381E-26 1.55381E-26 1.55381E-26 1.55381E-26 1.55381E-26 ++ 1.55381E-26 1.55381E-26 1.55381E-26 1.55381E-26 1.55381E-26 1.55380E-26 1.55380E-26 1.55380E-26 1.55380E-26 1.55380E-26 ++ 1.55380E-26 1.55380E-26 1.55380E-26 1.55380E-26 1.55380E-26 1.55380E-26 1.55380E-26 1.55380E-26 1.55380E-26 1.55380E-26 ++ 1.55379E-26 1.55379E-26 1.55379E-26 1.55379E-26 1.55379E-26 1.55379E-26 1.55379E-26 1.55379E-26 1.55379E-26 1.55379E-26 ++ 1.55379E-26 1.55379E-26 1.55379E-26 1.55379E-26 1.55379E-26 1.55379E-26 1.55378E-26 1.55378E-26 1.55377E-26 1.55377E-26 ++ 1.55377E-26 1.55376E-26 1.55376E-26 1.55376E-26 1.55375E-26 1.55375E-26 1.55375E-26 1.55374E-26 1.55374E-26 1.55374E-26 ++ 1.55373E-26 1.55373E-26 1.55373E-26 1.55372E-26 1.55372E-26 1.55372E-26 1.55371E-26 1.55371E-26 1.55371E-26 1.55370E-26 ++ 1.55370E-26 1.55370E-26 1.55369E-26 1.55369E-26 1.55369E-26 1.55369E-26 1.55368E-26 1.55368E-26 1.55368E-26 1.55367E-26 ++ 9.64879E-27 9.64881E-27 9.64882E-27 9.64884E-27 9.64886E-27 9.64888E-27 9.64890E-27 9.64891E-27 9.64893E-27 9.64895E-27 ++ 9.64897E-27 9.64899E-27 9.64901E-27 9.64903E-27 9.64905E-27 9.64907E-27 9.64909E-27 9.64911E-27 9.64913E-27 9.64915E-27 ++ 9.64917E-27 9.64919E-27 9.64921E-27 9.64923E-27 9.64926E-27 9.64928E-27 9.64930E-27 9.64932E-27 9.64935E-27 9.64937E-27 ++ 9.64939E-27 9.64942E-27 9.64944E-27 9.64946E-27 9.64949E-27 9.64951E-27 9.64951E-27 9.64951E-27 9.64951E-27 9.64952E-27 ++ 9.64952E-27 9.64952E-27 9.64952E-27 9.64952E-27 9.64953E-27 9.64953E-27 9.64953E-27 9.64954E-27 9.64954E-27 9.64954E-27 ++ 9.64955E-27 9.64955E-27 9.64956E-27 9.64956E-27 9.64956E-27 9.64957E-27 9.64957E-27 9.64958E-27 9.64958E-27 9.64959E-27 ++ 9.64959E-27 9.64959E-27 9.64960E-27 9.64960E-27 9.64961E-27 9.64961E-27 9.64961E-27 9.64961E-27 9.64962E-27 9.64962E-27 ++ 9.64962E-27 9.64962E-27 9.64962E-27 9.64962E-27 9.64963E-27 9.64963E-27 9.64962E-27 9.64962E-27 9.64962E-27 9.64962E-27 ++ 9.64962E-27 9.64962E-27 9.64961E-27 9.64961E-27 9.64961E-27 9.64961E-27 9.64960E-27 9.64960E-27 9.64959E-27 9.64959E-27 ++ 9.64959E-27 9.64958E-27 9.64958E-27 9.64957E-27 9.64957E-27 9.64956E-27 9.64956E-27 9.64956E-27 9.64955E-27 9.64955E-27 ++ 9.64954E-27 9.64954E-27 9.64954E-27 9.64953E-27 9.64953E-27 9.64953E-27 9.64952E-27 9.64952E-27 9.64952E-27 9.64952E-27 ++ 9.64952E-27 9.64951E-27 9.64951E-27 9.64951E-27 9.64951E-27 9.64949E-27 9.64946E-27 9.64944E-27 9.64942E-27 9.64939E-27 ++ 9.64937E-27 9.64935E-27 9.64932E-27 9.64930E-27 9.64928E-27 9.64926E-27 9.64923E-27 9.64921E-27 9.64919E-27 9.64917E-27 ++ 9.64915E-27 9.64913E-27 9.64911E-27 9.64909E-27 9.64907E-27 9.64905E-27 9.64903E-27 9.64901E-27 9.64899E-27 9.64897E-27 ++ 9.64895E-27 9.64893E-27 9.64891E-27 9.64890E-27 9.64888E-27 9.64886E-27 9.64884E-27 9.64882E-27 9.64881E-27 9.64879E-27 ++ 5.97095E-27 5.97096E-27 5.97097E-27 5.97098E-27 5.97100E-27 5.97101E-27 5.97102E-27 5.97103E-27 5.97104E-27 5.97105E-27 ++ 5.97106E-27 5.97108E-27 5.97109E-27 5.97110E-27 5.97111E-27 5.97112E-27 5.97114E-27 5.97115E-27 5.97116E-27 5.97118E-27 ++ 5.97119E-27 5.97120E-27 5.97122E-27 5.97123E-27 5.97124E-27 5.97126E-27 5.97127E-27 5.97129E-27 5.97130E-27 5.97131E-27 ++ 5.97133E-27 5.97134E-27 5.97136E-27 5.97137E-27 5.97139E-27 5.97140E-27 5.97140E-27 5.97140E-27 5.97141E-27 5.97141E-27 ++ 5.97141E-27 5.97141E-27 5.97141E-27 5.97141E-27 5.97141E-27 5.97141E-27 5.97142E-27 5.97142E-27 5.97142E-27 5.97142E-27 ++ 5.97143E-27 5.97143E-27 5.97143E-27 5.97143E-27 5.97144E-27 5.97144E-27 5.97144E-27 5.97144E-27 5.97145E-27 5.97145E-27 ++ 5.97145E-27 5.97146E-27 5.97146E-27 5.97146E-27 5.97146E-27 5.97146E-27 5.97147E-27 5.97147E-27 5.97147E-27 5.97147E-27 ++ 5.97147E-27 5.97147E-27 5.97147E-27 5.97147E-27 5.97147E-27 5.97147E-27 5.97147E-27 5.97147E-27 5.97147E-27 5.97147E-27 ++ 5.97147E-27 5.97147E-27 5.97147E-27 5.97147E-27 5.97146E-27 5.97146E-27 5.97146E-27 5.97146E-27 5.97146E-27 5.97145E-27 ++ 5.97145E-27 5.97145E-27 5.97144E-27 5.97144E-27 5.97144E-27 5.97144E-27 5.97143E-27 5.97143E-27 5.97143E-27 5.97143E-27 ++ 5.97142E-27 5.97142E-27 5.97142E-27 5.97142E-27 5.97141E-27 5.97141E-27 5.97141E-27 5.97141E-27 5.97141E-27 5.97141E-27 ++ 5.97141E-27 5.97141E-27 5.97140E-27 5.97140E-27 5.97140E-27 5.97139E-27 5.97137E-27 5.97136E-27 5.97134E-27 5.97133E-27 ++ 5.97131E-27 5.97130E-27 5.97129E-27 5.97127E-27 5.97126E-27 5.97124E-27 5.97123E-27 5.97122E-27 5.97120E-27 5.97119E-27 ++ 5.97118E-27 5.97116E-27 5.97115E-27 5.97114E-27 5.97112E-27 5.97111E-27 5.97110E-27 5.97109E-27 5.97108E-27 5.97106E-27 ++ 5.97105E-27 5.97104E-27 5.97103E-27 5.97102E-27 5.97101E-27 5.97100E-27 5.97098E-27 5.97097E-27 5.97096E-27 5.97095E-27 ++ 3.68191E-27 3.68191E-27 3.68192E-27 3.68193E-27 3.68193E-27 3.68194E-27 3.68195E-27 3.68195E-27 3.68196E-27 3.68197E-27 ++ 3.68198E-27 3.68198E-27 3.68199E-27 3.68200E-27 3.68201E-27 3.68201E-27 3.68202E-27 3.68203E-27 3.68204E-27 3.68205E-27 ++ 3.68205E-27 3.68206E-27 3.68207E-27 3.68208E-27 3.68209E-27 3.68210E-27 3.68210E-27 3.68211E-27 3.68212E-27 3.68213E-27 ++ 3.68214E-27 3.68215E-27 3.68216E-27 3.68217E-27 3.68218E-27 3.68219E-27 3.68219E-27 3.68219E-27 3.68219E-27 3.68219E-27 ++ 3.68219E-27 3.68219E-27 3.68219E-27 3.68219E-27 3.68219E-27 3.68219E-27 3.68220E-27 3.68220E-27 3.68220E-27 3.68220E-27 ++ 3.68220E-27 3.68220E-27 3.68221E-27 3.68221E-27 3.68221E-27 3.68221E-27 3.68221E-27 3.68221E-27 3.68222E-27 3.68222E-27 ++ 3.68222E-27 3.68222E-27 3.68222E-27 3.68222E-27 3.68222E-27 3.68223E-27 3.68223E-27 3.68223E-27 3.68223E-27 3.68223E-27 ++ 3.68223E-27 3.68223E-27 3.68223E-27 3.68223E-27 3.68223E-27 3.68223E-27 3.68223E-27 3.68223E-27 3.68223E-27 3.68223E-27 ++ 3.68223E-27 3.68223E-27 3.68223E-27 3.68223E-27 3.68223E-27 3.68222E-27 3.68222E-27 3.68222E-27 3.68222E-27 3.68222E-27 ++ 3.68222E-27 3.68222E-27 3.68221E-27 3.68221E-27 3.68221E-27 3.68221E-27 3.68221E-27 3.68221E-27 3.68220E-27 3.68220E-27 ++ 3.68220E-27 3.68220E-27 3.68220E-27 3.68220E-27 3.68219E-27 3.68219E-27 3.68219E-27 3.68219E-27 3.68219E-27 3.68219E-27 ++ 3.68219E-27 3.68219E-27 3.68219E-27 3.68219E-27 3.68219E-27 3.68218E-27 3.68217E-27 3.68216E-27 3.68215E-27 3.68214E-27 ++ 3.68213E-27 3.68212E-27 3.68211E-27 3.68210E-27 3.68210E-27 3.68209E-27 3.68208E-27 3.68207E-27 3.68206E-27 3.68205E-27 ++ 3.68205E-27 3.68204E-27 3.68203E-27 3.68202E-27 3.68201E-27 3.68201E-27 3.68200E-27 3.68199E-27 3.68198E-27 3.68198E-27 ++ 3.68197E-27 3.68196E-27 3.68195E-27 3.68195E-27 3.68194E-27 3.68193E-27 3.68193E-27 3.68192E-27 3.68191E-27 3.68191E-27 ++ 2.26235E-27 2.26236E-27 2.26236E-27 2.26237E-27 2.26237E-27 2.26238E-27 2.26238E-27 2.26238E-27 2.26239E-27 2.26239E-27 ++ 2.26240E-27 2.26240E-27 2.26241E-27 2.26241E-27 2.26242E-27 2.26242E-27 2.26243E-27 2.26243E-27 2.26244E-27 2.26244E-27 ++ 2.26245E-27 2.26245E-27 2.26246E-27 2.26246E-27 2.26247E-27 2.26247E-27 2.26248E-27 2.26248E-27 2.26249E-27 2.26249E-27 ++ 2.26250E-27 2.26251E-27 2.26251E-27 2.26252E-27 2.26252E-27 2.26253E-27 2.26253E-27 2.26253E-27 2.26253E-27 2.26253E-27 ++ 2.26253E-27 2.26253E-27 2.26253E-27 2.26253E-27 2.26253E-27 2.26253E-27 2.26253E-27 2.26254E-27 2.26254E-27 2.26254E-27 ++ 2.26254E-27 2.26254E-27 2.26254E-27 2.26254E-27 2.26254E-27 2.26254E-27 2.26254E-27 2.26255E-27 2.26255E-27 2.26255E-27 ++ 2.26255E-27 2.26255E-27 2.26255E-27 2.26255E-27 2.26255E-27 2.26255E-27 2.26255E-27 2.26255E-27 2.26256E-27 2.26256E-27 ++ 2.26256E-27 2.26256E-27 2.26256E-27 2.26256E-27 2.26256E-27 2.26256E-27 2.26256E-27 2.26256E-27 2.26256E-27 2.26256E-27 ++ 2.26256E-27 2.26256E-27 2.26255E-27 2.26255E-27 2.26255E-27 2.26255E-27 2.26255E-27 2.26255E-27 2.26255E-27 2.26255E-27 ++ 2.26255E-27 2.26255E-27 2.26255E-27 2.26254E-27 2.26254E-27 2.26254E-27 2.26254E-27 2.26254E-27 2.26254E-27 2.26254E-27 ++ 2.26254E-27 2.26254E-27 2.26254E-27 2.26253E-27 2.26253E-27 2.26253E-27 2.26253E-27 2.26253E-27 2.26253E-27 2.26253E-27 ++ 2.26253E-27 2.26253E-27 2.26253E-27 2.26253E-27 2.26253E-27 2.26252E-27 2.26252E-27 2.26251E-27 2.26251E-27 2.26250E-27 ++ 2.26249E-27 2.26249E-27 2.26248E-27 2.26248E-27 2.26247E-27 2.26247E-27 2.26246E-27 2.26246E-27 2.26245E-27 2.26245E-27 ++ 2.26244E-27 2.26244E-27 2.26243E-27 2.26243E-27 2.26242E-27 2.26242E-27 2.26241E-27 2.26241E-27 2.26240E-27 2.26240E-27 ++ 2.26239E-27 2.26239E-27 2.26238E-27 2.26238E-27 2.26238E-27 2.26237E-27 2.26237E-27 2.26236E-27 2.26236E-27 2.26235E-27 ++ 1.38518E-27 1.38519E-27 1.38519E-27 1.38519E-27 1.38520E-27 1.38520E-27 1.38520E-27 1.38520E-27 1.38521E-27 1.38521E-27 ++ 1.38521E-27 1.38521E-27 1.38522E-27 1.38522E-27 1.38522E-27 1.38523E-27 1.38523E-27 1.38523E-27 1.38524E-27 1.38524E-27 ++ 1.38524E-27 1.38525E-27 1.38525E-27 1.38525E-27 1.38526E-27 1.38526E-27 1.38526E-27 1.38527E-27 1.38527E-27 1.38527E-27 ++ 1.38528E-27 1.38528E-27 1.38528E-27 1.38529E-27 1.38529E-27 1.38529E-27 1.38529E-27 1.38529E-27 1.38529E-27 1.38529E-27 ++ 1.38529E-27 1.38530E-27 1.38530E-27 1.38530E-27 1.38530E-27 1.38530E-27 1.38530E-27 1.38530E-27 1.38530E-27 1.38530E-27 ++ 1.38530E-27 1.38530E-27 1.38530E-27 1.38530E-27 1.38530E-27 1.38530E-27 1.38530E-27 1.38530E-27 1.38530E-27 1.38531E-27 ++ 1.38531E-27 1.38531E-27 1.38531E-27 1.38531E-27 1.38531E-27 1.38531E-27 1.38531E-27 1.38531E-27 1.38531E-27 1.38531E-27 ++ 1.38531E-27 1.38531E-27 1.38531E-27 1.38531E-27 1.38531E-27 1.38531E-27 1.38531E-27 1.38531E-27 1.38531E-27 1.38531E-27 ++ 1.38531E-27 1.38531E-27 1.38531E-27 1.38531E-27 1.38531E-27 1.38531E-27 1.38531E-27 1.38531E-27 1.38531E-27 1.38531E-27 ++ 1.38531E-27 1.38530E-27 1.38530E-27 1.38530E-27 1.38530E-27 1.38530E-27 1.38530E-27 1.38530E-27 1.38530E-27 1.38530E-27 ++ 1.38530E-27 1.38530E-27 1.38530E-27 1.38530E-27 1.38530E-27 1.38530E-27 1.38530E-27 1.38530E-27 1.38530E-27 1.38529E-27 ++ 1.38529E-27 1.38529E-27 1.38529E-27 1.38529E-27 1.38529E-27 1.38529E-27 1.38529E-27 1.38528E-27 1.38528E-27 1.38528E-27 ++ 1.38527E-27 1.38527E-27 1.38527E-27 1.38526E-27 1.38526E-27 1.38526E-27 1.38525E-27 1.38525E-27 1.38525E-27 1.38524E-27 ++ 1.38524E-27 1.38524E-27 1.38523E-27 1.38523E-27 1.38523E-27 1.38522E-27 1.38522E-27 1.38522E-27 1.38521E-27 1.38521E-27 ++ 1.38521E-27 1.38521E-27 1.38520E-27 1.38520E-27 1.38520E-27 1.38520E-27 1.38519E-27 1.38519E-27 1.38519E-27 1.38518E-27 ++ 8.45113E-28 8.45114E-28 8.45116E-28 8.45118E-28 8.45119E-28 8.45121E-28 8.45123E-28 8.45124E-28 8.45126E-28 8.45128E-28 ++ 8.45130E-28 8.45131E-28 8.45133E-28 8.45135E-28 8.45137E-28 8.45139E-28 8.45140E-28 8.45142E-28 8.45144E-28 8.45146E-28 ++ 8.45148E-28 8.45150E-28 8.45152E-28 8.45154E-28 8.45156E-28 8.45158E-28 8.45160E-28 8.45162E-28 8.45165E-28 8.45167E-28 ++ 8.45169E-28 8.45171E-28 8.45173E-28 8.45176E-28 8.45178E-28 8.45180E-28 8.45180E-28 8.45180E-28 8.45180E-28 8.45181E-28 ++ 8.45181E-28 8.45181E-28 8.45181E-28 8.45181E-28 8.45182E-28 8.45182E-28 8.45182E-28 8.45182E-28 8.45183E-28 8.45183E-28 ++ 8.45184E-28 8.45184E-28 8.45184E-28 8.45185E-28 8.45185E-28 8.45186E-28 8.45186E-28 8.45186E-28 8.45187E-28 8.45187E-28 ++ 8.45188E-28 8.45188E-28 8.45188E-28 8.45189E-28 8.45189E-28 8.45189E-28 8.45190E-28 8.45190E-28 8.45190E-28 8.45190E-28 ++ 8.45191E-28 8.45191E-28 8.45191E-28 8.45191E-28 8.45191E-28 8.45191E-28 8.45191E-28 8.45191E-28 8.45191E-28 8.45191E-28 ++ 8.45190E-28 8.45190E-28 8.45190E-28 8.45190E-28 8.45189E-28 8.45189E-28 8.45189E-28 8.45188E-28 8.45188E-28 8.45188E-28 ++ 8.45187E-28 8.45187E-28 8.45186E-28 8.45186E-28 8.45186E-28 8.45185E-28 8.45185E-28 8.45184E-28 8.45184E-28 8.45184E-28 ++ 8.45183E-28 8.45183E-28 8.45182E-28 8.45182E-28 8.45182E-28 8.45182E-28 8.45181E-28 8.45181E-28 8.45181E-28 8.45181E-28 ++ 8.45181E-28 8.45180E-28 8.45180E-28 8.45180E-28 8.45180E-28 8.45178E-28 8.45176E-28 8.45173E-28 8.45171E-28 8.45169E-28 ++ 8.45167E-28 8.45165E-28 8.45162E-28 8.45160E-28 8.45158E-28 8.45156E-28 8.45154E-28 8.45152E-28 8.45150E-28 8.45148E-28 ++ 8.45146E-28 8.45144E-28 8.45142E-28 8.45140E-28 8.45139E-28 8.45137E-28 8.45135E-28 8.45133E-28 8.45131E-28 8.45130E-28 ++ 8.45128E-28 8.45126E-28 8.45124E-28 8.45123E-28 8.45121E-28 8.45119E-28 8.45118E-28 8.45116E-28 8.45114E-28 8.45113E-28 ++ 5.13786E-28 5.13786E-28 5.13787E-28 5.13789E-28 5.13790E-28 5.13791E-28 5.13792E-28 5.13793E-28 5.13794E-28 5.13795E-28 ++ 5.13796E-28 5.13797E-28 5.13798E-28 5.13799E-28 5.13800E-28 5.13801E-28 5.13802E-28 5.13804E-28 5.13805E-28 5.13806E-28 ++ 5.13807E-28 5.13808E-28 5.13810E-28 5.13811E-28 5.13812E-28 5.13813E-28 5.13815E-28 5.13816E-28 5.13817E-28 5.13819E-28 ++ 5.13820E-28 5.13821E-28 5.13823E-28 5.13824E-28 5.13826E-28 5.13827E-28 5.13827E-28 5.13827E-28 5.13827E-28 5.13827E-28 ++ 5.13827E-28 5.13827E-28 5.13827E-28 5.13828E-28 5.13828E-28 5.13828E-28 5.13828E-28 5.13828E-28 5.13829E-28 5.13829E-28 ++ 5.13829E-28 5.13829E-28 5.13829E-28 5.13830E-28 5.13830E-28 5.13830E-28 5.13830E-28 5.13831E-28 5.13831E-28 5.13831E-28 ++ 5.13832E-28 5.13832E-28 5.13832E-28 5.13832E-28 5.13832E-28 5.13833E-28 5.13833E-28 5.13833E-28 5.13833E-28 5.13833E-28 ++ 5.13833E-28 5.13833E-28 5.13833E-28 5.13834E-28 5.13834E-28 5.13834E-28 5.13834E-28 5.13833E-28 5.13833E-28 5.13833E-28 ++ 5.13833E-28 5.13833E-28 5.13833E-28 5.13833E-28 5.13833E-28 5.13832E-28 5.13832E-28 5.13832E-28 5.13832E-28 5.13832E-28 ++ 5.13831E-28 5.13831E-28 5.13831E-28 5.13830E-28 5.13830E-28 5.13830E-28 5.13830E-28 5.13829E-28 5.13829E-28 5.13829E-28 ++ 5.13829E-28 5.13829E-28 5.13828E-28 5.13828E-28 5.13828E-28 5.13828E-28 5.13828E-28 5.13827E-28 5.13827E-28 5.13827E-28 ++ 5.13827E-28 5.13827E-28 5.13827E-28 5.13827E-28 5.13827E-28 5.13826E-28 5.13824E-28 5.13823E-28 5.13821E-28 5.13820E-28 ++ 5.13819E-28 5.13817E-28 5.13816E-28 5.13815E-28 5.13813E-28 5.13812E-28 5.13811E-28 5.13810E-28 5.13808E-28 5.13807E-28 ++ 5.13806E-28 5.13805E-28 5.13804E-28 5.13802E-28 5.13801E-28 5.13800E-28 5.13799E-28 5.13798E-28 5.13797E-28 5.13796E-28 ++ 5.13795E-28 5.13794E-28 5.13793E-28 5.13792E-28 5.13791E-28 5.13790E-28 5.13789E-28 5.13787E-28 5.13786E-28 5.13786E-28 ++ 3.11250E-28 3.11251E-28 3.11251E-28 3.11252E-28 3.11253E-28 3.11253E-28 3.11254E-28 3.11255E-28 3.11255E-28 3.11256E-28 ++ 3.11256E-28 3.11257E-28 3.11258E-28 3.11258E-28 3.11259E-28 3.11260E-28 3.11261E-28 3.11261E-28 3.11262E-28 3.11263E-28 ++ 3.11263E-28 3.11264E-28 3.11265E-28 3.11266E-28 3.11266E-28 3.11267E-28 3.11268E-28 3.11269E-28 3.11270E-28 3.11270E-28 ++ 3.11271E-28 3.11272E-28 3.11273E-28 3.11274E-28 3.11275E-28 3.11276E-28 3.11276E-28 3.11276E-28 3.11276E-28 3.11276E-28 ++ 3.11276E-28 3.11276E-28 3.11276E-28 3.11276E-28 3.11276E-28 3.11276E-28 3.11276E-28 3.11276E-28 3.11277E-28 3.11277E-28 ++ 3.11277E-28 3.11277E-28 3.11277E-28 3.11277E-28 3.11277E-28 3.11278E-28 3.11278E-28 3.11278E-28 3.11278E-28 3.11278E-28 ++ 3.11278E-28 3.11279E-28 3.11279E-28 3.11279E-28 3.11279E-28 3.11279E-28 3.11279E-28 3.11279E-28 3.11279E-28 3.11279E-28 ++ 3.11279E-28 3.11280E-28 3.11280E-28 3.11280E-28 3.11280E-28 3.11280E-28 3.11280E-28 3.11280E-28 3.11280E-28 3.11279E-28 ++ 3.11279E-28 3.11279E-28 3.11279E-28 3.11279E-28 3.11279E-28 3.11279E-28 3.11279E-28 3.11279E-28 3.11279E-28 3.11278E-28 ++ 3.11278E-28 3.11278E-28 3.11278E-28 3.11278E-28 3.11278E-28 3.11277E-28 3.11277E-28 3.11277E-28 3.11277E-28 3.11277E-28 ++ 3.11277E-28 3.11277E-28 3.11276E-28 3.11276E-28 3.11276E-28 3.11276E-28 3.11276E-28 3.11276E-28 3.11276E-28 3.11276E-28 ++ 3.11276E-28 3.11276E-28 3.11276E-28 3.11276E-28 3.11276E-28 3.11275E-28 3.11274E-28 3.11273E-28 3.11272E-28 3.11271E-28 ++ 3.11270E-28 3.11270E-28 3.11269E-28 3.11268E-28 3.11267E-28 3.11266E-28 3.11266E-28 3.11265E-28 3.11264E-28 3.11263E-28 ++ 3.11263E-28 3.11262E-28 3.11261E-28 3.11261E-28 3.11260E-28 3.11259E-28 3.11258E-28 3.11258E-28 3.11257E-28 3.11256E-28 ++ 3.11256E-28 3.11255E-28 3.11255E-28 3.11254E-28 3.11253E-28 3.11253E-28 3.11252E-28 3.11251E-28 3.11251E-28 3.11250E-28 ++ 1.87888E-28 1.87888E-28 1.87888E-28 1.87889E-28 1.87889E-28 1.87890E-28 1.87890E-28 1.87890E-28 1.87891E-28 1.87891E-28 ++ 1.87892E-28 1.87892E-28 1.87892E-28 1.87893E-28 1.87893E-28 1.87894E-28 1.87894E-28 1.87894E-28 1.87895E-28 1.87895E-28 ++ 1.87896E-28 1.87896E-28 1.87897E-28 1.87897E-28 1.87898E-28 1.87898E-28 1.87899E-28 1.87899E-28 1.87900E-28 1.87900E-28 ++ 1.87901E-28 1.87901E-28 1.87902E-28 1.87902E-28 1.87903E-28 1.87903E-28 1.87903E-28 1.87903E-28 1.87903E-28 1.87903E-28 ++ 1.87903E-28 1.87903E-28 1.87903E-28 1.87903E-28 1.87904E-28 1.87904E-28 1.87904E-28 1.87904E-28 1.87904E-28 1.87904E-28 ++ 1.87904E-28 1.87904E-28 1.87904E-28 1.87904E-28 1.87904E-28 1.87904E-28 1.87905E-28 1.87905E-28 1.87905E-28 1.87905E-28 ++ 1.87905E-28 1.87905E-28 1.87905E-28 1.87905E-28 1.87905E-28 1.87905E-28 1.87905E-28 1.87905E-28 1.87906E-28 1.87906E-28 ++ 1.87906E-28 1.87906E-28 1.87906E-28 1.87906E-28 1.87906E-28 1.87906E-28 1.87906E-28 1.87906E-28 1.87906E-28 1.87906E-28 ++ 1.87906E-28 1.87906E-28 1.87905E-28 1.87905E-28 1.87905E-28 1.87905E-28 1.87905E-28 1.87905E-28 1.87905E-28 1.87905E-28 ++ 1.87905E-28 1.87905E-28 1.87905E-28 1.87905E-28 1.87904E-28 1.87904E-28 1.87904E-28 1.87904E-28 1.87904E-28 1.87904E-28 ++ 1.87904E-28 1.87904E-28 1.87904E-28 1.87904E-28 1.87904E-28 1.87904E-28 1.87903E-28 1.87903E-28 1.87903E-28 1.87903E-28 ++ 1.87903E-28 1.87903E-28 1.87903E-28 1.87903E-28 1.87903E-28 1.87903E-28 1.87902E-28 1.87902E-28 1.87901E-28 1.87901E-28 ++ 1.87900E-28 1.87900E-28 1.87899E-28 1.87899E-28 1.87898E-28 1.87898E-28 1.87897E-28 1.87897E-28 1.87896E-28 1.87896E-28 ++ 1.87895E-28 1.87895E-28 1.87894E-28 1.87894E-28 1.87894E-28 1.87893E-28 1.87893E-28 1.87892E-28 1.87892E-28 1.87892E-28 ++ 1.87891E-28 1.87891E-28 1.87890E-28 1.87890E-28 1.87890E-28 1.87889E-28 1.87889E-28 1.87888E-28 1.87888E-28 1.87888E-28 ++ 1.13018E-28 1.13019E-28 1.13019E-28 1.13019E-28 1.13019E-28 1.13019E-28 1.13020E-28 1.13020E-28 1.13020E-28 1.13020E-28 ++ 1.13021E-28 1.13021E-28 1.13021E-28 1.13021E-28 1.13022E-28 1.13022E-28 1.13022E-28 1.13022E-28 1.13023E-28 1.13023E-28 ++ 1.13023E-28 1.13023E-28 1.13024E-28 1.13024E-28 1.13024E-28 1.13025E-28 1.13025E-28 1.13025E-28 1.13026E-28 1.13026E-28 ++ 1.13026E-28 1.13026E-28 1.13027E-28 1.13027E-28 1.13027E-28 1.13028E-28 1.13028E-28 1.13028E-28 1.13028E-28 1.13028E-28 ++ 1.13028E-28 1.13028E-28 1.13028E-28 1.13028E-28 1.13028E-28 1.13028E-28 1.13028E-28 1.13028E-28 1.13028E-28 1.13028E-28 ++ 1.13028E-28 1.13028E-28 1.13028E-28 1.13028E-28 1.13028E-28 1.13028E-28 1.13029E-28 1.13029E-28 1.13029E-28 1.13029E-28 ++ 1.13029E-28 1.13029E-28 1.13029E-28 1.13029E-28 1.13029E-28 1.13029E-28 1.13029E-28 1.13029E-28 1.13029E-28 1.13029E-28 ++ 1.13029E-28 1.13029E-28 1.13029E-28 1.13029E-28 1.13029E-28 1.13029E-28 1.13029E-28 1.13029E-28 1.13029E-28 1.13029E-28 ++ 1.13029E-28 1.13029E-28 1.13029E-28 1.13029E-28 1.13029E-28 1.13029E-28 1.13029E-28 1.13029E-28 1.13029E-28 1.13029E-28 ++ 1.13029E-28 1.13029E-28 1.13029E-28 1.13029E-28 1.13028E-28 1.13028E-28 1.13028E-28 1.13028E-28 1.13028E-28 1.13028E-28 ++ 1.13028E-28 1.13028E-28 1.13028E-28 1.13028E-28 1.13028E-28 1.13028E-28 1.13028E-28 1.13028E-28 1.13028E-28 1.13028E-28 ++ 1.13028E-28 1.13028E-28 1.13028E-28 1.13028E-28 1.13028E-28 1.13027E-28 1.13027E-28 1.13027E-28 1.13026E-28 1.13026E-28 ++ 1.13026E-28 1.13026E-28 1.13025E-28 1.13025E-28 1.13025E-28 1.13024E-28 1.13024E-28 1.13024E-28 1.13023E-28 1.13023E-28 ++ 1.13023E-28 1.13023E-28 1.13022E-28 1.13022E-28 1.13022E-28 1.13022E-28 1.13021E-28 1.13021E-28 1.13021E-28 1.13021E-28 ++ 1.13020E-28 1.13020E-28 1.13020E-28 1.13020E-28 1.13019E-28 1.13019E-28 1.13019E-28 1.13019E-28 1.13019E-28 1.13018E-28 ++ 6.77425E-29 6.77426E-29 6.77428E-29 6.77429E-29 6.77430E-29 6.77432E-29 6.77433E-29 6.77435E-29 6.77436E-29 6.77437E-29 ++ 6.77439E-29 6.77440E-29 6.77442E-29 6.77443E-29 6.77445E-29 6.77447E-29 6.77448E-29 6.77450E-29 6.77451E-29 6.77453E-29 ++ 6.77455E-29 6.77456E-29 6.77458E-29 6.77460E-29 6.77461E-29 6.77463E-29 6.77465E-29 6.77467E-29 6.77469E-29 6.77470E-29 ++ 6.77472E-29 6.77474E-29 6.77476E-29 6.77478E-29 6.77480E-29 6.77482E-29 6.77482E-29 6.77482E-29 6.77482E-29 6.77482E-29 ++ 6.77482E-29 6.77483E-29 6.77483E-29 6.77483E-29 6.77483E-29 6.77483E-29 6.77484E-29 6.77484E-29 6.77484E-29 6.77485E-29 ++ 6.77485E-29 6.77485E-29 6.77486E-29 6.77486E-29 6.77486E-29 6.77487E-29 6.77487E-29 6.77487E-29 6.77488E-29 6.77488E-29 ++ 6.77488E-29 6.77489E-29 6.77489E-29 6.77489E-29 6.77490E-29 6.77490E-29 6.77490E-29 6.77490E-29 6.77491E-29 6.77491E-29 ++ 6.77491E-29 6.77491E-29 6.77491E-29 6.77491E-29 6.77491E-29 6.77491E-29 6.77491E-29 6.77491E-29 6.77491E-29 6.77491E-29 ++ 6.77491E-29 6.77491E-29 6.77490E-29 6.77490E-29 6.77490E-29 6.77490E-29 6.77489E-29 6.77489E-29 6.77489E-29 6.77488E-29 ++ 6.77488E-29 6.77488E-29 6.77487E-29 6.77487E-29 6.77487E-29 6.77486E-29 6.77486E-29 6.77486E-29 6.77485E-29 6.77485E-29 ++ 6.77485E-29 6.77484E-29 6.77484E-29 6.77484E-29 6.77483E-29 6.77483E-29 6.77483E-29 6.77483E-29 6.77483E-29 6.77482E-29 ++ 6.77482E-29 6.77482E-29 6.77482E-29 6.77482E-29 6.77482E-29 6.77480E-29 6.77478E-29 6.77476E-29 6.77474E-29 6.77472E-29 ++ 6.77470E-29 6.77469E-29 6.77467E-29 6.77465E-29 6.77463E-29 6.77461E-29 6.77460E-29 6.77458E-29 6.77456E-29 6.77455E-29 ++ 6.77453E-29 6.77451E-29 6.77450E-29 6.77448E-29 6.77447E-29 6.77445E-29 6.77443E-29 6.77442E-29 6.77440E-29 6.77439E-29 ++ 6.77437E-29 6.77436E-29 6.77435E-29 6.77433E-29 6.77432E-29 6.77430E-29 6.77429E-29 6.77428E-29 6.77426E-29 6.77425E-29 ++ 4.04610E-29 4.04610E-29 4.04611E-29 4.04612E-29 4.04613E-29 4.04614E-29 4.04614E-29 4.04615E-29 4.04616E-29 4.04617E-29 ++ 4.04618E-29 4.04619E-29 4.04620E-29 4.04621E-29 4.04622E-29 4.04623E-29 4.04623E-29 4.04624E-29 4.04625E-29 4.04626E-29 ++ 4.04627E-29 4.04628E-29 4.04629E-29 4.04630E-29 4.04632E-29 4.04633E-29 4.04634E-29 4.04635E-29 4.04636E-29 4.04637E-29 ++ 4.04638E-29 4.04639E-29 4.04640E-29 4.04642E-29 4.04643E-29 4.04644E-29 4.04644E-29 4.04644E-29 4.04644E-29 4.04644E-29 ++ 4.04644E-29 4.04644E-29 4.04644E-29 4.04645E-29 4.04645E-29 4.04645E-29 4.04645E-29 4.04645E-29 4.04645E-29 4.04646E-29 ++ 4.04646E-29 4.04646E-29 4.04646E-29 4.04646E-29 4.04647E-29 4.04647E-29 4.04647E-29 4.04647E-29 4.04647E-29 4.04648E-29 ++ 4.04648E-29 4.04648E-29 4.04648E-29 4.04648E-29 4.04649E-29 4.04649E-29 4.04649E-29 4.04649E-29 4.04649E-29 4.04649E-29 ++ 4.04649E-29 4.04650E-29 4.04650E-29 4.04650E-29 4.04650E-29 4.04650E-29 4.04650E-29 4.04650E-29 4.04650E-29 4.04649E-29 ++ 4.04649E-29 4.04649E-29 4.04649E-29 4.04649E-29 4.04649E-29 4.04649E-29 4.04648E-29 4.04648E-29 4.04648E-29 4.04648E-29 ++ 4.04648E-29 4.04647E-29 4.04647E-29 4.04647E-29 4.04647E-29 4.04647E-29 4.04646E-29 4.04646E-29 4.04646E-29 4.04646E-29 ++ 4.04646E-29 4.04645E-29 4.04645E-29 4.04645E-29 4.04645E-29 4.04645E-29 4.04645E-29 4.04644E-29 4.04644E-29 4.04644E-29 ++ 4.04644E-29 4.04644E-29 4.04644E-29 4.04644E-29 4.04644E-29 4.04643E-29 4.04642E-29 4.04640E-29 4.04639E-29 4.04638E-29 ++ 4.04637E-29 4.04636E-29 4.04635E-29 4.04634E-29 4.04633E-29 4.04632E-29 4.04630E-29 4.04629E-29 4.04628E-29 4.04627E-29 ++ 4.04626E-29 4.04625E-29 4.04624E-29 4.04623E-29 4.04623E-29 4.04622E-29 4.04621E-29 4.04620E-29 4.04619E-29 4.04618E-29 ++ 4.04617E-29 4.04616E-29 4.04615E-29 4.04614E-29 4.04614E-29 4.04613E-29 4.04612E-29 4.04611E-29 4.04610E-29 4.04610E-29 ++ 2.40810E-29 2.40810E-29 2.40811E-29 2.40811E-29 2.40812E-29 2.40812E-29 2.40813E-29 2.40813E-29 2.40814E-29 2.40814E-29 ++ 2.40815E-29 2.40815E-29 2.40816E-29 2.40817E-29 2.40817E-29 2.40818E-29 2.40818E-29 2.40819E-29 2.40819E-29 2.40820E-29 ++ 2.40821E-29 2.40821E-29 2.40822E-29 2.40822E-29 2.40823E-29 2.40824E-29 2.40824E-29 2.40825E-29 2.40826E-29 2.40826E-29 ++ 2.40827E-29 2.40828E-29 2.40828E-29 2.40829E-29 2.40830E-29 2.40831E-29 2.40831E-29 2.40831E-29 2.40831E-29 2.40831E-29 ++ 2.40831E-29 2.40831E-29 2.40831E-29 2.40831E-29 2.40831E-29 2.40831E-29 2.40831E-29 2.40831E-29 2.40831E-29 2.40832E-29 ++ 2.40832E-29 2.40832E-29 2.40832E-29 2.40832E-29 2.40832E-29 2.40832E-29 2.40832E-29 2.40833E-29 2.40833E-29 2.40833E-29 ++ 2.40833E-29 2.40833E-29 2.40833E-29 2.40833E-29 2.40833E-29 2.40834E-29 2.40834E-29 2.40834E-29 2.40834E-29 2.40834E-29 ++ 2.40834E-29 2.40834E-29 2.40834E-29 2.40834E-29 2.40834E-29 2.40834E-29 2.40834E-29 2.40834E-29 2.40834E-29 2.40834E-29 ++ 2.40834E-29 2.40834E-29 2.40834E-29 2.40834E-29 2.40834E-29 2.40833E-29 2.40833E-29 2.40833E-29 2.40833E-29 2.40833E-29 ++ 2.40833E-29 2.40833E-29 2.40833E-29 2.40832E-29 2.40832E-29 2.40832E-29 2.40832E-29 2.40832E-29 2.40832E-29 2.40832E-29 ++ 2.40832E-29 2.40831E-29 2.40831E-29 2.40831E-29 2.40831E-29 2.40831E-29 2.40831E-29 2.40831E-29 2.40831E-29 2.40831E-29 ++ 2.40831E-29 2.40831E-29 2.40831E-29 2.40831E-29 2.40831E-29 2.40830E-29 2.40829E-29 2.40828E-29 2.40828E-29 2.40827E-29 ++ 2.40826E-29 2.40826E-29 2.40825E-29 2.40824E-29 2.40824E-29 2.40823E-29 2.40822E-29 2.40822E-29 2.40821E-29 2.40821E-29 ++ 2.40820E-29 2.40819E-29 2.40819E-29 2.40818E-29 2.40818E-29 2.40817E-29 2.40817E-29 2.40816E-29 2.40815E-29 2.40815E-29 ++ 2.40814E-29 2.40814E-29 2.40813E-29 2.40813E-29 2.40812E-29 2.40812E-29 2.40811E-29 2.40811E-29 2.40810E-29 2.40810E-29 ++ 1.42816E-29 1.42816E-29 1.42817E-29 1.42817E-29 1.42817E-29 1.42817E-29 1.42818E-29 1.42818E-29 1.42818E-29 1.42819E-29 ++ 1.42819E-29 1.42819E-29 1.42820E-29 1.42820E-29 1.42820E-29 1.42821E-29 1.42821E-29 1.42821E-29 1.42822E-29 1.42822E-29 ++ 1.42822E-29 1.42823E-29 1.42823E-29 1.42823E-29 1.42824E-29 1.42824E-29 1.42825E-29 1.42825E-29 1.42825E-29 1.42826E-29 ++ 1.42826E-29 1.42827E-29 1.42827E-29 1.42828E-29 1.42828E-29 1.42828E-29 1.42828E-29 1.42828E-29 1.42828E-29 1.42828E-29 ++ 1.42828E-29 1.42829E-29 1.42829E-29 1.42829E-29 1.42829E-29 1.42829E-29 1.42829E-29 1.42829E-29 1.42829E-29 1.42829E-29 ++ 1.42829E-29 1.42829E-29 1.42829E-29 1.42829E-29 1.42829E-29 1.42829E-29 1.42829E-29 1.42830E-29 1.42830E-29 1.42830E-29 ++ 1.42830E-29 1.42830E-29 1.42830E-29 1.42830E-29 1.42830E-29 1.42830E-29 1.42830E-29 1.42830E-29 1.42830E-29 1.42830E-29 ++ 1.42830E-29 1.42830E-29 1.42830E-29 1.42830E-29 1.42830E-29 1.42830E-29 1.42830E-29 1.42830E-29 1.42830E-29 1.42830E-29 ++ 1.42830E-29 1.42830E-29 1.42830E-29 1.42830E-29 1.42830E-29 1.42830E-29 1.42830E-29 1.42830E-29 1.42830E-29 1.42830E-29 ++ 1.42830E-29 1.42830E-29 1.42830E-29 1.42829E-29 1.42829E-29 1.42829E-29 1.42829E-29 1.42829E-29 1.42829E-29 1.42829E-29 ++ 1.42829E-29 1.42829E-29 1.42829E-29 1.42829E-29 1.42829E-29 1.42829E-29 1.42829E-29 1.42829E-29 1.42829E-29 1.42828E-29 ++ 1.42828E-29 1.42828E-29 1.42828E-29 1.42828E-29 1.42828E-29 1.42828E-29 1.42828E-29 1.42827E-29 1.42827E-29 1.42826E-29 ++ 1.42826E-29 1.42825E-29 1.42825E-29 1.42825E-29 1.42824E-29 1.42824E-29 1.42823E-29 1.42823E-29 1.42823E-29 1.42822E-29 ++ 1.42822E-29 1.42822E-29 1.42821E-29 1.42821E-29 1.42821E-29 1.42820E-29 1.42820E-29 1.42820E-29 1.42819E-29 1.42819E-29 ++ 1.42819E-29 1.42818E-29 1.42818E-29 1.42818E-29 1.42817E-29 1.42817E-29 1.42817E-29 1.42817E-29 1.42816E-29 1.42816E-29 ++ 8.44006E-30 8.44008E-30 8.44010E-30 8.44011E-30 8.44013E-30 8.44015E-30 8.44017E-30 8.44019E-30 8.44020E-30 8.44022E-30 ++ 8.44024E-30 8.44026E-30 8.44028E-30 8.44030E-30 8.44032E-30 8.44034E-30 8.44036E-30 8.44038E-30 8.44040E-30 8.44042E-30 ++ 8.44045E-30 8.44047E-30 8.44049E-30 8.44051E-30 8.44053E-30 8.44056E-30 8.44058E-30 8.44060E-30 8.44063E-30 8.44065E-30 ++ 8.44068E-30 8.44070E-30 8.44073E-30 8.44075E-30 8.44078E-30 8.44081E-30 8.44081E-30 8.44081E-30 8.44081E-30 8.44081E-30 ++ 8.44081E-30 8.44081E-30 8.44081E-30 8.44082E-30 8.44082E-30 8.44082E-30 8.44083E-30 8.44083E-30 8.44083E-30 8.44084E-30 ++ 8.44084E-30 8.44085E-30 8.44085E-30 8.44086E-30 8.44086E-30 8.44087E-30 8.44087E-30 8.44088E-30 8.44088E-30 8.44088E-30 ++ 8.44089E-30 8.44089E-30 8.44090E-30 8.44090E-30 8.44091E-30 8.44091E-30 8.44091E-30 8.44092E-30 8.44092E-30 8.44092E-30 ++ 8.44092E-30 8.44092E-30 8.44093E-30 8.44093E-30 8.44093E-30 8.44093E-30 8.44093E-30 8.44093E-30 8.44092E-30 8.44092E-30 ++ 8.44092E-30 8.44092E-30 8.44092E-30 8.44091E-30 8.44091E-30 8.44091E-30 8.44090E-30 8.44090E-30 8.44089E-30 8.44089E-30 ++ 8.44088E-30 8.44088E-30 8.44088E-30 8.44087E-30 8.44087E-30 8.44086E-30 8.44086E-30 8.44085E-30 8.44085E-30 8.44084E-30 ++ 8.44084E-30 8.44083E-30 8.44083E-30 8.44083E-30 8.44082E-30 8.44082E-30 8.44082E-30 8.44081E-30 8.44081E-30 8.44081E-30 ++ 8.44081E-30 8.44081E-30 8.44081E-30 8.44081E-30 8.44081E-30 8.44078E-30 8.44075E-30 8.44073E-30 8.44070E-30 8.44068E-30 ++ 8.44065E-30 8.44063E-30 8.44060E-30 8.44058E-30 8.44056E-30 8.44053E-30 8.44051E-30 8.44049E-30 8.44047E-30 8.44045E-30 ++ 8.44042E-30 8.44040E-30 8.44038E-30 8.44036E-30 8.44034E-30 8.44032E-30 8.44030E-30 8.44028E-30 8.44026E-30 8.44024E-30 ++ 8.44022E-30 8.44020E-30 8.44019E-30 8.44017E-30 8.44015E-30 8.44013E-30 8.44011E-30 8.44010E-30 8.44008E-30 8.44006E-30 ++ 4.97035E-30 4.97036E-30 4.97037E-30 4.97038E-30 4.97039E-30 4.97040E-30 4.97041E-30 4.97042E-30 4.97043E-30 4.97045E-30 ++ 4.97046E-30 4.97047E-30 4.97048E-30 4.97049E-30 4.97050E-30 4.97052E-30 4.97053E-30 4.97054E-30 4.97055E-30 4.97056E-30 ++ 4.97058E-30 4.97059E-30 4.97060E-30 4.97062E-30 4.97063E-30 4.97064E-30 4.97066E-30 4.97067E-30 4.97069E-30 4.97070E-30 ++ 4.97072E-30 4.97073E-30 4.97075E-30 4.97076E-30 4.97078E-30 4.97079E-30 4.97079E-30 4.97079E-30 4.97079E-30 4.97079E-30 ++ 4.97079E-30 4.97080E-30 4.97080E-30 4.97080E-30 4.97080E-30 4.97080E-30 4.97080E-30 4.97081E-30 4.97081E-30 4.97081E-30 ++ 4.97081E-30 4.97082E-30 4.97082E-30 4.97082E-30 4.97082E-30 4.97083E-30 4.97083E-30 4.97083E-30 4.97084E-30 4.97084E-30 ++ 4.97084E-30 4.97084E-30 4.97085E-30 4.97085E-30 4.97085E-30 4.97085E-30 4.97086E-30 4.97086E-30 4.97086E-30 4.97086E-30 ++ 4.97086E-30 4.97086E-30 4.97086E-30 4.97086E-30 4.97086E-30 4.97086E-30 4.97086E-30 4.97086E-30 4.97086E-30 4.97086E-30 ++ 4.97086E-30 4.97086E-30 4.97086E-30 4.97086E-30 4.97085E-30 4.97085E-30 4.97085E-30 4.97085E-30 4.97084E-30 4.97084E-30 ++ 4.97084E-30 4.97084E-30 4.97083E-30 4.97083E-30 4.97083E-30 4.97082E-30 4.97082E-30 4.97082E-30 4.97082E-30 4.97081E-30 ++ 4.97081E-30 4.97081E-30 4.97081E-30 4.97080E-30 4.97080E-30 4.97080E-30 4.97080E-30 4.97080E-30 4.97080E-30 4.97079E-30 ++ 4.97079E-30 4.97079E-30 4.97079E-30 4.97079E-30 4.97079E-30 4.97078E-30 4.97076E-30 4.97075E-30 4.97073E-30 4.97072E-30 ++ 4.97070E-30 4.97069E-30 4.97067E-30 4.97066E-30 4.97064E-30 4.97063E-30 4.97062E-30 4.97060E-30 4.97059E-30 4.97058E-30 ++ 4.97056E-30 4.97055E-30 4.97054E-30 4.97053E-30 4.97052E-30 4.97050E-30 4.97049E-30 4.97048E-30 4.97047E-30 4.97046E-30 ++ 4.97045E-30 4.97043E-30 4.97042E-30 4.97041E-30 4.97040E-30 4.97039E-30 4.97038E-30 4.97037E-30 4.97036E-30 4.97035E-30 ++ 2.91687E-30 2.91688E-30 2.91688E-30 2.91689E-30 2.91690E-30 2.91690E-30 2.91691E-30 2.91691E-30 2.91692E-30 2.91693E-30 ++ 2.91693E-30 2.91694E-30 2.91695E-30 2.91695E-30 2.91696E-30 2.91697E-30 2.91697E-30 2.91698E-30 2.91699E-30 2.91700E-30 ++ 2.91700E-30 2.91701E-30 2.91702E-30 2.91703E-30 2.91704E-30 2.91704E-30 2.91705E-30 2.91706E-30 2.91707E-30 2.91708E-30 ++ 2.91709E-30 2.91709E-30 2.91710E-30 2.91711E-30 2.91712E-30 2.91713E-30 2.91713E-30 2.91713E-30 2.91713E-30 2.91713E-30 ++ 2.91713E-30 2.91713E-30 2.91713E-30 2.91713E-30 2.91714E-30 2.91714E-30 2.91714E-30 2.91714E-30 2.91714E-30 2.91714E-30 ++ 2.91714E-30 2.91714E-30 2.91715E-30 2.91715E-30 2.91715E-30 2.91715E-30 2.91715E-30 2.91715E-30 2.91716E-30 2.91716E-30 ++ 2.91716E-30 2.91716E-30 2.91716E-30 2.91716E-30 2.91717E-30 2.91717E-30 2.91717E-30 2.91717E-30 2.91717E-30 2.91717E-30 ++ 2.91717E-30 2.91717E-30 2.91717E-30 2.91717E-30 2.91717E-30 2.91717E-30 2.91717E-30 2.91717E-30 2.91717E-30 2.91717E-30 ++ 2.91717E-30 2.91717E-30 2.91717E-30 2.91717E-30 2.91717E-30 2.91717E-30 2.91716E-30 2.91716E-30 2.91716E-30 2.91716E-30 ++ 2.91716E-30 2.91716E-30 2.91715E-30 2.91715E-30 2.91715E-30 2.91715E-30 2.91715E-30 2.91715E-30 2.91714E-30 2.91714E-30 ++ 2.91714E-30 2.91714E-30 2.91714E-30 2.91714E-30 2.91714E-30 2.91714E-30 2.91713E-30 2.91713E-30 2.91713E-30 2.91713E-30 ++ 2.91713E-30 2.91713E-30 2.91713E-30 2.91713E-30 2.91713E-30 2.91712E-30 2.91711E-30 2.91710E-30 2.91709E-30 2.91709E-30 ++ 2.91708E-30 2.91707E-30 2.91706E-30 2.91705E-30 2.91704E-30 2.91704E-30 2.91703E-30 2.91702E-30 2.91701E-30 2.91700E-30 ++ 2.91700E-30 2.91699E-30 2.91698E-30 2.91697E-30 2.91697E-30 2.91696E-30 2.91695E-30 2.91695E-30 2.91694E-30 2.91693E-30 ++ 2.91693E-30 2.91692E-30 2.91691E-30 2.91691E-30 2.91690E-30 2.91690E-30 2.91689E-30 2.91688E-30 2.91688E-30 2.91687E-30 +diff --git a/2020-10-mirror_3D_scripts/interpolate_numerical_distribution.m b/2020-10-mirror_3D_scripts/interpolate_numerical_distribution.m +new file mode 100644 +index 0000000..cfc6596 +--- /dev/null ++++ b/2020-10-mirror_3D_scripts/interpolate_numerical_distribution.m +@@ -0,0 +1,61 @@ ++function F_out = interpolate_numerical_distribution() ++ ++ function out = F2(u,z) ++ out = ones(numel(u),numel(z)); ++ if size(u) == size(z) ++ for i = 1:numel(u) ++ for j = 1:numel(z) ++ out(i,j) = F(u(i),z(j)); ++ end ++ end ++ elseif isscalar(u) ++ for j = 1:numel(z) ++ out(j) = F(u,z(j)); ++ end ++ end ++ end ++ ++pitch_file = fopen('pitch_i.txt', 'r'); ++vel_file = fopen('u_j.txt', 'r'); ++dist_file = fopen('f_ij.txt', 'r'); ++ ++z = fscanf(pitch_file, '%f'); ++u = fscanf(vel_file, '%f'); ++f_vals = fscanf(dist_file, '%f'); ++ ++size_f = length(f_vals); ++num = sqrt(size_f); ++ ++n_o = 8e14; ++temp = 1.6022e-10; %temperature in erg ++m_e = 9.109*10^-28; ++u_th = sqrt(2*temp/m_e); ++lIndex = [0 1 2]; ++ ++%[u,z] = meshgrid(vel_vals,pitch_vals); ++%maxwell = n_o.*exp(-u.^2./u_th^2).*(z.*0 + 1)./(u_th.^3.*pi^(3/2)); ++ ++analytic = @(x,y) n_o.*exp(-x.^2./u_th^2).*(y.*0 + 1)./(u_th.^3.*pi^(3/2)); ++f_vals = reshape(f_vals, [num num]); ++ ++% ax1 = subplot(1,3,1); ++% contour(vel_vals,pitch_vals,f_vals); ++% ax2 = subplot(1,3,2); ++% contour(u,z,analytic(u,z)); ++ ++%u = u'; ++ ++%z = z'; ++ ++F = griddedInterpolant({u,z},f_vals'); ++F_out = @F2; ++ ++%ax3 = subplot(1,3,3); ++%f_plot = F_out(u(:),z(:)); ++%f_plot = reshape(f_plot, size(u)); ++%contour(u,z,f_plot); ++% ++ ++ ++ ++end +\ No newline at end of file +diff --git a/2020-10-mirror_3D_scripts/pitch_i.txt b/2020-10-mirror_3D_scripts/pitch_i.txt +new file mode 100644 +index 0000000..0ed041c +--- /dev/null ++++ b/2020-10-mirror_3D_scripts/pitch_i.txt +@@ -0,0 +1,15 @@ ++ 0.00000E+00 1.59049E-01 2.25899E-01 2.77884E-01 3.22310E-01 3.62002E-01 3.98405E-01 4.32379E-01 4.64487E-01 4.95121E-01 ++ 5.24568E-01 5.53050E-01 5.80739E-01 6.07778E-01 6.34284E-01 6.60359E-01 6.86091E-01 7.11558E-01 7.36834E-01 7.61986E-01 ++ 7.87078E-01 8.12175E-01 8.37340E-01 8.62637E-01 8.88136E-01 9.13909E-01 9.40036E-01 9.66607E-01 9.93726E-01 1.02151E+00 ++ 1.05011E+00 1.07971E+00 1.11052E+00 1.14285E+00 1.17711E+00 1.21390E+00 1.21416E+00 1.21495E+00 1.21627E+00 1.21810E+00 ++ 1.22045E+00 1.22331E+00 1.22668E+00 1.23054E+00 1.23489E+00 1.23971E+00 1.24499E+00 1.25073E+00 1.25690E+00 1.26349E+00 ++ 1.27049E+00 1.27787E+00 1.28561E+00 1.29371E+00 1.30212E+00 1.31084E+00 1.31983E+00 1.32908E+00 1.33854E+00 1.34818E+00 ++ 1.35798E+00 1.36788E+00 1.37785E+00 1.38783E+00 1.39776E+00 1.40756E+00 1.41716E+00 1.42646E+00 1.43532E+00 1.44362E+00 ++ 1.45118E+00 1.45779E+00 1.46327E+00 1.46737E+00 1.46992E+00 1.67167E+00 1.67422E+00 1.67833E+00 1.68380E+00 1.69042E+00 ++ 1.69797E+00 1.70627E+00 1.71513E+00 1.72443E+00 1.73403E+00 1.74384E+00 1.75377E+00 1.76374E+00 1.77371E+00 1.78362E+00 ++ 1.79341E+00 1.80306E+00 1.81252E+00 1.82176E+00 1.83075E+00 1.83947E+00 1.84789E+00 1.85598E+00 1.86373E+00 1.87111E+00 ++ 1.87810E+00 1.88469E+00 1.89086E+00 1.89660E+00 1.90188E+00 1.90670E+00 1.91105E+00 1.91491E+00 1.91828E+00 1.92114E+00 ++ 1.92349E+00 1.92533E+00 1.92664E+00 1.92743E+00 1.92770E+00 1.96448E+00 1.99874E+00 2.03107E+00 2.06189E+00 2.09148E+00 ++ 2.12008E+00 2.14787E+00 2.17499E+00 2.20156E+00 2.22768E+00 2.25346E+00 2.27896E+00 2.30425E+00 2.32942E+00 2.35451E+00 ++ 2.37961E+00 2.40476E+00 2.43003E+00 2.45550E+00 2.48123E+00 2.50731E+00 2.53381E+00 2.56085E+00 2.58854E+00 2.61702E+00 ++ 2.64647E+00 2.67711E+00 2.70921E+00 2.74319E+00 2.77959E+00 2.81928E+00 2.86371E+00 2.91569E+00 2.98254E+00 3.14159E+00 +diff --git a/2020-10-mirror_3D_scripts/pitch_long_i.txt b/2020-10-mirror_3D_scripts/pitch_long_i.txt +new file mode 100644 +index 0000000..de49d7c +--- /dev/null ++++ b/2020-10-mirror_3D_scripts/pitch_long_i.txt +@@ -0,0 +1,15 @@ ++ 0.000000000E+00 1.590490534E-01 2.258985802E-01 2.778836005E-01 3.223102271E-01 3.620017501E-01 3.984047825E-01 4.323793097E-01 4.644872161E-01 4.951208624E-01 ++ 5.245683382E-01 5.530498037E-01 5.807392091E-01 6.077780260E-01 6.342843416E-01 6.603591323E-01 6.860907561E-01 7.115582866E-01 7.368340852E-01 7.619858662E-01 ++ 7.870784373E-01 8.121752455E-01 8.373398344E-01 8.626373084E-01 8.881358978E-01 9.139087343E-01 9.400359728E-01 9.666074475E-01 9.937261353E-01 1.021512844E+00 ++ 1.050112789E+00 1.079705184E+00 1.110517798E+00 1.142850143E+00 1.177112606E+00 1.213897480E+00 1.214162863E+00 1.214952170E+00 1.216265424E+00 1.218101499E+00 ++ 1.220451805E+00 1.223314399E+00 1.226680385E+00 1.230539803E+00 1.234888081E+00 1.239709580E+00 1.244993984E+00 1.250729503E+00 1.256899533E+00 1.263490865E+00 ++ 1.270485659E+00 1.277865479E+00 1.285612671E+00 1.293705420E+00 1.302122526E+00 1.310840321E+00 1.319834092E+00 1.329075726E+00 1.338535765E+00 1.348182895E+00 ++ 1.357977001E+00 1.367881501E+00 1.377849444E+00 1.387825928E+00 1.397755162E+00 1.407560756E+00 1.417160946E+00 1.426459260E+00 1.435322932E+00 1.443620138E+00 ++ 1.451177149E+00 1.457793269E+00 1.463266902E+00 1.467371383E+00 1.469923030E+00 1.671669623E+00 1.674221270E+00 1.678325751E+00 1.683799385E+00 1.690415505E+00 ++ 1.697972515E+00 1.706269722E+00 1.715133393E+00 1.724431707E+00 1.734031898E+00 1.743837491E+00 1.753766726E+00 1.763743210E+00 1.773711152E+00 1.783615652E+00 ++ 1.793409758E+00 1.803056889E+00 1.812516928E+00 1.821758561E+00 1.830752332E+00 1.839470128E+00 1.847887234E+00 1.855979983E+00 1.863727175E+00 1.871106995E+00 ++ 1.878101789E+00 1.884693121E+00 1.890863151E+00 1.896598670E+00 1.901883073E+00 1.906704572E+00 1.911052850E+00 1.914912269E+00 1.918278255E+00 1.921140848E+00 ++ 1.923491154E+00 1.925327229E+00 1.926640483E+00 1.927429790E+00 1.927695174E+00 1.964480048E+00 1.998742511E+00 2.031074856E+00 2.061887470E+00 2.091479865E+00 ++ 2.120079810E+00 2.147866518E+00 2.174985206E+00 2.201556681E+00 2.227683919E+00 2.253456756E+00 2.278955345E+00 2.304252819E+00 2.329417408E+00 2.354514216E+00 ++ 2.379606787E+00 2.404758568E+00 2.430034367E+00 2.455501898E+00 2.481233521E+00 2.507308312E+00 2.533814628E+00 2.560853444E+00 2.588542850E+00 2.617024315E+00 ++ 2.646471791E+00 2.677105438E+00 2.709213344E+00 2.743187871E+00 2.779590904E+00 2.819282426E+00 2.863709053E+00 2.915694073E+00 2.982543600E+00 3.141592654E+00 +diff --git a/2020-10-mirror_3D_scripts/plot_mirror_output.m b/2020-10-mirror_3D_scripts/plot_mirror_output.m +index 86bc30d..b57281f 100644 +--- a/2020-10-mirror_3D_scripts/plot_mirror_output.m ++++ b/2020-10-mirror_3D_scripts/plot_mirror_output.m +@@ -1,45 +1,196 @@ +-function plot_mirror_output(nodes, f_nD, f_nD_analytic, pde) ++function plot_mirror_output(nodes, outputs, pde, opts) + +- x = nodes{1}; +- y = nodes{2}; +- z = nodes{3}; +- +- nx = numel(x); +- ny = numel(y); +- nz = numel(z); +- +- %% ++ n_cgs = 8e14; %equilibrium density in cm.^-3 ++ m_e_cgs = 9.109*10^-28; %electron mass in g ++ m_D_cgs = 3.3443*10^-24; %Deuterium mass in g ++ m_He_cgs = 6.7*10^-24; %helium 4 mass in g ++ m_B_cgs = 1.82*10^-23; %Boron 11 mass in g ++ m_Ne_cgs = 3.3509177*10^-23; %Neon mass in g ++ temp_cgs = 1.6022e-10; %temperature in erg ++ params_cgs.a.n = n_cgs; ++ params_cgs.b.n = n_cgs; ++ params_cgs.b2.n = n_cgs; ++ % params_cgs.a.vth = sqrt(2*temp_cgs/m_e_cgs); ++ % params_cgs.b.vth = sqrt(2*temp_cgs/m_e_cgs); ++ params_cgs.a.m = m_e_cgs; %beam is electrons ++ params_cgs.b.m = m_D_cgs; %background ions ++ params_cgs.b2.m = m_e_cgs; %background electrons ++ params_cgs.e = 4.803*10^-10; %charge in Fr ++ params_cgs.c = 3*10^10; %speed of light in cm/s ++ params_cgs.a.theta = pde.params.a.T_eV/(params_cgs.a.m*params_cgs.c^2); ++ nu_ee = 4*pi*params_cgs.a.n.*params_cgs.e.^4*pde.params.ln_delt/(params_cgs.a.theta^(3/2)... ++ *params_cgs.a.m^3*params_cgs.c^3); ++ franz_conduct = params_cgs.a.n*params_cgs.e^2/(pde.params.b.Z*params_cgs.a.m*nu_ee); ++ x = nodes{1}; ++ y = nodes{2}; ++ nx = numel(x); ++ ny = numel(y); ++ sx = max(1, floor(nx/2)); ++ sy = max(1, floor(2*ny/8)); ++ energy_func_v = @(x) 0.5*pde.params.a.m.*x.^2/(1.602*10^-19); ++ energy_func_z = @(z) z.*0 + 2*pi; ++ current_func_v = @(x) 2*pi*pde.params.a.Z.*pde.params.e.*x; ++ current_func_z = @(x) cos(x); ++ coord = get_realspace_coords(pde,nodes); ++ mass_func = @(x) x.*0 + sqrt(2*pi); ++ zero_func = @(x) x.*0; ++ num_dims = numel(pde.dimensions); ++ moment_func_nD{1} = energy_func_v; ++ moment_func_nD{2} = energy_func_z; ++ mass_func_nD{1} = mass_func; ++ mass_func_nD{2} = mass_func; ++ current_func_nD{1} = current_func_v; ++ current_func_nD{2} = current_func_z; ++ x_E = 0.5.*pde.params.a.m*x.^2/pde.params.e; ++ num_steps = length(outputs.time_array); ++ spitzer_conduct = (3/(4*sqrt(2*pi)))*(4*pi*pde.params.eps0)^2*(1.38e-23*pde.params.a.T_eV*11604)^(3/2)... ++ /(pde.params.b.Z*pde.params.e^2*pde.params.a.m^(1/2)*pde.params.ln_delt); ++ spitzer_conduct2 = 4*pi*pde.params.eps0^2*(pde.params.a.m*pde.params.a.vth^2)^(3/2) ... ++ /(pde.params.a.m^(1/2)*pde.params.e^2*pde.params.ln_delt*pde.params.b2.Z); ++ f1d_analytic = outputs.f_realspace_analytic_nD_t{1,num_steps}; ++ f1d_ic = outputs.f_realspace_analytic_nD_t{1,1}; ++ %getting energy density ++ lev_vec = [opts.lev, opts.lev]; ++ % data = struct2cell(outputs); ++ % f_data = cell2mat(data{6,1}); ++ % f_data = reshape(f_data, [num_steps size(f1d_ic)]); ++% [x_grid, y_grid] = meshgrid(outputs.time_array,x_E); ++ outputs.time_array(1) = 0; ++for i = 1:numel(outputs.time_array) ++ f_data(i,:) = outputs.f_realspace_nD_t{i}(ny/2,:); ++end ++ %contourf(outputs.time_array,x_E,real(f_data)',50); ++% f_data = permute(f_data,[1 3 2]); ++ ++% contour(outputs.time_array',x',squeeze(f_data(:,:,sy))'); ++for j = 1:num_steps ++ %plot(x,f1d); ++ hold on ++ fval_realspace = reshape(outputs.f_realspace_nD_t{j}, [numel(f1d_ic) 1]); ++ mass_vals(j) = moment_integral(lev_vec, opts.deg, coord, fval_realspace, mass_func_nD, pde.dimensions); ++ mass = moment_integral(lev_vec, opts.deg, coord, fval_realspace, mass_func_nD, pde.dimensions); ++ conduct_vals(j) = moment_integral(lev_vec,opts.deg,coord,fval_realspace, current_func_nD,pde.dimensions)/(pde.params.E); ++ conduct_vals(j) = conduct_vals(j)/spitzer_conduct; ++ energy_vals(j) = moment_integral(lev_vec, opts.deg, coord, fval_realspace, moment_func_nD, pde.dimensions)./mass; ++ % vel_vals(i) = sum(outputs.f_realspace_nD_t{1,i}(:).*coord{:,:}*1e-4); ++% x_hint_t = @(t) -x_hint(t,pde.params.a.vel_vals(j),pde.params.a,pde.params.b); ++ %e_hint = integral(x_hint_t, 0, outputs.time_array(j)); ++ %hint_func(j) = energy_vals(1)*exp(-e_hint); ++ for i = 1:length(x) ++ f1d_new(i) = fval_realspace(i); ++ f1d_analytic_new(i) = f1d_analytic(i); ++ end ++ time = outputs.dt*j; ++ %loglog(x,f_data(j,:),'DisplayName',[num2str(time)]); ++ hold on ++end ++legend(); ++hold off ++ %formulating the Hinton solution ++ % timespan = [0 1e-3]; %time span in seconds ++ % x0 = 3e3; %initial energy in eV ++ % y = @(x) sqrt(1.602e-19.*x./(0.5.*3.3443e-27)); %velocity function in terms of energy ++ % [t,E] = ode45(@(t,E) (-params.nu_E(y(E),params.a,params.b)-params.nu_E(y(E),params.a,params.b2)).*E,timespan,x0); ++ %plot(x,f1d_ic,'--'); ++ %plotting Hinton solution alongside numerical values ++ %x = x./x0; ++ %hold on ++ %plot(t,E,'r','LineWidth', 2); ++ %plot(outputs.time_array,energy_vals,'-o','LineWidth',1); ++ %figure ++ %plot(outputs.time_array,mass_vals,'-o','LineWidth',2); ++ %hold off ++ %f_slice = outputs.f_realspace_nD_t{1,num_steps}; ++ %v_norm = x./pde.params.b.vth; ++ %plot(v_norm,f_slice); ++ %figure ++ plot(outputs.time_array,conduct_vals,'-','LineWidth',2); ++ hold on ++ %loglog(x_E,f1d_analytic_new, '-o'); ++ %semilogy(outputs.time_array,hint_func,'k'); ++ % hold off ++% hold off; ++% y = nodes{2}; ++% z = nodes{3}; ++% nx = numel(x); ++% ny = numel(y); ++% ax1 = subplot(2,2,1); ++% contourf(y,x,squeeze(f_nD{1,1}(:,:))'); ++% ax2 = subplot(2,2,2); ++% contourf(y,x,squeeze(f_nD{1,num_steps}(:,:))'); ++ %title('Pitch vs Velocity'); ++ ++% sy = numel(f_nD{1,1}(:,1))/4; ++% sx = 1; ++% f1d = f_nD{1,num_steps}(:,sx); ++% f1d_ic = f_nD{1,1}(:,sx); ++% ax3 = subplot(2,2,3); ++% plot(y,f1d,'-o'); ++% hold on ++% plot(y,f1d_ic, '-'); ++% hold off ++% f1d = f_nD{1,num_steps}(sy,:); ++% f1d_ic = f_nD{1,1}(sy,:); ++% ax4 = subplot(2,2,4); ++% plot(x,f1d,'-o'); ++% hold on ++% plot(x,f1d_ic, '-'); ++ ++% nz = numel(z); ++% num_dims = 3; ++% subset_dimensions = 2; ++% deg = 6; ++% space_func = @(x) x.*0 + 1; ++% energy_func = @(x) x.^2; ++% perp_func = @(x) sin(x).^2; ++% par_func = @(x) cos(x).^2; ++% coord = get_realspace_coords(pde,nodes); ++% moment_func_nD = {energy_func,perp_func,space_func}; ++% % v_perp_temp = moment_integral(pde.get_lev_vec,deg,coord,f_nD,moment_func_nD,pde.dimensions,subset_dimensions); ++% moment_func_nD = {energy_func,par_func,space_func}; ++% % v_par_temp = moment_integral(pde.get_lev_vec,deg,coord,f_nD,moment_func_nD,pde.dimensions,subset_dimensions); ++% %% + % Plot a 1D line through the solution ++ for i = 1:nx ++ for j = 1:ny ++ v_par(i,j) = x(i).*cos(y(j)); ++ v_perp(i,j) = x(i).*sin(y(j)); ++ end ++ end ++% ++% sz = numel(f_nD{1,1}(:,1,1))/2 + 1; ++ + +- sz = numel(f_nD(:,1,1))/2; +- sy = numel(f_nD(1,:,1))/2; +- sx = numel(f_nD(1,1,:)) - 1; +- ++% contourf(v_par,v_perp,outputs.f_realspace_nD_t{1,num_steps}(:,sx)); ++% hold on ++%plot(v_par,fval_realspace); ++% plot(z,v_perp_temp, 'r'); ++% plot(z,v_par_temp, 'b'); ++% hold off + %plotting +- f1d = f_nD(:,sy,sx); +- f1d = f1d(1,:); +- x = nodes{1}; +- y = nodes{2}; +- z = nodes{3}; +- x = 9.109*10^-31*x.^2/(1.602*10^-19); +- plot(z,f1d,'-o'); ++% f1d = f1d(1,:); ++% x = nodes{1}; ++% y = nodes{2}; ++% z = nodes{3}; ++% x = 9.109*10^-31*x.^2/(1.602*10^-19); + %xlim([0.01,1e4]); + %ylim([0.01,1e4]); +- title('Mirror 2D Relaxation'); +- +- %% +- +- %% +- % Overplot analytic solution +- +- if pde.checkAnalytic +- f_1d_analytic = f_nD_analytic(:,sy,sx); +- f_1d_analytic = f_1d_analytic(1,:); +- hold on; +- plot(z,f_1d_analytic,'-'); +- hold off; +- end +- ++% title('Mirror 2D Relaxation'); ++% ++% %% ++% ++% %% ++% % Overplot analytic solution ++% ++% % if pde.checkAnalytic ++% % f_1d_analytic = f_nD_analytic(:,sy,sx); ++% % f_1d_analytic = f_1d_analytic(1,:); ++% hold on; ++% f_1d_analytic = f_nD_analytic{1,2}; ++% plot(x,f_1d_analytic,'-'); ++% hold off; ++% % end ++% + % sx = max(1,floor(nx/2)); + % if nx > 2 + % sx = sx+2; % just to get off the exact middle +@@ -56,12 +207,22 @@ function plot_mirror_output(nodes, f_nD, f_nD_analytic, pde) + % %% + % % Plot 2D + % +-% ax1 = subplot(2,2,3); +-% f_nD_with_noise = f_nD; +-% f_nD_with_noise(1,1) = f_nD_with_noise(1,1)*1.0001; +-% contourf(x,y,f_nD_with_noise,'LineColor','none'); +-% title('numeric 2D solution'); ++% ax1 = subplot(2,3,1); ++% contourf(z,y,squeeze(f_nD{1,num_steps}(:,:,sx))'); ++% title('Space vs. Pitch'); ++% ax2 = subplot(2,3,2); ++% contourf(z,x,squeeze(f_nD{1,num_steps}(:,sy,:))'); ++% title('Space vs. Velocity'); ++% %sx = 46; ++% ax3 = subplot(2,3,3); ++% + % +- +- ++% n_total = zeros(nz, num_steps); ++% for i = 1:num_steps ++% n_total(:,i) = squeeze(sum(f_nD{1,i}, [2 3])); ++% end ++% ax4 = subplot(2,3,5); ++% contourf(z,time_array,squeeze(n_total(:,:))'); ++% title('Number Density vs. Time'); ++ + end +diff --git a/2020-10-mirror_3D_scripts/spitzer_test.m b/2020-10-mirror_3D_scripts/spitzer_test.m +new file mode 100644 +index 0000000..d4e17e6 +--- /dev/null ++++ b/2020-10-mirror_3D_scripts/spitzer_test.m +@@ -0,0 +1,35 @@ ++function spitzer_test() ++ ++% modify PDE ++m_D_cgs = 3.3443*10^-24; %Deuterium mass in g ++m_He_cgs = 6.7*10^-24; %helium 4 mass in g ++m_B_cgs = 1.82*10^-23; %Boron 11 mass in g ++m_vals = 0.001.*[m_D_cgs,m_He_cgs,m_B_cgs]; ++z_vals = [1,2,5]; ++vals.E = 9.17e-05; ++vals.E_D = 73.84; ++vals.Z = 1; ++vals.m = m_vals(1); ++vals.dt = 3.9e-6; ++args = {'timestep_method','BE','case',3,'lev',4, 'deg', 4, 'num_steps', 5,'quiet',true,'save_output',true, 'cmd_args', vals,'update_params_each_timestep', true}; ++opts = OPTS(args); ++pde = mirror2_velocity_div(opts); ++ratio_max = 0.1; ++N = 15; ++ratio = linspace(0.02,ratio_max,N); ++ ++for i = 1:length(ratio) ++ vals.E = ratio(i)*pde.params.E_dreicer_si; ++ vals.dt = 3.9e-6*vals.E/vals.E_D; ++ vals.num_steps = 12*3.9e-6/vals.dt; ++ args{16} = vals; ++ opts = OPTS(args); ++ pde = mirror2_velocity_div(opts); ++ [~,~,~,nodes,~,outputs(i)] = asgard_run_pde(opts,pde); ++ alpha_nr(i,vals.Z) = outputs(i).alpha_t{end}; ++ %plot_mirror_output(nodes,outputs,pde,opts); ++ %legend( sprintf('Z = %g', vals.Z) ); ++end ++semilogy(ratio,alpha_nr(:,1),'LineWidth',5,'DisplayName','ASGarD (nr, Z=1)','color','red'); ++ ++end +\ No newline at end of file +diff --git a/2020-10-mirror_3D_scripts/spitzer_test.m.bak b/2020-10-mirror_3D_scripts/spitzer_test.m.bak +new file mode 100644 +index 0000000..3c0002b +--- /dev/null ++++ b/2020-10-mirror_3D_scripts/spitzer_test.m.bak +@@ -0,0 +1,59 @@ ++function spitzer_test() ++ ++m_D_cgs = 3.3443*10^-24; %Deuterium mass in g ++m_He_cgs = 6.7*10^-24; %helium 4 mass in g ++m_B_cgs = 1.82*10^-23; %Boron 11 mass in g ++m_Ne_cgs = 3.3509177*10^-23; %Neon mass in g ++m_vals = [m_D_cgs,m_He_cgs,m_B_cgs,m_Ne_cgs]/1000; ++ ++z_vals = [1,2,5,10]; ++dt = 0.001; ++ ++for i = 1:length(z_vals) ++ args = {'timestep_method','BE','dt',dt,'lev',4,'deg', 3,'num_steps',3,'update_params_each_timestep', true,'save_output',true,'quiet',true}; ++ opts = OPTS(args); ++ pde = mirror2_velocity_div(opts); ++ lev_vec = [opts.lev, opts.lev]; ++ pde.params.a.m = 9.1093*10^-31; ++ pde.params.b.m = m_vals(i); ++ pde.params.b.Z = z_vals(i); ++ pde.params.a.T_eV = 1000; ++ pde.params.b.T_eV = pde.params.a.T_eV; ++ pde.params.b2.T_eV = pde.params.a.T_eV; ++ pde.params.a.vth = pde.params.v_th(pde.params.a.T_eV,pde.params.a.m); ++ pde.params.b.vth = pde.params.v_th(pde.params.b.T_eV,pde.params.b.m); ++ pde.params.b2.vth = pde.params.v_th(pde.params.b2.T_eV,pde.params.b2.m); ++ pde.params.ln_delt = 15; ++ pde.params.a.n = 8e20; ++ pde.params.e = 1.602*10^-19; %charge in Coulombs ++ E_dreicer_si = pde.params.a.n.*pde.params.e^3*pde.params.ln_delt/(2*pi*pde.params.eps0^2*pde.params.a.m ... ++ *pde.params.a.vth^2); ++ frac = 1e-3; ++ pde.params.E = frac*E_dreicer_si; ++ %vel_norm = @(v,vth) v./vth; %normalized velocity to thermal velocity ++ pde.params.maxwell = @(v,offset,vth) pde.params.a.n/(pi.^(3/2)*vth^3).*exp(-((v-offset)/vth).^2); ++ pde.params.soln_v = @(v,p,t) solution_v(v,p,t); ++ pde.params.f0_v = @(v) pde.params.maxwell(v,0,pde.params.a.vth); ++ pde.params.init_cond_v = @(v,p,t) pde.params.f0_v(v); ++ [err,fval,fval_realspace,nodes,err_realspace] = asgard_run_pde(opts,pde); ++ close all; ++ load('asgard-out-l'+ lev_vec(1) + '-d'+ opts.deg(1) +'-SG-dt'+dt+'-adapt-n.mat'); ++ num_steps = length(outputs.time_array); ++ coord = get_realspace_coords(pde,nodes); ++ f1d_ic = outputs.f_realspace_analytic_nD_t{1,1}; ++ fval_realspace = reshape(outputs.f_realspace_nD_t{num_steps}, [numel(f1d_ic) 1]); ++ current_func_v = @(x) 2*pi*pde.params.a.Z.*pde.params.e.*x; ++ current_func_z = @(x) cos(x); ++ current_func_nD{1} = current_func_v; ++ current_func_nD{2} = current_func_z; ++ conduct_vals(i) = moment_integral(lev_vec,opts.deg,coord,fval_realspace, current_func_nD,pde.dimensions)/(pde.params.E); ++ func = (1 + 1.198*pde.params.b.Z + 0.222*pde.params.b.Z^2)/(1 + 2.966*pde.params.b.Z + 0.753*pde.params.b.Z^2); ++ spitzer_conduct = func*(3/(4*sqrt(2*pi)))*(4*pi*pde.params.eps0)^2*(1.38e-23*pde.params.a.T_eV*11604)^(3/2)... ++ /(pde.params.b.Z*pde.params.e^2*pde.params.a.m^(1/2)*pde.params.ln_delt); ++ conduct_vals(i) = conduct_vals(i)/spitzer_conduct; ++end ++ ++plot(z_vals,conduct_vals); ++ ++ ++end +\ No newline at end of file +diff --git a/2020-10-mirror_3D_scripts/u_j.txt b/2020-10-mirror_3D_scripts/u_j.txt +new file mode 100644 +index 0000000..be3d167 +--- /dev/null ++++ b/2020-10-mirror_3D_scripts/u_j.txt +@@ -0,0 +1,15 @@ ++ 0.00000E+00 2.52242E+07 5.04485E+07 7.56727E+07 1.00897E+08 1.26121E+08 1.51345E+08 1.76570E+08 2.01794E+08 2.27018E+08 ++ 2.52242E+08 2.77467E+08 3.02691E+08 3.27915E+08 3.53139E+08 3.78364E+08 4.03588E+08 4.28812E+08 4.54036E+08 4.79261E+08 ++ 5.04485E+08 5.29709E+08 5.54933E+08 5.80157E+08 6.05382E+08 6.30606E+08 6.55830E+08 6.81054E+08 7.06279E+08 7.31503E+08 ++ 7.56727E+08 7.81951E+08 8.07176E+08 8.32400E+08 8.57624E+08 8.82848E+08 9.08073E+08 9.33297E+08 9.58521E+08 9.83745E+08 ++ 1.00897E+09 1.03419E+09 1.05942E+09 1.08464E+09 1.10987E+09 1.13509E+09 1.16031E+09 1.18554E+09 1.21076E+09 1.23599E+09 ++ 1.26121E+09 1.28644E+09 1.31166E+09 1.33688E+09 1.36211E+09 1.38733E+09 1.41256E+09 1.43778E+09 1.46301E+09 1.48823E+09 ++ 1.51345E+09 1.53868E+09 1.56390E+09 1.58913E+09 1.61435E+09 1.63958E+09 1.66480E+09 1.69002E+09 1.71525E+09 1.74047E+09 ++ 1.76570E+09 1.79092E+09 1.81615E+09 1.84137E+09 1.86659E+09 1.89182E+09 1.91704E+09 1.94227E+09 1.96749E+09 1.99271E+09 ++ 2.01794E+09 2.04316E+09 2.06839E+09 2.09361E+09 2.11884E+09 2.14406E+09 2.16928E+09 2.19451E+09 2.21973E+09 2.24496E+09 ++ 2.27018E+09 2.29541E+09 2.32063E+09 2.34585E+09 2.37108E+09 2.39630E+09 2.42153E+09 2.44675E+09 2.47198E+09 2.49720E+09 ++ 2.52242E+09 2.54765E+09 2.57287E+09 2.59810E+09 2.62332E+09 2.64854E+09 2.67377E+09 2.69899E+09 2.72422E+09 2.74944E+09 ++ 2.77467E+09 2.79989E+09 2.82511E+09 2.85034E+09 2.87556E+09 2.90079E+09 2.92601E+09 2.95124E+09 2.97646E+09 3.00168E+09 ++ 3.02691E+09 3.05213E+09 3.07736E+09 3.10258E+09 3.12781E+09 3.15303E+09 3.17825E+09 3.20348E+09 3.22870E+09 3.25393E+09 ++ 3.27915E+09 3.30438E+09 3.32960E+09 3.35482E+09 3.38005E+09 3.40527E+09 3.43050E+09 3.45572E+09 3.48094E+09 3.50617E+09 ++ 3.53139E+09 3.55662E+09 3.58184E+09 3.60707E+09 3.63229E+09 3.65751E+09 3.68274E+09 3.70796E+09 3.73319E+09 3.75841E+09 +diff --git a/OPTS.m b/OPTS.m +index eeebf8d..7078cda 100644 +--- a/OPTS.m ++++ b/OPTS.m +@@ -194,6 +194,13 @@ classdef OPTS + end + end + ++ if ~strcmp(opts.output_grid,'quadrature') ++ ++ opts.calculate_mass = false; ++ opts.normalize_by_mass = false; ++ ++ end ++ + if ~isempty(fieldnames(input_parser.Unmatched)) + disp('Extra inputs:') + disp(input_parser.Unmatched) +diff --git a/asgard_run_pde.m b/asgard_run_pde.m +index a3934de..07fdec7 100644 +--- a/asgard_run_pde.m ++++ b/asgard_run_pde.m +@@ -75,11 +75,7 @@ end + + for d=1:num_dims + if strcmp(opts.output_grid,'fixed') +- if d==1 +- num_fixed_grid = 51; +- else +- num_fixed_grid = 21; +- end ++ num_fixed_grid = 51; + nodes_nodups{d} = ... + linspace(pde.dimensions{d}.min,pde.dimensions{d}.max,num_fixed_grid); + [Meval{d},nodes{d},nodes_count{d}] = ... +@@ -104,8 +100,8 @@ coord_nodups = get_realspace_coords(pde,nodes_nodups); + if num_dims <=3 + + %% +- % Get the real space solution +- ++ % Get the real space solution ++ + fval_realspace = wavelet_to_realspace(pde,opts,Meval,fval,hash_table); + if ~isempty(pde.solutions) + fval_realspace_analytic = get_analytic_realspace_solution_D(pde,opts,coord,t); +@@ -244,7 +240,9 @@ end + + % need to clean up this interface! + outputs = save_output([],0,pde,opts,num_dims,fval,fval_realspace,f_realspace_analytic_nD,nodes,nodes_nodups,nodes_count,t,dt,toc,root_directory,hash_table); +-%outputs.mass_t = mass_t; ++if opts.calculate_mass ++ outputs.mass_t = mass_t; ++end + + %% Time Loop + count=1; +@@ -527,20 +525,60 @@ for L = 1:opts.num_steps + + if opts.update_params_each_timestep + +- f_p0 = f_realspace_nD(:,1); % get the f(0,z) value (or as close to p=0 as the nodes allow) +-% alpha_z = @(z) (2/sqrt(pi)-interp1(nodes{2},f_p0,z,'spline','extrap'))/dt; +- alpha_z = @(z) (pde.params.f0_p(nodes_nodups{1}(1))-interp1(nodes_nodups{2},f_p0,z,'spline','extrap'))/dt; ++ f_v0 = f_realspace_nD(:,1); % get the f(0,z) value (or as close to p=0 as the nodes allow) ++% alpha_z = @(z) (2/sqrt(pi)-interp1(nodes{2},f_p0,z,'spline','extrap'))/dt; ++% alpha_z = @(z) (pde.params.f0_v(nodes{1}(1))-interp1(nodes{2},f_v0,z,'spline','extrap'))/dt; ++% pde.params.f0_v(nodes_nodups{1}(1))-f_v0 ++ alpha_z = @(z) (pde.params.f0_v(nodes_nodups{1}(1))-interp1(nodes_nodups{2},f_v0,z,'spline','extrap'))/dt; ++% alpha_z = @(z) z.*0; %+ f_v0(1)./dt; + pde.params.alpha_z = alpha_z; +- z = linspace(-1,1,100); ++% z = linspace(0,pi,100); + outputs.alpha_t0{L+1} = alpha_z; +-% outputs.alpha_t{L+1} = sum(alpha_z(z)); ++% outputs.alpha_t{L+1} = sum(alpha_z(z)); + outputs.alpha_t{L+1} = alpha_z(0); +- +- end ++ alpha_z(0) ++ ++ background_species = [pde.params.b, pde.params.b2]; ++ uVals = nodes{1}; ++% for k = 1:numel(background_species) ++% % for i = 1:length(uVals) ++% % uVal = uVals(i); ++% for j = 1:length(lIndex) ++% gamma_a = 4*pi*(params.a.Z)^2*e^4/((params.a.m)^2); ++% % numerVals = mirror_FokkerPlanckCoeffs(numer_func,uVal,lIndex(j),z,params,background_species(k)); ++% coeffVals = @(x) mirror_FokkerPlanckCoeffs(func,x,lIndex(j),z,params,background_species(k)); ++% test_Avals(j) = test_Avals(j) + testVals(1); ++% test_Bvals(j) = test_Bvals(j) + testVals(2); ++% test_Cvals(j) = test_Cvals(j) + testVals(3); ++% test_Dvals(j) = test_Dvals(j) + testVals(4); ++% test_Evals(j) = test_Evals(j) + testVals(5); ++% test_Fvals(j) = test_Fvals(j) + testVals(6); ++% end ++% % total_numA(i) = sum(numer_Avals(i,:)); ++% % total_numB(i) = sum(numer_Bvals(i,:)); ++% % total_numC(i) = sum(numer_Cvals(i,:)); ++% % total_numD(i) = sum(numer_Dvals(i,:)); ++% % total_numE(i) = sum(numer_Evals(i,:)); ++% % total_numF(i) = sum(numer_Fvals(i,:)); ++% pde.params.fp_Coeffs = coeffVals; ++% end ++% % end ++% end + + end + + outputs.pde = pde; + outputs.opts = opts; + ++% delta_mass(1) = 0; ++% for i=1:numel(outputs.mass_t)-1 ++% z=outputs.nodes_t{end}{2}; ++% f=outputs.f_realspace_nD_t{i+1}(:,end); ++% dz=abs(z(1)-z(2)); ++% delta_mass(i+1) = sum(f.*z'*.25*outputs.dt*dz); ++% end ++% plot(outputs.mass_t/outputs.mass_t(1)); ++% hold on ++% plot(cumsum(delta_mass)/outputs.mass_t(1)) ++% plot((outputs.mass_t+cumsum(delta_mass))/outputs.mass_t(1)) + end +diff --git a/asgard_test.m b/asgard_test.m +index 2373f89..13a73d7 100644 +--- a/asgard_test.m ++++ b/asgard_test.m +@@ -322,6 +322,15 @@ disp('Testing fokkerplanck1_momentum_C (CN / TIA)'); + verifyLessThan(testCase,err,5.4e-2); + end + ++function asgard_mirror1_collision_div_test(testCase) ++addpath(genpath(pwd)); ++disp('Testing mirror1_collision_div (matrix_exponential)'); ++[err,act_f,act_frs] = asgard(@mirror1_collision_div,'timestep_method','BE', ... ++ 'lev',4, 'deg', 5,'dt',1e-3,'num_steps',20,'quiet',false,'calculate_mass', true, ... ++ 'normalize_by_mass', true); ++verifyLessThan(testCase,err,2.5e-2); ++end ++ + function end_points_grid_test(testCase) + addpath(genpath(pwd)); + disp('Testing quadrature_with_end_points'); +diff --git a/moment_integral_test.m b/moment_integral_test.m +index 6dff358..963bcdb 100644 +--- a/moment_integral_test.m ++++ b/moment_integral_test.m +@@ -10,23 +10,34 @@ pde = mirror_velocity2(opts); + + num_dims = numel(pde.dimensions); + ++v_th = 0.2; ++ + function ans = my_func_v(v) +- v_th = 0.2; + ans = exp(-v.^2./v_th^2); + end + function ans = my_func_z(z) +- ans = z.*+1; ++ ans = z; + end + + pde.dimensions{1}.min = 0; + pde.dimensions{1}.max = 1; +-pde.dimensions{1}.moment_dV = @(v,p,t) v.^2; ++ + + pde.dimensions{2}.min = 0; + pde.dimensions{2}.max = pi; +-pde.dimensions{2}.moment_dV = @(z,p,t) sin(z); + +-pde = compute_dimension_mass_mat(opts,pde); ++% with jacobian ++pde.dimensions{1}.jacobian = @(v,p,t) v; ++pde.dimensions{2}.jacobian = @(z,p,t) z.*0+1; ++ ++ ++ ++ ++ ++ ++ ++ ++ + + % overwrite the initial conditions for this test + +@@ -46,7 +57,8 @@ coord = get_realspace_coords(pde,nodes); + + t = 0; + fval = initial_condition_vector(pde,opts,hash_table,t); +-fval_realspace = wavelet_to_realspace(pde,opts,Meval,fval,hash_table); ++fval_realspace = wavelet_to_realspace(pde,opts,Meval,fval,hash_table); ++f = singleD_to_multiD(num_dims,fval_realspace,nodes); + + do_plot = 0; + if do_plot +@@ -64,8 +76,8 @@ end + end + + moment_func_nD = {@mass_func_v,@mass_func_z}; +-mass = moment_integral(opts.lev, opts.deg, coord, fval_realspace, moment_func_nD, pde.dimensions); +-mass_analytic = 0.0111367; ++mass = moment_integral(opts.lev, opts.deg, f, moment_func_nD, pde.dimensions,nodes,[1,2]); ++mass_analytic = 0.098696; + diff1 = abs(mass-mass_analytic); + verifyLessThan(testCase, diff1, 1e-6); + +@@ -75,8 +87,8 @@ verifyLessThan(testCase, diff1, 1e-6); + end + + moment_func_nD = {@energy_func_v,@mass_func_z}; +-energy = moment_integral(opts.lev, opts.deg, coord, fval_realspace, moment_func_nD, pde.dimensions); +-energy_analytic = 0.000668199; ++energy = moment_integral(opts.lev, opts.deg, f, moment_func_nD, pde.dimensions,nodes,[1,2]); ++energy_analytic = 0.00394784; + diff2 = abs(energy-energy_analytic); + verifyLessThan(testCase, diff2, 1e-6); + +@@ -89,9 +101,52 @@ verifyLessThan(testCase, diff2, 1e-6); + end + + moment_func_nD = {@random_func_v,@random_func_z}; +-moment = moment_integral(opts.lev, opts.deg, coord, fval_realspace, moment_func_nD, pde.dimensions); +-moment_analytic = 0.00258567; ++moment = moment_integral(opts.lev, opts.deg, f, moment_func_nD, pde.dimensions,nodes,[1,2]); ++moment_analytic = 0.0194818; + diff3 = abs(moment-moment_analytic); + verifyLessThan(testCase, diff3, 1e-6); + ++% check the 1D mass moment of a 2D function, i.e., give back a vector ++ ++% with jacobian but over z only ++moment_func_nD = {@mass_func_v,@mass_func_z}; ++moment = moment_integral(opts.lev, opts.deg, f, moment_func_nD, pde.dimensions,nodes,[2]); ++moment_analytic_fn = @(v) 1/2*exp(-v.^2./v_th^2).*pi^2; ++moment_analytic = moment_analytic_fn(nodes{1}); ++moment_analytic = reshape(moment_analytic,size(moment)); ++diff5 = norm(moment-moment_analytic); ++plot(nodes{1},moment) ++hold on ++plot(nodes{1},moment_analytic,'o') ++hold off ++verifyLessThan(testCase, diff5, 2e-5); ++ ++% with jacobian but over v only ++moment_func_nD = {@mass_func_v,@mass_func_z}; ++moment = moment_integral(opts.lev, opts.deg, f, moment_func_nD, pde.dimensions,nodes,[1]); ++moment_analytic_fn = @(z) 1/2 * (1-exp(-1/v_th^2))*v_th^2.*z; ++moment_analytic = moment_analytic_fn(nodes{2}); ++moment_analytic = reshape(moment_analytic,size(moment)); ++diff6 = norm(moment-moment_analytic); ++plot(nodes{2},moment) ++hold on ++plot(nodes{2},moment_analytic,'o') ++hold off ++verifyLessThan(testCase, diff6, 2e-5); ++ ++% no jacobian and over z only ++pde.dimensions{1}.jacobian = @(v,p,t) v.*0+1; ++pde.dimensions{2}.jacobian = @(v,p,t) v.*0+1; ++moment_func_nD = {@mass_func_v,@mass_func_z}; ++moment = moment_integral(opts.lev, opts.deg, f, moment_func_nD, pde.dimensions,nodes,[2]); ++moment_analytic_fn = @(v) 1/2*exp(-v.^2./v_th^2).*pi^2; ++moment_analytic = moment_analytic_fn(nodes{1}); ++moment_analytic = reshape(moment_analytic,size(moment)); ++diff4 = norm(moment-moment_analytic); ++plot(nodes{1},moment) ++hold on ++plot(nodes{1},moment_analytic,'o') ++hold off ++verifyLessThan(testCase, diff4, 2e-5); ++ + end +diff --git a/moment_integral_test.nb b/moment_integral_test.nb +new file mode 100644 +index 0000000..366152e +--- /dev/null ++++ b/moment_integral_test.nb +@@ -0,0 +1,835 @@ ++(* Content-type: application/vnd.wolfram.mathematica *) ++ ++(*** Wolfram Notebook File ***) ++(* http://www.wolfram.com/nb *) ++ ++(* CreatedBy='Mathematica 12.1' *) ++ ++(*CacheID: 234*) ++(* Internal cache information: ++NotebookFileLineBreakTest 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f034487..f30f8df 100644 +--- a/pdes/fokkerplanck_parameters.m ++++ b/pdes/fokkerplanck_parameters.m +@@ -3,14 +3,8 @@ function p = fokkerplanck_parameters(opts) + %% + % Define a few relevant functions + +-nu_ee = 1; +-v_th = 1; +-E = 0; +-Z = 1; +-tau = 10^5; +-delta = 0.042; +-n = 1; +- ++nuEE = 1; ++vT = 1; + switch opts.case_ + case 1 + delta = 0.042; +@@ -33,43 +27,11 @@ switch opts.case_ + E = 0.4; + tau = 10^5; + case 5 % for the runaway production rate electric field scan +- if isfield(opts.cmd_args,'delta') +- delta = opts.cmd_args.delta; +- end +- if isfield(opts.cmd_args,'E') +- E = opts.cmd_args.E; +- end +- if isfield(opts.cmd_args,'Z') +- Z = opts.cmd_args.Z; +- end +- if isfield(opts.cmd_args,'tau') +- tau = opts.cmd_args.tau; +- end +- if isfield(opts.cmd_args,'nu_ee') +- nu_ee = opts.cmd_args.nu_ee; +- end +- if isfield(opts.cmd_args,'v_th') +- nu_ee = opts.cmd_args.v_th; +- end +- if isfield(opts.cmd_args,'v_th') +- v_th = opts.cmd_args.v_th; +- end +- if isfield(opts.cmd_args,'n') +- n = opts.cmd_args.n; +- end +- +- alpha_z = @(z) z.*0; +- +- disp(['--------']); +- disp(['n: ', num2str(n)]); +- disp(['delta: ', num2str(delta)]); +- disp(['tau: ', num2str(tau)]); % this is relative to the B field or some other thing not present in these calcs +- disp(['E: ', num2str(E), ' (this is E_D/2)']); +- disp(['v_th: ', num2str(v_th)]); +- disp(['nu_ee: ', num2str(nu_ee)]); +- disp(['Z: ', num2str(Z)]); +- disp(['--------']); +- ++ delta = 0.044; ++ Z = 1; ++ E = opts.cmd_args.E; ++ tau = 1.2e5; ++ alpha_z = @(z) z.*0; + end + + phi = @phi_; +@@ -80,51 +42,31 @@ soln_z = @soln_z_; + soln_p = @soln_p_; + + gamma = @(p)sqrt(1+(delta*p).^2); +-vx = @(p)1/v_th*(p./gamma(p)); +- +-Ca = @(p)nu_ee*v_th^2*(psi(vx(p))./vx(p)); ++vx = @(p)1/vT*(p./gamma(p)); + +-% Cb = @(p)1/2*nu_ee*v_th^2*1./vx(p).*(Z+phi(vx(p))-psi(vx(p))+delta^4*vx(p).^2/2); ++Ca = @(p)nuEE*vT^2*(psi(vx(p))./vx(p)); + +-function ans = cb_fun(p) +-% disp(Z); +- ans = 1/2*nu_ee*v_th^2*1./vx(p).*(Z+phi(vx(p))-psi(vx(p))+delta^4*vx(p).^2/2); +-% disp(ans); +-end +-Cb = @(p) cb_fun(p); ++Cb = @(p)1/2*nuEE*vT^2*1./vx(p).*(Z+phi(vx(p))-psi(vx(p))+delta^4*vx(p).^2/2); + +-Cf = @(p)2*nu_ee*v_th*psi(vx(p)); ++Cf = @(p)2*nuEE*vT*psi(vx(p)); + + function ret = phi_(x) + ret = erf(x); + end + +- function ret = psi_(x,t) ++ function ret = psi_(x,t) + dphi_dx = 2./sqrt(pi) * exp(-x.^2); +- ret = 1./(2*x.^2) .* (phi(x) - x.*dphi_dx); ++ ret = 1./(2*x.^2) .* (phi(x) - x.*dphi_dx); + ix = find(abs(x)<1e-5); % catch singularity at boundary + ret(ix) = 0; + end + +-% function ret = psi2(x,t) +-% phi2 = erf(x); +-% dphi_dx = 2./sqrt(pi) * exp(-x.^2); +-% ret = 1./(2*x.^2) .* (phi2 - x.*dphi_dx); +-% end +- + function ret = f0_z_(x) + test = opts.case_; + ret = zeros(size(x)); + switch test + case 1 +- % ret = x.*0+1; +- for i=1:numel(x) +- if x(i) <= 0 +- ret(i) = 3/(2*5^3); +- else +- ret(i) = 0; +- end +- end ++ ret = x.*0+1; + case 2 + ret = x.*0+1; + case 3 +@@ -147,7 +89,7 @@ Cf = @(p)2*nu_ee*v_th*psi(vx(p)); + end + + function ret = f0_p_(x) +- test = opts.case_; ++ test = opts.case_; + ret = zeros(size(x)); + switch test + +@@ -160,7 +102,7 @@ Cf = @(p)2*nu_ee*v_th*psi(vx(p)); + end + end + +- case 2 ++ case 2 + a = 2; + ret = 2/(sqrt(pi)*a^3) * exp(-x.^2/a^2); + case 3 +@@ -175,34 +117,21 @@ Cf = @(p)2*nu_ee*v_th*psi(vx(p)); + x1 = i*h; + [xi,w] = lgwt(20,x0,x1); + Q = Q+sum(w.*Fun(xi).*xi.^2); +- end ++ end + ret = exp(-2/delta^2*sqrt(1+delta^2*x.^2))/(2*Q); +- case 5 +- ret = n * 2/(sqrt(pi)*v_th^3) * exp(-x.^2/v_th^2); ++ case 5 ++ a = 1; ++ ret = 2/(sqrt(pi)*a^3) * exp(-x.^2/a^2); + end + end + +- function ret = soln_z_(x,p,t) ++ function ret = soln_z_(x,~) + ret = x.*0+1; + end +- function ret = soln_p_(x,p,t) ++ function ret = soln_p_(x,t) + ret = 2/sqrt(pi) * exp(-x.^2); +- if isfield(p,'norm_fac') +- ret = p.norm_fac .* ret; +- end + end + +-% % look at a few of these functions +-% +-% p = linspace(0,10,100); +-% figure +-% plot(p,Ca(p)); +-% hold on +-% plot(p,sqrt(psi(p)./p)); +-% plot(p,sqrt(psi2(p)./p),'LineStyle','--'); +-% legend('Ca','psi','psi2'); +-% hold off +- + % throw all these into a parameters structure for use elsewhere + + save_filename = 'parameters.mat'; +diff --git a/pdes/mirror1_collision.m b/pdes/mirror1_collision.m +new file mode 100644 +index 0000000..b9997cc +--- /dev/null ++++ b/pdes/mirror1_collision.m +@@ -0,0 +1,107 @@ ++function pde = mirror1_collision(opts) ++ ++%Testing the collision operator for the 1D form of the mirror equations ++% ++% df/dt = 1/v^2 (flux_v) ++% ++% flux_v == v^3[(m_a/(m_a + m_b))nu_s f) + 0.5*nu_par*v*d/dv(f)] ++% ++% df/dt = 1/v^2 (d/dv(v^3[(m_a/(m_a + m_b))nu_s f) + 0.5*nu_par*v*d/dv(f)])*v^2 ++% ++% Run with ++% ++% asgard(@mirror1_collision,'timestep_method','BE','dt',1e-5,'num_steps',50,'lev',5,'deg',2,'normalize_by_mass',false, 'calculate_mass', false) ++ ++params = mirror_parameters(); ++ ++%% Define the dimensions ++ ++dim_v = DIMENSION(0,1e6); ++dim_v.jacobian = @(v,p,t) 4*pi.*v.^2; ++dimensions = {dim_v}; ++num_dims = numel(dimensions); ++ ++%% Define the analytic solution (optional) ++ ++% function ret = solution(v,p,t) ++% ret = p.soln_v(v,p,t); ++% if isfield(p,'norm_fac') ++% ret = p.norm_fac .* ret; ++% end ++% end ++soln_v = @solution_v; ++ function ret = solution_v(v,p,t) ++ ret = p.maxwell(v,0,p.v_th(p.b.T_eV,p.a.m)); ++ if isfield(p,'norm_fac') ++ ret = p.norm_fac .* ret; ++ end ++ end ++ ++soln1 = new_md_func(num_dims,{soln_v}); ++solutions = {soln1}; ++ ++%% Define the initial conditions ++ ++ic_v = @(v,p,t) p.init_cond_v(v); ++ic1 = new_md_func(num_dims,{ic_v}); ++initial_conditions = {ic1}; ++ ++%% Define the boundary conditions ++ ++%% Define the boundary conditions ++ ++BCL = new_md_func(num_dims,{... ++ @(v,p,t) v.*0, ... ++ params.boundary_cond_t}); ++ ++ ++BCR = new_md_func(num_dims,{... ++ params.boundary_cond_v, ... ++ params.boundary_cond_t}); ++ ++% term V1 == 1/v^2 d/dv(v^3(m_a/(m_a + m_b))nu_s f)) ++% term V1 == g(v) q(v) [mass, g(v) = 1/v^2, BC N/A] ++% q(v) == d/dv(g2(v)f(v)) [grad, g2(v) = v^3(m_a/(m_a + m_b))nu_s, BCL= N, BCR=N] ++ ++g1 = @(v,p,t,dat) 1./v.^2;%v.*0 + 1; ++g2 = @(v,p,t,dat) v.^3*p.a.m.*p.nu_s(v,p.a,p.b)./(p.a.m + p.b.m); ++ ++pterm1 = MASS(g1); ++pterm2 = GRAD(num_dims,g2,0,'N','D', BCL, BCR); ++termV_s = SD_TERM({pterm1,pterm2}); ++termV1 = MD_TERM(num_dims,{termV_s}); ++ ++%% ++% term V2 == 1/v^2 d/dv(v^4*0.5*nu_par*d/dv(f)) ++% term V2 == g(v) q(v) [mass, g(v) = 1/v^2, BC N/A] ++% q(v) == d/dv(g2(v)r(v)) [grad, g2(v) = v^4*0.5*nu_par, BCL= D, BCR=D] ++% r(v) = d/dv(g3(v)f) [grad, g3(v) = 1, BCL=N, BCR=N] ++ ++g1 = @(v,p,t,dat) 1./v.^2; %v.*0 + 1; ++g2 = @(v,p,t,dat) v.^4.*0.5.*p.nu_par(v,p.a,p.b); ++g3 = @(v,p,t,dat) v.*0 + 1; ++ ++pterm1 = MASS(g1); ++pterm2 = GRAD(num_dims,g2,-1,'D','N'); ++pterm3 = GRAD(num_dims,g3,+1,'N','D', BCL, BCR); ++termV_par = SD_TERM({pterm1,pterm2,pterm3}); ++termV2 = MD_TERM(num_dims,{termV_par}); ++ ++terms = {termV1,termV2}; ++ ++%% Define sources ++ ++sources = {}; ++ ++%% Define function to set time step ++ function dt=set_dt(pde,CFL) ++ Lmax = pde.dimensions{1}.max; ++ LevX = pde.dimensions{1}.lev; ++ dt = Lmax/2^LevX*CFL; ++ end ++ ++%% Construct PDE ++ ++pde = PDE(opts,dimensions,terms,[],sources,params,@set_dt,[],initial_conditions,solutions); ++ ++end +\ No newline at end of file +diff --git a/pdes/mirror1_collision_div.m b/pdes/mirror1_collision_div.m +new file mode 100644 +index 0000000..203a398 +--- /dev/null ++++ b/pdes/mirror1_collision_div.m +@@ -0,0 +1,157 @@ ++function pde = mirror1_collision_div(opts) ++ ++%Testing the collision operator for the 1D form of the mirror equations ++% ++% df/dt == 1/v^2 (d/dv(v^2[v (m_a/(m_a + m_b))nu_s f) + 0.5*nu_par*v^2*d/dv(f)]) ++% == 1/v^2 (d/dv (v^2[0.5*nu_par*v^2*d/dv(f)]) %%term1 ++% + 1/v^2 (d/dv(v^2[v (m_a/(m_a + m_b))nu_s f)]) %%term2 ++ % ++% v is a spherical coordinate (v,th,phi), so the div and grad look like ++% ++% div[] = 1/v^2 * d/dv * v^2[], grad[] = d/dv[] ++% ++% and the volument_element dV = v^2 ++% ++% ++% split into two div(flux) terms (term1 and term2) ++% ++% term1 is done using SLDG defining A(v)= sqrt(0.5*nu_par*v^2) ++% ++% eq1 : df/dt == div(A(v) * q) [pterm1: div (g(v)=A(v),+1, BCL=?, BCR=?)] ++% eq2 : q == A(v) * grad(f) [pterm2: grad(g(v)=A(v),-1, BCL=D, BCR=N)] ++% ++% term2 is a div using B(v) = v (m_a/(m_a + m_b))nu_s ++% ++% eq1 : df/dt == div(B(v) * f) [pterm1: div(g(p)=B(v),+1, BCL=?, BCR=?] ++% ++% ++% Run with ++% ++% asgard(@mirror1_collision_div,'timestep_method','BE','dt',1e-5,'num_steps',50,'lev',5,'deg',2,'normalize_by_mass',false, 'calculate_mass', false) ++ ++params = mirror_parameters(opts); ++ ++%% Define the dimensions ++ ++dim_v = DIMENSION(0,1e6); ++dV_v = @(x,p,t,d) x.^2; ++dim_v.moment_dV = dV_v; ++dimensions = {dim_v}; ++num_dims = numel(dimensions); ++ ++%% Define the analytic solution (optional) ++ ++% function ret = solution(v,p,t) ++% ret = p.soln_v(v,p,t); ++% if isfield(p,'norm_fac') ++% ret = p.norm_fac .* ret; ++% end ++% end ++soln_v = @solution_v; ++ function ret = solution_v(v,p,t) ++ ret = p.maxwell(v,0,p.v_th(p.b.T_eV,p.a.m))./p.a.n; ++ if isfield(p,'norm_fac') ++ ret = p.norm_fac .* ret; ++ end ++ end ++ ++soln1 = new_md_func(num_dims,{soln_v}); ++solutions = {soln1}; ++ ++%% Define the initial conditions ++ ++ic_v = @(v,p,t) p.init_cond_v(v)./p.a.n; ++ic1 = new_md_func(num_dims,{ic_v}); ++initial_conditions = {ic1}; ++ ++%% LHS terms (mass only) ++ ++LHS_terms = {}; ++ ++%% Define the boundary conditions ++ ++%% Define the boundary conditions ++ ++BCL = new_md_func(num_dims,{... ++ @(v,p,t) v.*0, ... ++ params.boundary_cond_t}); ++ ++ ++BCR = new_md_func(num_dims,{... ++ params.boundary_cond_v, ... ++ params.boundary_cond_t}); ++ ++ ++%% ++% term1 is done using SLDG defining A(v)= sqrt(0.5*nu_par*v^2) ++% ++% eq1 : df/dt == div(A(v) * q) [pterm1: div (g(v)=A(v),+1, BCL=?, BCR=?)] ++% eq2 : q == A(v) * grad(f) [pterm2: grad(g(v)=A(v),-1, BCL=D, BCR=N)] ++ ++A = @(v,p) sqrt(0.5.*v.^2.*p.nu_par(v,p.a,p.b)); ++g1 = @(v,p,t,dat) A(v,p); ++g2 = @(v,p,t,dat) A(v,p); ++ ++pterm1 = DIV (num_dims,g1,'',+1,'D','N','','','',dV_v); ++pterm2 = GRAD(num_dims,g2,'',-1,'N','D','','','',dV_v); ++term1_v = SD_TERM({pterm1,pterm2}); ++term1 = MD_TERM(num_dims,{term1_v}); ++ ++% term2 is a div using B(v) = v (m_a/(m_a + m_b))nu_s ++% ++% eq1 : df/dt == div(B(v) * f) [pterm1: div(g(p)=B(v),+1, BCL=?, BCR=?] ++ ++B = @(v,p) v*p.a.m.*p.nu_s(v,p.a,p.b)./(p.a.m + p.b.m); ++g3 = @(v,p,t,dat) B(v,p); ++ ++pterm3 = DIV(num_dims,g3,'',-1,'N','D','','','',dV_v); ++ ++term2_v = SD_TERM({pterm3}); ++term2 = MD_TERM(num_dims,{term2_v}); ++ ++%repeating but adding second background species ++ ++% term3 is done using SLDG defining A(v)= sqrt(0.5*nu_par*v^2) ++% ++% eq1 : df/dt == div(A(v) * q) [pterm1: div (g(v)=A(v),+1, BCL=?, BCR=?)] ++% eq2 : q == A(v) * grad(f) [pterm2: grad(g(v)=A(v),-1, BCL=D, BCR=N)] ++ ++A = @(v,p) sqrt(0.5.*v.^2.*p.nu_par(v,p.a,p.b2)); ++g1 = @(v,p,t,dat) A(v,p); ++g2 = @(v,p,t,dat) A(v,p); ++ ++pterm1 = DIV (num_dims,g1,'',+1,'D','N','','','',dV_v); ++pterm2 = GRAD(num_dims,g2,'',-1,'N','D','','','',dV_v); ++term3_v = SD_TERM({pterm1,pterm2}); ++term3 = MD_TERM(num_dims,{term3_v}); ++ ++% term4 is a div using B(v) = v (m_a/(m_a + m_b2))nu_s ++% ++% eq1 : df/dt == div(B(v) * f) [pterm1: div(g(p)=B(v),+1, BCL=?, BCR=?] ++ ++B = @(v,p) v*p.a.m.*p.nu_s(v,p.a,p.b2)./(p.a.m + p.b2.m); ++g3 = @(v,p,t,dat) B(v,p); ++ ++pterm3 = DIV(num_dims,g3,'',-1,'N','D','','','',dV_v); ++ ++term4_v = SD_TERM({pterm3}); ++term4 = MD_TERM(num_dims,{term4_v}); ++ ++terms = {term1,term2,term3,term4}; ++ ++%% Define sources ++ ++sources = {}; ++ ++%% Define function to set time step ++ function dt=set_dt(pde,CFL) ++ Lmax = pde.dimensions{1}.max; ++ LevX = pde.dimensions{1}.lev; ++ dt = Lmax/2^LevX*CFL; ++ end ++ ++%% Construct PDE ++ ++pde = PDE(opts,dimensions,terms,LHS_terms,sources,params,@set_dt,[],initial_conditions,solutions); ++ ++end +\ No newline at end of file +diff --git a/pdes/mirror1_pitch.m b/pdes/mirror1_pitch.m +index 8c9c4ce..405907b 100644 +--- a/pdes/mirror1_pitch.m ++++ b/pdes/mirror1_pitch.m +@@ -6,10 +6,10 @@ function pde = mirror1_pitch(opts) + % distribution that has a Maxwellian form. + % PDE: + % +-% df/dt == nu_D/(2*sin(z)) d/dz ( sin(z) df/dz ) ++% df/dt == -cos(z)*f + nu_D/(2*sin(z)) d/dz ( sin(z) df/dz ) + % + % nu_D is the deflection frequency +-% Domain is [-pi,pi] ++% Domain is [0,pi] + % Homogeneous Neumann boundary condition + % Code will be added to equation involving velocity dimension + % +@@ -19,7 +19,7 @@ function pde = mirror1_pitch(opts) + % Run with + % + % implicit +-% asgard(@mirror1_pitch,'timestep_method','matrix_exponential','dt',5e-7,'num_steps',20,'lev',3,'deg',3); ++% asgard(@mirror1_pitch,'timestep_method','BE','dt',5e-7,'num_steps',20,'lev',3,'deg',3, 'calculate_mass', true, 'normalize_by_mass', true); + % + + function ret = psi(x) +@@ -31,29 +31,29 @@ function pde = mirror1_pitch(opts) + end + + %Background Parameters +-k_b = 1.380*10^-23; %Boltzmann constant in Joules/Kelvin ++boltz = 1.380*10^-23; %Boltzmann constant in Joules/Kelvin + n_b = 10^19; %background density in SI units (particles/m.^3) +-T_b = 116050; %background temperature in Kelvin +-z_b = 1; %atomic number of background specie ++temp_b = 116050; %background temperature in Kelvin ++% z_b = 1; %atomic number of background specie + m_b = 9.109*10^-31; %background mass in kg +-v_b = sqrt(2*k_b*T_b/m_b); %background velocity in m/s +-eps_o = 8.85*10^-12; %permittivity of free space in Farad/m +- +-%Target Specie Parameters +-z_a = 1; +-e = 1.602*10^-19; %charge in Coulombs +-ln_Delt = 10; %Coulomb logarithm +-m_a = 1.6726*10^-27; %target mass in kg +-L_ab = (e^2/(m_a*eps_o))^2; %Coefficient accounting for Coluomb force ++v_b = sqrt(2*boltz*temp_b/m_b); %background velocity in m/s ++% eps_o = 8.85*10^-12; %permittivity of free space in Farad/m ++% ++% %Target Specie Parameters ++% z_a = 1; ++% e = 1.602*10^-19; %charge in Coulombs ++% ln_Delt = 10; %Coulomb logarithm ++% m_a = 1.6726*10^-27; %target mass in kg ++% coeff_ab = (e^2/(m_a*eps_o))^2; %Coefficient accounting for Coluomb force + nu_D = 10^4; %deflection frequency in s^-1 + + %Initial parameters for target specie +-n_o = 0.5*n_b; %initial number density for specie at specific velocity +-v_o = 0.5*v_b; %initial known velocity ++ n_o = 0.5*n_b; %initial number density for specie at specific velocity ++ v_o = 0.5*v_b; %initial known velocity + + %% Define the dimensions + +-dim_z = DIMENSION(0,pi/2); ++dim_z = DIMENSION(0,pi); + dim_z.jacobian = @(z,p,t) sin(z); + dimensions = {dim_z}; + num_dims = numel(dimensions); +@@ -83,15 +83,30 @@ BCR = soln1; + % Here we have 1 term1, having only nDims=1 (x) operators. + + %% +-% termC == nu_D/(2*sin(z))*d/dz sin(z)*df/dz ++ ++% LHS_term == df/dt sin(z) ++g1 = @(z,p,t,dat) dim_z.jacobian(z,p,t); ++pterm1 = MASS(g1); ++LHS_term_z = SD_TERM({pterm1}); ++LHS_term = MD_TERM(num_dims,{LHS_term_z}); ++LHS_terms = {LHS_term}; ++ ++%term V2 == -cos(z)*f ++%term V2 == g1(v)*f [mass, g1(v) = -cos(z), BC = N/A] ++g1 = @(z,p,t,dat) -cos(z); ++pterm1 = MASS(g1); ++termM_z = SD_TERM({pterm1}); ++termM= MD_TERM(num_dims,{termM_z}); ++ ++% termC == nu_D/(2sin(z))*d/dz sin(z)*df/dz + % + % becomes + % +-% termC == g1(z) q(z) [mass, g1(p) = nu_D/(2*sin(z)), BC N/A] ++% termC == g1(z) q(z) [mass, g1(p) = nu_D/2, BC N/A] + % q(p) == d/dz g2(z) r(z) [grad, g2(p) = sin(z), BCL=N,BCR=D] + % r(p) == d/dp g3(z) f(z) [grad, g3(p) = 1, BCL=D,BCR=N] + +-g1 = @(z,p,t,dat) nu_D./(2*sin(z)); ++g1 = @(z,p,t,dat) nu_D./(2.*sin(z)); + g2 = @(z,p,t,dat) sin(z); + g3 = @(z,p,t,dat) z.*0 + 1; + pterm1 = MASS(g1); +@@ -100,7 +115,7 @@ pterm3 = GRAD(num_dims,g3,-1,'N','D', BCL, BCR); + termC_z = SD_TERM({pterm1,pterm2,pterm3}); + termC = MD_TERM(num_dims,{termC_z}); + +-terms = {termC}; ++terms = {termM,termC}; + + %% Define some parameters and add to pde object. + % These might be used within the various functions below. +diff --git a/pdes/mirror1_pitch_div.m b/pdes/mirror1_pitch_div.m +new file mode 100644 +index 0000000..90a61d1 +--- /dev/null ++++ b/pdes/mirror1_pitch_div.m +@@ -0,0 +1,133 @@ ++function pde = mirror1_pitch_div(opts) ++% PDE using the 1D Diffusion Equation for a case involving pitcha angle to axis \ ++% of the magnetic field line in a mirror configuration. This PDE is ++% time dependent (although not all the terms are time dependent). The test ++% particle is a hydrogen ion colliding with a background electron ++% distribution that has a Maxwellian form. ++% PDE: ++% ++% df/dt == -cos(z)*f + 1/sin(z) d/dz ( sin(z) nu_D/2 df/dz ) ++% ++% nu_D is the deflection frequency ++% Domain is [0,pi] ++% Homogeneous Neumann boundary condition ++% Code will be added to equation involving velocity dimension ++% ++% Diffusion term is dealt with via LDG, i.e., splitting into two first ++% order equations ++% ++% Run with ++% ++% implicit ++% asgard(@mirror1_pitch_div,'timestep_method','BE','dt',5e-7,'num_steps',20,'lev',3,'deg',3, 'calculate_mass', true, 'normalize_by_mass', true); ++% ++ ++ function ret = psi(x) ++ ++ phi = erf(x); ++ dphi_dx = 2./sqrt(pi) * exp(-x.^2); ++ ++ ret = 1./(2*x.^2) .* (phi - x.*dphi_dx); ++ end ++ ++%Background Parameters ++boltz = 1.380*10^-23; %Boltzmann constant in Joules/Kelvin ++n_b = 10^19; %background density in SI units (particles/m.^3) ++temp_b = 116050; %background temperature in Kelvin ++% z_b = 1; %atomic number of background specie ++m_b = 9.109*10^-31; %background mass in kg ++v_b = sqrt(2*boltz*temp_b/m_b); %background velocity in m/s ++% eps_o = 8.85*10^-12; %permittivity of free space in Farad/m ++% ++% %Target Specie Parameters ++% z_a = 1; ++% e = 1.602*10^-19; %charge in Coulombs ++% ln_Delt = 10; %Coulomb logarithm ++% m_a = 1.6726*10^-27; %target mass in kg ++% coeff_ab = (e^2/(m_a*eps_o))^2; %Coefficient accounting for Coluomb force ++nu_D = 10^4; %deflection frequency in s^-1 ++ ++%Initial parameters for target specie ++ n_o = 0.5*n_b; %initial number density for specie at specific velocity ++ v_o = 0.5*v_b; %initial known velocity ++ ++%% Define the dimensions ++ ++dim_th = DIMENSION(0,pi); ++dV_th = @(x,p,t,d) sin(x); ++dim_th.moment_dV = dV_th; ++ ++dimensions = {dim_th}; ++num_dims = numel(dimensions); ++ ++%% Define the analytic solution (optional) ++ ++soln_z = @(z,p,t) n_o.*cos(z); ++soln_t = @(t,p) exp(-nu_D*t); ++soln1 = new_md_func(num_dims,{soln_z,soln_t}); ++solutions = {soln1}; ++ ++%% Define the initial conditions ++ ++ic1 = soln1; ++initial_conditions = {ic1}; ++ ++%% Define the boundary conditions ++ ++bcl_x = @(x,p,t) x.*0; ++bcl_t = soln_t; ++BCL = new_md_func(num_dims,{bcl_x,bcl_t}); ++ ++BCR = soln1; ++ ++%% Define the terms of the PDE ++% ++% Here we have 1 term1, having only nDims=1 (x) operators. ++ ++%% ++ ++%term V2 == -cos(z)*f ++%term V2 == g1(v)*f [mass, g1(v) = -cos(z), BC = N/A] ++g1 = @(z,p,t,dat) -cos(z); ++pterm1 = MASS(g1,'','',dV_th); ++termM_z = SD_TERM({pterm1}); ++termM = MD_TERM(num_dims,{termM_z}); ++ ++% termC is done using SLDG defining C(v) = sqrt(nu_D(v)/2) ++% ++% eq1 : df/dt == div( q) [pterm1: div (g(v)=C(v),+1, BCL=D, BCR=D] ++% eq2 : q == grad(f) [pterm2: grad(g(v)=C(v),-1, BCL=N, BCR=N] ++ ++ ++D = @(v,p) v.*0 + sqrt(nu_D/2); ++g5 = @(v,p,t,dat) D(v,p); ++pterm1 = DIV (num_dims,g5,'',+1,'D','D','','','',dV_th); ++pterm2 = GRAD(num_dims,g5,'',-1,'N','N','','','',dV_th); ++termC_z = SD_TERM({pterm1,pterm2}); ++termC = MD_TERM(num_dims,{termC_z}); ++ ++terms = {termM,termC}; ++ ++%% Define some parameters and add to pde object. ++% These might be used within the various functions below. ++ ++params.parameter1 = 0; ++params.parameter2 = 1; ++ ++%% Define sources ++ ++sources = {}; ++ ++ function dt=set_dt(pde,CFL) ++ dims = pde.dimensions; ++ % for Diffusion equation: dt = C * dx^2 ++ lev = dims{1}.lev; ++ dx = 1/2^lev; ++ dt = CFL*dx^2; ++ end ++ ++%% Construct PDE ++ ++pde = PDE(opts,dimensions,terms,[],sources,params,@set_dt,[],initial_conditions,solutions); ++ ++end +\ No newline at end of file +diff --git a/pdes/mirror1_space_div.m b/pdes/mirror1_space_div.m +new file mode 100644 +index 0000000..86a2e6b +--- /dev/null ++++ b/pdes/mirror1_space_div.m +@@ -0,0 +1,112 @@ ++function pde = mirror1_space_div(opts) ++% 1D mirror case along magnetic axis direction, i.e., ++% ++% df/dt f B(s) == -cos(pi/4)*df/ds B(s) - cos(pi/4)*dB/ds/B(s) f B(s) ++% ++% Run with ++% ++% explicit ++% asgard(@mirror1_space_div, 'calculate_mass', false, 'normalize_by_mass', false) ++ ++% implicit ++% asgard(@mirror1_space_div,'timestep_method','BE', 'calculate_mass', true, 'normalize_by_mass', true) ++ ++params = mirror_parameters(opts); ++ ++params.B_func = @(s) exp(s); %magnetic field as a function of spatial coordinate ++params.dB_ds = @(s) params.B_func(s); %derivative of magnetic field ++ ++params.vel_test = 1; %test value for velocity in coefficient ++params.pitch_test = pi/4; %test value for pitch angle in coefficient ++decay_coeff = @(v,z) v.*cos(z); ++ ++%% Define the dimensions ++ ++dim_s = DIMENSION(-3,3); ++dV_s = @(x,p,t,d) params.B_func(x); ++dim_s.moment_dV = dV_s; ++dimensions = {dim_s}; ++num_dims = numel(dimensions); ++ ++%% Define the analytic solution ++ ++sol_s = @(s,p,t) exp(s); ++sol_t = @(t,p) exp(-2*decay_coeff(params.vel_test,params.pitch_test).*t); ++soln1 = new_md_func(num_dims,{sol_s,sol_t}); ++solutions = {soln1}; ++ ++%% Define the initial conditions ++ ++ic1 = new_md_func(num_dims,{sol_s}); ++initial_conditions = {ic1}; ++ ++%% Define the boundary conditions ++ ++BCL = soln1; ++BCR = soln1; ++ ++%% Define the terms of the PDE ++% ++ ++% We have an advection and mass term ++ ++%% Advection term ++% -B(s)*d(vtest*cos(ztest)f)/ds ++g1 = @(s,p,t,dat) s.*0 - decay_coeff(p.vel_test,p.pitch_test)*(p.pitch_test > pi/2); ++pterm1 = DIV(num_dims,g1,'',-1,'D','D','','','', dV_s); ++%pterm1 = GRAD(num_dims,g1,-1,'N','N'); ++term1a_s = SD_TERM({pterm1}); ++term1a = MD_TERM(num_dims,{term1a_s}); ++ ++g1 = @(s,p,t,dat) s.*0 - decay_coeff(p.vel_test,p.pitch_test)*(p.pitch_test < pi/2); ++pterm1 = DIV(num_dims,g1,'',+1,'D','D','','','', dV_s); ++%pterm1 = GRAD(num_dims,g1,-1,'N','N'); ++term1b_s = SD_TERM({pterm1}); ++term1b = MD_TERM(num_dims,{term1b_s}); ++ ++%% ++% Add terms to the pde object ++ ++%% Mass term ++% B(s)*(vcosz/B)dB/ds f ++g2 = @(s,p,t,dat) s.*0 - decay_coeff(p.vel_test,p.pitch_test).*(p.dB_ds(s)./p.B_func(s)).*(p.pitch_test < pi/2).*(p.B_func(s) > 0); ++pterm1 = MASS(g2,'','',dV_s); ++termB1a = SD_TERM({pterm1}); ++ ++term2a = MD_TERM(num_dims,{termB1a}); ++ ++g2 = @(s,p,t,dat) s.*0 - decay_coeff(p.vel_test,p.pitch_test).*(p.dB_ds(s)./p.B_func(s)).*(p.pitch_test > pi/2).*(p.B_func(s) < 0); ++pterm1 = MASS(g2,'','',dV_s); ++termB1b = SD_TERM({pterm1}); ++ ++term2b = MD_TERM(num_dims,{termB1b}); ++ ++terms = {term1a,term1b,term2a,term2b}; ++ ++%% Define some parameters and add to pde object. ++% These might be used within the various functions below. ++ ++params.parameter1 = 0; ++params.parameter2 = 1; ++ ++%% Define sources ++ ++sources = {}; ++ ++%% Define function to set time step ++ ++ function dt=set_dt(pde,CFL) ++ dim = pde.dimensions{1}; ++ lev = dim.lev; ++ xMax = dim.max; ++ xMin = dim.min; ++ xRange = xMax-xMin; ++ dx = xRange/(2^lev); ++ dt = CFL*dx; ++ end ++ ++%% Construct PDE ++ ++pde = PDE(opts,dimensions,terms,[],sources,params,@set_dt,[],initial_conditions,solutions); ++ ++end +diff --git a/pdes/mirror1_velocity.m b/pdes/mirror1_velocity.m +index 6a104f8..c11eb8d 100644 +--- a/pdes/mirror1_velocity.m ++++ b/pdes/mirror1_velocity.m +@@ -1,21 +1,25 @@ + function pde = mirror1_velocity(opts) +-% One-dimensional magnetic mirror from the FP paper - evolution of the ion velocity dependence ++% Strong form of one-dimensional magnetic mirror from the FP paper - evolution of the ion velocity dependence + % of f in the presence of Coulomb collisions with background electrons + % +-% df/dt == 1/v^2 (d/dv(flux_v)) ++% df/dt == -(1 - v^2/2*sin^2(pi/4))*cos(pi/4)*df/dv - v*cos(pi/4)*f + 1/v^2 (d/dv(flux_v)) + % + % flux_v == v^3[(m_a/(m_a + m_b))nu_s f) + 0.5*nu_par*v*d/dv(f)] + % ++% df/dt == -( 1-v^2/4)*sqrt(2)/2*df/dv*v^2 -v*sqrt(2)/2*f + 1/v^2 (d/dv(v^3[(m_a/(m_a + ++% m_b))nu_s f) + 0.5*nu_par*v*d/dv(f)])*v^2 ++% ++% + % Run with + % +-% asgard(@mirror1_velocity,'timestep_method','matrix_exponential','case',3,'dt',1e-8,'num_steps',50,'lev',3,'deg',4,'normalize_by_mass',true) ++% asgard(@mirror1_velocity,'timestep_method','BE','dt',1e-7,'num_steps',50,'lev',5,'deg',2,'normalize_by_mass',false, 'calculate_mass', false) + + params = mirror_parameters(); + + %% Define the dimensions + +-dim_v = DIMENSION(0,0.5e7); +-dim_v.jacobian = @(v,p,t) 2.*pi.*v.^2; ++dim_v = DIMENSION(0,1e6); ++dim_v.jacobian = @(v,p,t) 2*pi.*v.^2; + dimensions = {dim_v}; + num_dims = numel(dimensions); + +@@ -33,14 +37,22 @@ solutions = {soln1}; + + %% Define the initial conditions + +-ic_v = @(v,p,t) p.init_cond_v(v); ++ic_v = @(v,p,t) p.a.n.*p.init_cond_v(v); + ic1 = new_md_func(num_dims,{ic_v}); + initial_conditions = {ic1}; + + %% Define the boundary conditions + +-BCL = ic1; +-BCR = ic1; ++%% Define the boundary conditions ++ ++BCL = new_md_func(num_dims,{... ++ @(v,p,t) v.*0, ... ++ params.boundary_cond_t}); ++ ++ ++BCR = new_md_func(num_dims,{... ++ params.boundary_cond_v, ... ++ params.boundary_cond_t}); + + %% Define the terms of the PDE + +@@ -54,21 +66,40 @@ BCR = ic1; + + %% + +-% term V1 == 1/v^2 d/dv(v^3(m_a/(m_a + m_b))nu_s f)) +-% term V1 == g(v) q(v) [mass, g(v) = 1/v^2, BC N/A] ++ ++% term V1 == -(1 - v^2/4)*sqrt(2)/2*df/dv ++% term V1 == g(v) q(v) ++% g(v) = g1(v) [mass, g1(z) = (1 - v^2/4)*sqrt(2)/2, BC = N/A] ++% q(v) = d/dv (g2(v) f) [grad, g2(v) = 1, BCL=N, BCR=D ] ++g1 = @(v,p,t,dat) -(1-v.^2./4.)*sqrt(2)/2; ++g2 = @(v,p,t,dat) v.*0 + 1; ++pterm1 = MASS(g1); ++pterm2 = GRAD(num_dims,g2,0,'N','D', BCL, BCR); ++termV_v = SD_TERM({pterm1,pterm2}); ++termV1 = MD_TERM(num_dims,{termV_v}); ++ ++%term V2 == -v*sqrt(2)/2*f ++%term V2 == g1(v)*f [ma.ss, g1(v) = -v, BC = N/A] ++g1 = @(v,p,t,dat) -v.^3*sqrt(2)./2; ++pterm1 = MASS(g1); ++termV_v = SD_TERM({pterm1}); ++termV2 = MD_TERM(num_dims,{termV_v}); ++ ++% term V3 == 1/v^2 d/dv(v^3(m_a/(m_a + m_b))nu_s f))*v^2 ++% term V3 == g(v) q(v) [mass, g(v) = 1/v^2, BC N/A] + % q(v) == d/dv(g2(v)f(v)) [grad, g2(v) = v^3(m_a/(m_a + m_b))nu_s, BCL= N, BCR=N] + + g1 = @(v,p,t,dat) 1./v.^2; + g2 = @(v,p,t,dat) v.^3*p.a.m.*p.nu_s(v,p.a,p.b)./(p.a.m + p.b.m); + + pterm1 = MASS(g1); +-pterm2 = GRAD(num_dims,g2,-1,'N','D', BCL, BCR); ++pterm2 = GRAD(num_dims,g2,0,'N','D', BCL, BCR); + termV_s = SD_TERM({pterm1,pterm2}); +-termV1 = MD_TERM(num_dims,{termV_s}); ++termV3 = MD_TERM(num_dims,{termV_s}); + + %% +-% term V2 == 1/v^2 d/dv(v^4*0.5*nu_par*d/dv(f)) +-% term V2 == g(v) q(v) [mass, g(v) = 1/v^2, BC N/A] ++% term V4 == 1/v^2 d/dv(v^4*0.5*nu_par*d/dv(f)) ++% term V4 == g(v) q(v) [mass, g(v) = 1/v^2, BC N/A] + % q(v) == d/dv(g2(v)r(v)) [grad, g2(v) = v^4*0.5*nu_par, BCL= D, BCR=D] + % r(v) = d/dv(g3(v)f) [grad, g3(v) = 1, BCL=N, BCR=N] + +@@ -78,11 +109,11 @@ g3 = @(v,p,t,dat) v.*0 + 1; + + pterm1 = MASS(g1); + pterm2 = GRAD(num_dims,g2,+1,'D','N'); +-pterm3 = GRAD(num_dims,g3, -1,'N','D', BCL, BCR); ++pterm3 = GRAD(num_dims,g3,-1,'N','D', BCL, BCR); + termV_par = SD_TERM({pterm1,pterm2,pterm3}); +-termV2 = MD_TERM(num_dims,{termV_par}); ++termV4 = MD_TERM(num_dims,{termV_par}); + +-terms = {termV1,termV2}; ++terms = {termV1,termV3,termV4}; + + %% Define sources + +diff --git a/pdes/mirror2_advection_Efield_div.m b/pdes/mirror2_advection_Efield_div.m +new file mode 100644 +index 0000000..e014ca3 +--- /dev/null ++++ b/pdes/mirror2_advection_Efield_div.m +@@ -0,0 +1,179 @@ ++function pde = mirror2_advection_Efield_div(opts) ++ ++params_si = mirror_parameters(opts); ++ ++ ++switch opts.case_ ++ case 1 ++ params_si.a.T_eV = 0.05*params_si.b.T_eV; %Target temperature in Kelvin\ ++ offset = 10^6; %case with offset and change in Temperature ++ case 2 ++ params_si.a.T_eV = 0.05*params_si.b.T_eV; ++ offset = 0; %case with no offset but change in Temperature ++ case 3 ++ n_cgs = 5e13; %equilibrium density in cm.^-3 ++ m_e_cgs = 9.109*10^-28; %electron mass in g ++ m_D_cgs = 3.3443*10^-24; %Deuterium mass in g ++ m_He_cgs = 6.7*10^-24; %helium 4 mass in g ++ m_B_cgs = 1.82*10^-23; %Boron 11 mass in g ++ temp_cgs = 1.6022e-10; %temperature in erg ++ params_cgs.a.n = n_cgs; ++ params_cgs.b.n = n_cgs; ++ params_cgs.b2.n = n_cgs; ++% params_cgs.a.vth = sqrt(2*temp_cgs/m_e_cgs); ++% params_cgs.b.vth = sqrt(2*temp_cgs/m_e_cgs); ++ params_cgs.a.m = m_e_cgs; %beam is electrons ++ params_cgs.b.m = m_e_cgs; %background is electrons ++ params_cgs.b2.m = m_B_cgs; ++ params_cgs.a.Z = -1; ++ params_cgs.b.Z = -1; ++ params_cgs.b2.Z = 5; ++ params_cgs.e = 4.803*10^-10; %charge in Fr ++ params_cgs.E = 2.6e-5; %E field in statvolt/cm ++ params_si.a.n = 10^6*params_cgs.a.n;%converting to m^-3 ++ params_si.b.n = 10^6*params_cgs.b.n; ++ params_si.b2.n = 10^6*params_cgs.b2.n; ++% params_si.a.vth = 0.01*params_cgs.a.vth; %converting to m/s ++% params_si.b.vth = 0.01*params_cgs.b.vth; ++ params_si.a.m = 0.001*params_cgs.a.m; %converting to kg ++ params_si.b.m = 0.001*params_cgs.b.m; ++ params_si.b2.m = 0.001*params_cgs.b2.m; ++ params_si.a.Z = params_cgs.a.Z; ++ params_si.b.Z = params_cgs.b.Z; ++ params_si.b2.Z = params_cgs.b2.Z; ++ %params_si.E = 2.9979*10^4*params_cgs.E; %converting to V/m ++ params_si.a.E_eV = 7.665; ++ params_si.a.T_eV = 1000;%2/3*params_si.a.E_eV; ++ params_si.b.T_eV = params_si.a.T_eV; ++ params_si.b2.T_eV = params_si.a.T_eV; ++ params_si.a.vth = params_si.v_th(params_si.a.T_eV,params_si.a.m); ++ params_si.b.vth = params_si.v_th(params_si.b.T_eV,params_si.b.m); ++ params_si.b2.v.th = params_si.v_th(params_si.b2.T_eV,params_si.b2.m); ++ params_si.ln_delt = 15; ++ E_dreicer_si = params_si.a.n.*params_si.e^3*params_si.ln_delt/(4*pi*params_si.eps0^2*params_si.a.m ... ++ *params_si.a.vth^2); ++ params_si.E = 10^-3*E_dreicer_si; ++ %vel_norm = @(v,vth) v./vth; %normalized velocity to thermal velocity ++ params_si.maxwell = @(v,offset,vth) params_si.a.n/(pi.^(3/2)*vth^3).*exp(-((v-offset)/vth).^2); ++ params_si.init_cond_v = @(v,p,t) params_si.maxwell(v,0,params_si.a.vth); ++ params_si.soln_v = @(v,p,t) solution_v(v,p,t); ++ %params_cgs.nu_ab0 = @(a,b) b.n * params_cgs.e^4 * a.Z^2 * b.Z^2 * params_cgs.ln_delt / (pi^3/2.*a.m^2*b.vth^3); %scaling coefficient ++ %params.eps0 = 1/(4*pi); ++end ++ ++ function ret = solution_v(v,p,t) ++ ret = params_si.a.n/(pi^3/2.*params_si.v_th(params_si.b.T_eV,params_si.a.m).^3).*... ++ exp(-(v./params_si.v_th(params_si.b.T_eV,params_si.a.m)).^2); ++ if isfield(p,'norm_fac') ++ ret = p.norm_fac .* ret; ++ end ++ end ++ ++dim_v = DIMENSION(0,15*params_si.a.vth); ++dV_v = @(x,p,t,d) x.^2; ++dim_v.moment_dV = dV_v; ++ ++dim_th = DIMENSION(0,pi); ++dV_th = @(x,p,t,d) sin(x); ++dim_th.moment_dV = dV_th; ++ ++dimensions = {dim_v, dim_th}; ++num_dims = numel(dimensions); ++ ++%% Define the analytic solution (optional) ++ ++soln1 = new_md_func(num_dims,{ ... ++ params_si.soln_v, ... ++ params_si.soln_z, ... ++ }); ++solutions = {soln1}; ++ ++%% Define the initial conditions ++ ++ic1 = new_md_func(num_dims,{params_si.init_cond_v,params_si.init_cond_z,params_si.init_cond_t}); ++initial_conditions = {ic1}; ++ ++%% Define the boundary conditions ++ ++BCL = new_md_func(num_dims,{... ++ params_si.init_cond_v, ... ++ params_si.boundary_cond_z, ... ++ params_si.boundary_cond_t}); ++ ++BCR = new_md_func(num_dims,{... ++ @(v,p,t) v.*0, ... ++ params_si.boundary_cond_z, ... ++ params_si.boundary_cond_t}); ++ ++%% Define the terms of the PDE ++ ++% termE1a is done combining mass and div defining F(th) = (ZeE/m cos(th)) and ++% G(v) = 1 ++% ++% eq1 : df/dt == div(F(th) f) [pterm1: div(g(v)=G(v),-1, BCL=D,BCR=N)] ++ ++ dV_v = @(x,p,t,d) x.^2; ++ dV_th = @(x,p,t,d) sin(x); ++ ++F = @(x,p) cos(x); ++g1 = @(x,p,t,dat) F(x,p).*(x>pi/2); ++pterm1 = MASS(g1,'','',dV_th); ++termE1_th = SD_TERM({pterm1}); ++ ++G = @(v,p) v.*0 - params_si.a.Z.*params_si.e.*params_si.E./params_si.a.m; ++g2 = @(v,p,t,dat) G(v,p); ++pterm1 = DIV(num_dims,g2,'',+1,'D','N',BCL,'','',dV_v); ++termE1_v = SD_TERM({pterm1}); ++termE1a = MD_TERM(num_dims,{termE1_v,termE1_th}); ++ ++%termE1b is the same form as term1 but accounting for the flow in the ++%opposite direction ++ ++F = @(x,p) cos(x); ++g1 = @(x,p,t,dat) F(x,p).*(x 0 and therefore we use upwinding ++%eq1: df/dt == div(mag(s) f) [pterm1: div(g(th)=C(th),-1, BCL=N,BCR=N)] ++ ++dV_th = @(x,p,t,d) sin(x); ++dV_s = @(x,p,t,d) params.B_func(x)/params.a.m; ++ ++g1 = @(x,p,t,d) mag(x).*(mag(x) > 0); ++pterm1 = MASS(g1,'','',dV_s); ++termZa_s = SD_TERM({pterm1}); ++ ++C = @(z) sin(z); ++g2 = @(z,p,t,dat) C(z); ++pterm2 = DIV(num_dims,g2,'',-1,'N','D','',BCR,'',dV_th); ++termZa_z = SD_TERM({pterm2}); ++ ++termZa = MD_TERM(num_dims,{termZa_z,termZa_s}); ++ ++%termZb is a done combining mass ad div defining C(th) = sin(th) and using ++%the function mag(s) = dB/ds/(2*B). This applies to the domain where ++% mag(s) < 0 and therefore we use downwinding ++%eq1: df/dt == div(mag(s) f) [pterm1: div(g(th)=C(th),+1, BCL=N,BCR=N)] ++ ++dV_th = @(x,p,t,d) sin(x); ++dV_s = @(x,p,t,d) params.B_func(x)/params.a.m; ++ ++g1 = @(x,p,t,d) mag(x).*(mag(x) < 0); ++pterm1 = MASS(g1,'','',dV_s); ++termZb_s = SD_TERM({pterm1}); ++ ++C = @(z) sin(z); ++g2 = @(z,p,t,dat) C(z); ++pterm2 = DIV(num_dims,g2,'',+1,'D','N',BCL,'','',dV_th); ++termZb_z = SD_TERM({pterm2}); ++ ++termZb = MD_TERM(num_dims,{termZb_z,termZb_s}); ++ ++%termSa is done combining mass and div G(th) = ++%cos(th) and H(s) = -1. Here we restrict to z < pi/2 and use upwinding ++%eq1 : df/dt == div(G(th) f) [pterm1: div(g(s)=H(s),-1, BCL=D,BCR=N)] ++ ++dV_th = @(x,p,t,d) sin(x); ++dV_s = @(x,p,t,d) params.B_func(x)./params.a.m; ++ ++G = @(z) cos(z).*(z < pi/2); ++g2 = @(z,p,t,dat) G(z); ++pterm1 = MASS(g2,'','',dV_th); ++termSa_z = SD_TERM({pterm1}); ++ ++H = @(s) s.*0 - 1; ++g3 = @(s,p,t,dat) H(s); ++pterm2 = DIV(num_dims,g3,'',-1,'D','N','',BCR,'',dV_s); ++termSa_s = SD_TERM({pterm2}); ++ ++termSa = MD_TERM(num_dims,{termSa_z,termSa_s}); ++ ++%termSb is done combining mass and div G(th) = ++%cos(th) and H(s) = -1. Here we restrict to z > pi/2 and use downwinding ++%eq1 : df/dt == div(G(th) f) [pterm1: div(g(s)=H(s),-1, BCL=D,BCR=N)] ++ ++dV_th = @(x,p,t,d) sin(x); ++dV_s = @(x,p,t,d) params.B_func(x)/params.a.m; ++ ++G = @(z) cos(z).*(z > pi/2); ++g2 = @(z,p,t,dat) G(z); ++pterm1 = MASS(g2,'','',dV_th); ++termSb_z = SD_TERM({pterm1}); ++ ++H = @(s) s.*0 - 1; ++g3 = @(s,p,t,dat) H(s); ++pterm2 = DIV(num_dims,g3,'',+1,'N','D',BCL,'','',dV_s); ++termSb_s = SD_TERM({pterm2}); ++ ++termSb = MD_TERM(num_dims,{termSb_z,termSb_s}); ++ ++%% Mass term ++% termM == cos(z)dB/ds/(2*B) f ++% termM == r(z)*w(s) ++% r(z) == g1(z) [mass, g1(z) = -cos(z), BC N/A] ++% w(s) == g2(s) f [mass, g2(s) = mag(s), BC N/A] ++ ++% dV_th = @(x,p,t,d) sin(x); ++% dV_s = @(x,p,t,d) params.B_func(x); ++% ++% G = @(z) cos(z); ++% g2 = @(z,p,t,dat) G(z); ++% pterm2 = MASS(g2,'','',dV_th); ++% termB1_z = SD_TERM({pterm2}); ++% ++% g3 = @(s,p,t,dat) mag(s); ++% pterm3 = MASS(g3,'','',dV_s); ++% termB1_s = SD_TERM({pterm3}); ++% ++% termM = MD_TERM(num_dims,{termB1_z,termB1_s}); ++ ++terms = {termZa,termZb,termSa,termSb}; ++ ++ ++ ++%% Define the analytic solution (optional) ++ ++ ++soln1_z = @(z,p,t,d) cos(z); ++soln1_s = @(s,p,t,d) s; ++solution = new_md_func(num_dims,{soln1_z,soln1_s}); ++solutions = {solution}; ++ ++ ++%% Define sources ++%source1_v = @(x,p,t,d) p.f0_v(x); ++source1_z = @(x,p,t,d) (sin(x)).^2 - (cos(x)).^2; ++source1 = new_md_func(num_dims,{source1_z,[]}); ++sources = {source1}; ++ ++%% Define function to set time step ++ function dt=set_dt(pde,CFL) ++ Lmax = pde.dimensions{1}.max; ++ LevX = pde.dimensions{1}.lev; ++ dt = Lmax/2^LevX*CFL; ++ end ++ ++ ++ ++%% Construct PDE ++ ++pde = PDE(opts,dimensions,terms,[],sources,params,@set_dt,[],initial_conditions,solutions); ++end +\ No newline at end of file +diff --git a/pdes/mirror2_velocity.m b/pdes/mirror2_velocity.m +new file mode 100644 +index 0000000..95d3618 +--- /dev/null ++++ b/pdes/mirror2_velocity.m +@@ -0,0 +1,178 @@ ++function pde = mirror2_velocity(opts) ++% Two-dimensional magnetic mirror from the FP paper - evolution of the ion velocity dependence ++% of f in the presence of Coulomb collisions with background electrons ++% Also applied to the 2D test for CQL4D equations ++ ++% df/dt == -eE/m cos(th) df/dv + eE/m sin(th) df/dth + sum_{b} ( nu_D/(2*sin(th)) d/dth ( sin(th) 1/v d (v f) /dth ) + ++% 1/v^2 (d/dv(v^2[(m_a/(m_a + m_b))v nu_s f) + 0.5*nu_par*v^2*d/dv(f)]) ++% ++% v,th are spherical coordinates (v,th,phi), so the div and grad look like ++% ++% div[] = 1/v^2 * d/dv * v^2[] + 1/sin(th) d/dth (sin(th)[]), grad[] = ++% d/dv[],1/v * d/dth[] ++% ++% Run with ++% ++% asgard(@mirror2_velocity,'timestep_method','BE','case',3,'dt',1e-6) ++ ++params = mirror_parameters(); ++ ++switch opts.case_ ++ case 1 ++ params.a.T_eV = 0.05*params.b.T_eV; %Target temperature in Kelvin\ ++ offset = 10^6; %case with offset and change in Temperature ++ case 2 ++ params.a.T_eV = 0.05*params.b.T_eV; ++ offset = 0; %case with no offset but change in Temperature ++ case 3 ++ n_o = 8e14; %equilibrium density in cm.^-3 ++ m_e = 9.109*10^-28; %electron mass in g ++ temp = 1.6022e-10; %temperature in erg ++ params.a.n = n_o; ++ params.b.n = n_o; ++ params.a.vth = sqrt(2*temp/m_e); ++ params.b.vth = sqrt(2*temp/m_e); ++ params.a.m = m_e; %beam is electrons ++ params.b.m = m_e; %background is electrons ++ params.E = 3.33e-7; %E field in statvolt/cm ++ params.init_cond_v = @(v,p,t) params.maxwell(v,0,a.vth); ++end ++ ++maxwell = @(v,x,y) a.n/(pi^3/2.*y^3).*exp(-((v-x)/y).^2); ++ ++%% Define the dimensions ++ ++dim_v = DIMENSION(0,1e6); ++dim_z = DIMENSION(0,pi); ++ ++dim_v.jacobian = @(v,p,t) 2.*pi.*v.^2; ++dim_z.jacobian = @(z,p,t) sin(z); ++ ++dimensions = {dim_v, dim_z}; ++num_dims = numel(dimensions); ++ ++%% Define the analytic solution (optional) ++ ++soln1 = new_md_func(num_dims,{ ... ++ params.soln_v, ... ++ params.soln_z, ... ++ }); ++solutions = {soln1}; ++ ++%% Define the initial conditions ++ ++ic1 = new_md_func(num_dims,{params.init_cond_v,params.init_cond_z,params.init_cond_t}); ++initial_conditions = {ic1}; ++ ++%% Define the boundary conditions ++ ++BCL = new_md_func(num_dims,{... ++ @(v,p,t) v.*0, ... ++ params.boundary_cond_z, ... ++ params.boundary_cond_t}); ++ ++BCR = new_md_func(num_dims,{... ++ params.boundary_cond_v, ... ++ params.boundary_cond_z, ... ++ params.boundary_cond_t}); ++ ++ ++%% Define the terms of the PDE ++ ++% -eE*Z_a/m_a cos(z) d/dv(f) ++ ++g1 = @(v,p,t,dat) -p.e.*p.E.*p.a.Z./p.a.m; ++g2 = @(v,p,t,dat) v.*0 + 1; ++ ++pterm1 = MASS(g1); ++pterm2 = GRAD(num_dims,g2,-1,'N','D',BCL,BCR); ++termE_v = SD_TERM({pterm1,pterm2}); ++ ++g3 = @(z,p,t,dat) cos(z); ++ ++pterm1 = MASS(g3); ++termE_z = SD_TERM({pterm1}); ++termE1 = MD_TERM(num_dims,{termE_v,termE_z}); ++ ++% eE/m sin(z)vdf/dz ++ ++g1 = @(v,p,t,dat) p.e.*p.E*v./p.a.m; ++g2 = @(z,p,t,dat) sin(z); ++g3 = @(z,p,t,dat) z.*0 + 1; ++ ++pterm1 = MASS(g1); ++pterm2 = MASS(g2); ++pterm3 = GRAD(num_dims,g3,-1,'N','N'); ++ ++termE_v = SD_TERM({pterm1}); ++termE_z = SD_TERM({pterm2,pterm3}); ++termE2 = MD_TERM(num_dims,{termE_v,termE_z}); ++ ++% termC == v.^2.*nu_D/(2*sin(z))*d/dz sin(z)*df/dz ++% ++% becomes ++% ++% termC == g1(v) g2(z) q(z) [mass, g1(p) = nu_D(v), g2(z) = 1/(2sin(z)) BC N/A] ++% q(z) == d/dz g3(z) r(z) [grad, g3(z) = sin(z), BCL=D,BCR=D] ++% r(z) == d/dp g4(z) f(z) [grad, g3(p) = 1, BCL=N,BCR=N] ++ ++g1 = @(v,p,t,dat) p.nu_D(v,p.a,p.b)/2; ++g2 = @(z,p,t,dat) 1./sin(z); ++g3 = @(z,p,t,dat) sin(z); ++g4 = @(z,p,t,dat) z.*0 + 1; ++pterm1 = MASS(g1); ++pterm2 = MASS(g2); ++pterm3 = GRAD(num_dims,g3,+1,'D','N'); ++pterm4 = GRAD(num_dims,g4,-1,'N', 'D',BCL,BCR); ++termC_v = SD_TERM({pterm1}); ++termC_z = SD_TERM({pterm2,pterm3,pterm4}); ++termC = MD_TERM(num_dims,{termC_v,termC_z}); ++ ++ ++% term V1 == 1/v^2 d/dv(v^3(m_a/(m_a + m_b))nu_s f)) ++% term V1 == g(v) q(v) [mass, g(v) = 1/v^2, BC N/A] ++% q(v) == d/dv(g2(v)f(v)) [grad, g2(v) = v^3(m_a/(m_a + m_b))nu_s, BCL= N, BCR=N] ++ ++g1 = @(v,p,t,dat) 1./v.^2; ++g2 = @(v,p,t,dat) v.^3*p.a.m.*p.nu_s(v,p.a,p.b)./(p.a.m + p.b.m); ++ ++pterm1 = MASS(g1); ++pterm2 = GRAD(num_dims,g2,-1,'N','D', BCL, BCR); ++termV_s = SD_TERM({pterm1,pterm2}); ++termV1 = MD_TERM(num_dims,{termV_s,[]}); ++ ++% term V2 == 1/v^2 d/dv(v^4*0.5*nu_par*d/dv(f)) ++% term V2 == g(v) q(v) [mass, g(v) = 1/v^2, BC N/A] ++% q(v) == d/dv(g2(v)r(v)) [grad, g2(v) = v^4*0.5*nu_par, BCL= D, BCR=D] ++% r(v) = d/dv(g3(v)f) [grad, g3(v) = 1, BCL=N, BCR=N] ++ ++g1 = @(v,p,t,dat) 1./v.^2; ++g2 = @(v,p,t,dat) v.^4.*0.5.*p.nu_par(v,p.a,p.b); ++g3 = @(v,p,t,dat) v.*0 + 1; ++ ++pterm1 = MASS(g1); ++pterm2 = GRAD(num_dims,g2,-1,'D','N'); ++pterm3 = GRAD(num_dims,g3,+1,'N','D', BCL, BCR); ++termV_par = SD_TERM({pterm1,pterm2,pterm3}); ++termV2 = MD_TERM(num_dims,{termV_par,[]}); ++ ++terms = {termV1,termV2,termC,termE1,termE2}; ++ ++ ++%% Define sources ++ ++sources = {}; ++ ++%% Define function to set time step ++ function dt=set_dt(pde,CFL) ++ Lmax = pde.dimensions{1}.max; ++ LevX = pde.dimensions{1}.lev; ++ dt = Lmax/2^LevX*CFL; ++ end ++ ++ ++%% Construct PDE ++ ++pde = PDE(opts,dimensions,terms,[],sources,params,@set_dt,[],initial_conditions,solutions); ++ ++end +diff --git a/pdes/mirror2_velocity_div.m b/pdes/mirror2_velocity_div.m +new file mode 100644 +index 0000000..6b8017f +--- /dev/null ++++ b/pdes/mirror2_velocity_div.m +@@ -0,0 +1,252 @@ ++function pde = mirror2_velocity_div(opts) ++% Two-dimensional magnetic mirror from the FP paper - evolution of the ion velocity dependence ++% of f in the presence of Coulomb collisions with background electrons ++% Also applied to the 2D test for CQL4D equations ++ ++% df/dt == -1/v^2 d(v^2 ZeE/m cos(th) f)/dv + 1/(vsin(th)) d(sin(th) ZeE/m sin(th) f)/dth ++% + sum_{b} ( nu_D/(2*sin(th)) d/dth ( sin(th) 1/v d (v f) /dth ) + ++% 1/v^2 (d/dv(v^2[(m_a/(m_a + m_b))v nu_s f) + 0.5*nu_par*v^2*d/dv(f)]) ++% ++% v,th are spherical coordinates (v,th,phi), so the div and grad look like ++% ++% div[] = 1/v^2 * d/dv * v^2[] + 1/sin(th) d/dth (sin(th)[]), grad[] = ++% d/dv[],1/v * d/dth[] ++% ++% and the volument_element dV = v^2 sin(th) ++% ++ ++% df/dt == -1/v^2 d(v^2 ZeE/m cos(th) f)/dv %term1 ++% + 1/(vsin(th)) d(sin(th) ZeE/m sin(th) f)/dth %term2 ++% + % sum_b (( 1/v^2 (d/dv (v^2[0.5*nu_par*v^2*d/dv(f)]) %%term3 ++% + 1/v^2 (d/dv(v^2[v (m_a/(m_a + m_b))nu_s f)]) %%term4 ++% + nu_D/(2 sin(z)) d/dth ( sin(th) df/dth )) %%term5 ++% ++% split into five div terms (term1,term2, term3, term4, and term5) ++% ++% term1 is done combining mass and div defining F(th) = -ZeE/m cos(th) and ++% G(v) = 1 ++% ++% eq1 : df/dt == div(F(th) f) [pterm1: div(g(v)=G(v),-1, BCL=D,BCR=N)] ++% ++% term2 is a simple div term, defining K(th) = ZeE/m sin(th) ++% ++% eq1 : df/dt == div(K(th) f) [pterm1:div(g(th)=K(th),-1, BCL=N,BCR=N)] ++% ++% term3 is done combining mass and div defining C(v) = (nu_D(v)/2) ++% ++% eq1 : df/dt == div( q) [pterm1: div (g(v)=D(v),+1, BCL=D, BCR=D] ++% eq2 : q == C(v) grad(f) [pterm2: grad(g(v)=D(v),-1, BCL=N, BCR=N] ++% ++% term4 is a div using B(v) = v (m_a/(m_a + m_b))nu_s ++% ++% eq1 : df/dt == div(B(v) * f) [pterm1: div(g(p)=B(v),+1, BCL=?, BCR=?] ++% ++% ++% term5 is done using SLDG defining C(v) = sqrt(v*nu_D(v)/2) ++% ++% eq1 : df/dt == div(C(v) * q) [pterm1: div (g(v)=C(v),+1, BCL=D, BCR=D] ++% eq2 : q == C(v) * grad(f) [pterm2: grad(g(v)=C(v),-1, BCL=N, BCR=N] ++% Run with ++% ++% asgard(@mirror2_velocity_div,'timestep_method','BE','case',3, 'grid_type','SG', 'lev', 3, 'deg', 3,'num_steps', 10, 'dt',5e-5, 'normalize_by_mass', true, 'calculate_mass', true,'save_output',true,'update_params_each_timestep', true) ++ ++% Run with ++% ++% asgard(@mirror2_velocity_div,'timestep_method','BE','case',3,'dt',1e-6) ++ ++params = mirror_parameters(opts); ++ ++ ++%% Define the dimensions ++ ++dim_v = DIMENSION(0,5*params.a.vth); ++dV_v = @(x,p,t,d) x.^2; ++dim_v.moment_dV = dV_v; ++ ++dim_th = DIMENSION(0,pi); ++dV_th = @(x,p,t,d) sin(x); ++dim_th.moment_dV = dV_th; ++ ++dimensions = {dim_v, dim_th}; ++num_dims = numel(dimensions); ++ ++%% Define the analytic solution (optional) ++ ++soln1 = new_md_func(num_dims,{ ... ++ params.soln_v, ... ++ params.soln_z, ... ++ }); ++solutions = {soln1}; ++ ++%% Define the initial conditions ++ ++ic1 = new_md_func(num_dims,{params.init_cond_v,params.init_cond_z,params.init_cond_t}); ++initial_conditions = {ic1}; ++ ++%% Define the boundary conditions ++ ++BCL = new_md_func(num_dims,{... ++ params.boundary_cond_v, ... ++ params.boundary_cond_z, ... %params.boundary_cond_z, ... ++ params.boundary_cond_t}); ++ ++BCR = new_md_func(num_dims,{... ++ params.boundary_cond_v, ... ++ params.boundary_cond_z, ... ++ params.boundary_cond_t}); ++ ++%% Define the terms of the PDE ++ ++% termE1a is done combining mass and div defining F(th) = (ZeE/m cos(th)) and ++% G(v) = 1 ++% ++% eq1 : df/dt == div(F(th) f) [pterm1: div(g(v)=G(v),-1, BCL=D,BCR=N)] ++ ++ dV_v = @(x,p,t,d) x.^2; ++ dV_th = @(x,p,t,d) sin(x); ++ ++F = @(x,p) -cos(x).*p.a.Z.*p.e.*p.E./p.a.m; ++g1 = @(x,p,t,dat) F(x,p).*(x>pi/2); ++pterm1 = MASS(g1,'','',dV_th); ++termE1_th = SD_TERM({pterm1}); ++ ++G = @(v,p) v.*0 + 1; ++g2 = @(v,p,t,dat) G(v,p); ++pterm1 = DIV(num_dims,g2,'',+1,'D','N',BCL,'','',dV_v); ++termE1_v = SD_TERM({pterm1}); ++termE1a = MD_TERM(num_dims,{termE1_v,termE1_th}); ++ ++%termE1b is the same form as term1 but accounting for the flow in the ++%opposite direction ++ ++F = @(x,p) -cos(x).*p.a.Z.*p.e.*p.E./p.a.m; ++g1 = @(x,p,t,dat) F(x,p).*(xpi/2); ++pterm1 = MASS(g1,'','',dV_th); ++termE1_th = SD_TERM({pterm1}); ++ ++G = @(v,p) v.*0 + 1; ++g2 = @(v,p,t,dat) G(v,p); ++pterm1 = DIV(num_dims,g2,'',-1,'N','D','',BCR,'',dV_v); ++termE1_v = SD_TERM({pterm1}); ++termE1a = MD_TERM(num_dims,{termE1_v,termE1_th}); ++ ++%termE1b is the same form as term1 but accounting for the flow in the ++%opposite direction ++ ++F = @(x,p) -cos(x).*params.a.Z.*params.e.*params.E./params.a.m; ++g1 = @(x,p,t,dat) F(x,p).*(xpi/2); ++pterm1 = MASS(g1,'','',dV_th); ++termE1_th = SD_TERM({pterm1}); ++ ++G = @(v,p) v.*0 - params_si.a.Z.*params_si.e.*params_si.E./params_si.a.m; ++g2 = @(v,p,t,dat) G(v,p); ++pterm1 = DIV(num_dims,g2,'',+1,'D','N',BCL,'','',dV_v); ++termE1_v = SD_TERM({pterm1}); ++termE1a = MD_TERM(num_dims,{termE1_v,termE1_th,[]}); ++ ++%termE1b is the same form as term1 but accounting for the flow in the ++%opposite direction ++ ++F = @(x,p) cos(x); ++g1 = @(x,p,t,dat) F(x,p).*(x 2 +- sy = sy+2; % just to get off the exact middle ++ sy = sy-1; % just to get off the exact middle + end + % sy=ny; + +@@ -51,6 +51,8 @@ if num_dims==2 + y = nodes{2}; + ax1 = subplot(2,2,1); + plot(x,f_slice,'-o'); ++ %xlim([0,10]) ++ %ylim([1e-5,1]) + title('1D slice (horizontal)'); + + %% diff --git a/diffusion_LDG_2_test.m b/diffusion_LDG_2_test.m new file mode 100644 index 00000000..46805302 --- /dev/null +++ b/diffusion_LDG_2_test.m @@ -0,0 +1,207 @@ +function pde = diffusion_LDG_2_test(opts) + +% Test 2D LDG diffusion in spherical coordinates +% +% df/dt == div(grad f) + S in spherical cordinates +% +% (p,th) is a spherical coordinate (p,th,ph), so the div and grad look like +% +% div[A] = 1/p^2 * d/dp * p^2[A_p] + 1/(p*sin(th)) d/dth(sin(th) A_th +% +% where A = A_p \hat{p} + A_th \hat{th} +% +% grad[f] = df/dp \hat{p} + 1/r df/dth \hat{th} +% +% and the volument_element dV = p^2*sin(th) +% +% Run with +% +% asgard(@diffusion_LDG_2_test,'timestep_method','BE','lev',3,'deg',4,'num_steps',50,'CFL',1.5) +% +% or +% +% asgard(@diffusion_LDG_2_test,'timestep_method','matrix_exponential','lev',2,'deg',4,'grid_type','FG','num_steps',1,'dt',3) +% +% Analytic solution: f(r,th,t) = (r-t)^2*(th^2+1) with source provided +% below +% using approprite Dirichlet or Neumann BCs + +%% Define some parameters and add to pde object. + +params.parameter1 = 0; + +%% Define the dimensions +dV_p = @(x,p,t,d) x.^2; +dim_p = DIMENSION(0.5,pi); +dim_p.moment_dV = dV_p; + +dim_th = DIMENSION(0.5,pi-0.5); +dim_th.moment_dV = @(x,p,t,d) sin(x); +dimensions = {dim_p,dim_th}; +num_dims = numel(dimensions); + +%% Define the analytic solution (optional). + +soln1 = new_md_func(num_dims,{@(x,p,t) soln_p(x,p,t),... + @(x,p,t) soln_th(x,p,t),... + @(t,p) 0*t+1 }); + +% Just f(p,th,t) = 1 used in Neumann Case +func_one = new_md_func(num_dims,{@(x,p,t) 0*x+1,... + @(x,p,t) 0*x+1,... + @(t,p) 0*t+1}); + +% Dirichlet +solutions = {soln1}; + +% Neumann +%solutions = {soln1,func_one}; + +% Define derivatives of analytic solution for Neumann BCs +dsoln_dp = new_md_func(num_dims,{@(x,p,t) dsoln_p(x,p,t),... + @(x,p,t) soln_th(x,p,t),... + @(t,p) exp(-t)}); + +dsoln_dth = new_md_func(num_dims,{@(x,p,t) soln_p(x,p,t)./x,... + @(x,p,t) -sin(x),... + @(t,p) exp(-t)}); %df/dth*1/v = grad f\cdot n + +%% Define initial conditions + +initial_conditions = solutions; + +%% LHS terms (mass only) + +LHS_terms = {}; + +%% RHS terms + +% term1 is done using SLDG in p with mass in th +% +% Dirichlet +% eq1 : df/dt == div(q) [pterm1: div (g1(p)=1,+1, BCL=N, BCR=N)] +% eq2 : q == grad(f) [pterm2: grad(g2(p)=1,-1, BCL=D, BCR=D)] +% +% Neumann +% eq1 : df/dt == div(q) [pterm1: div (g1(p)=1,+1, BCL=D, BCR=D)] +% eq2 : q == grad(f) [pterm2: grad(g2(p)=1,-1, BCL=N, BCR=N)] +% + +% Define gfuncs and surface jacobian: r^2*sin(th) +g1 = @(x,p,t,dat) x; +dV_p = @(x,p,t,d) x.^2; +dV_th = @(x,p,t,d) sin(x); + +% Dirichlet +pterm1 = DIV(num_dims,g1,'',+1,'N','N','','','',dV_p); +pterm2 = GRAD(num_dims,g1,'',-1,'D','D',soln1,soln1,'',dV_p); + +% Neumann +%pterm1 = DIV(num_dims,g1,'',+1,'D','D',dsoln_dp,dsoln_dp,'',dV_p); +%pterm2 = GRAD(num_dims,g1,'',-1,'N','N','','','',dV_p); + +term1_p = SD_TERM({pterm1,pterm2}); % order here is as in equation + +g1 = @(x,p,t,dat) 0*x+1; +pterm1 = MASS(g1,[],[],dV_th); +term1_th = SD_TERM({pterm1,pterm1}); +term1 = MD_TERM(num_dims,{term1_p,term1_th}); + +% term2 is done using mass in p with SLDG in th. +% +% Dirichlet +% eq1 : df/dt == div(q) [pterm1: div (g1(p)=1,+1, BCL=N, BCR=N)] +% eq2 : q == grad(f) [pterm2: grad(g2(p)=1,-1, BCL=D, BCR=D)] +% +% Neumann +% eq1 : df/dt == div(q) [pterm1: div (g1(p)=1,+1, BCL=D, BCR=D)] +% eq2 : q == grad(f) [pterm2: grad(g2(p)=1,-1, BCL=N, BCR=N)] +% + +% Define gfuncs and surface jacobian: r*sin(th) +dV_p = @(x,p,t,d) x; +dV_th = @(x,p,t,d) sin(x); + +g1 = @(x,p,t,dat) 0*x+1; +pterm1 = MASS(g1,[],[],dV_p); +term2_p = SD_TERM({pterm1,pterm1}); + +% Dirichlet +g1 = @(x,p,t,dat) x; +pterm1 = DIV(num_dims,g1,'',+1,'N','N','','','',dV_th); +pterm2 = GRAD(num_dims,g1,'',-1,'D','D',soln1,soln1,'',dV_th); + +% Neumann +%pterm1 = DIV(num_dims,g1,'',+1,'D','D',dsoln_dth,dsoln_dth,'',dV_th); +%pterm2 = GRAD(num_dims,g1,'',-1,'N','N','','','',dV_th); + +term2_th = SD_TERM({pterm1,pterm2}); +term2 = MD_TERM(num_dims,{term2_p,term2_th}); +terms = {term1,term2}; + +%% Define sources + +% -2(r-t)(th^2+1) +source1 = new_md_func(num_dims,{@(x,p,t,dat) 2*(x-t),... + @(x,p,t,dat) soln_th(x,p,t),... + @(t,p) 0*t-1}); + +% -2r(5r-4t)(th^2+1) +source2 = new_md_func(num_dims,{@(x,p,t,dat) 2*x.*(5*x-4*t),... + @(x,p,t,dat) x.^2+1,... + @(t,p) 0*t-1}); + +% -6(r-t)^2 th^2/r^2 +source3 = new_md_func(num_dims,{@(x,p,t,dat) 6*(x-t).^2./(x.^2),... + @(x,p,t,dat) x.^2,... + @(t,p) 0*t-1}); + +% -2(r-t)^2/r^2 th^3cot(th) +source4 = new_md_func(num_dims,{@(x,p,t,dat) 2*(x-t).^2./(x.^2),... + @(x,p,t,dat) tmp_func(x,p,t),... + @(t,p) 0*t-1}); + +sources = {source1,source2,source3,source4}; + +%% Define function to set time step + function dt=set_dt(pde,CFL) + dims = pde.dimensions; + xRange = dims{1}.max-dims{1}.min; + lev = dims{1}.lev; + dx = xRange/2^lev; + dt = CFL * dx; + end + +%% Construct PDE + +pde = PDE(opts,dimensions,terms,LHS_terms,sources,params,@set_dt,[],initial_conditions,solutions); + +end + +% p part of the solution (taylor expansion so there's no division by 0) +function z = soln_p(x,p,t) + z = (x-t).^2; +end + +% th part of the solution +function z = soln_th(x,p,t) + z = x.^2+1; +end + + +%df/dp +function z = dsoln_p(x,p,t) + if abs(x) < 1e-7 + z = 1/3 - x.^2/10 + x.^4/168 - x.^6/6480; + else + z = ((x.^2-2).*sin(x) + 2.*x.*cos(x))./(x.^3); + end +end + +function z = tmp_func(x,p,t) + if abs(x) < 1e-7 + z = x.^2 - x.^4/3 - x.^6/45 - 2*x.^8/945; + else + z = cot(x).*x.^3; + end +end \ No newline at end of file diff --git a/forward_wavelet_transform.m b/forward_wavelet_transform.m index 68c00925..d53ea966 100644 --- a/forward_wavelet_transform.m +++ b/forward_wavelet_transform.m @@ -1,4 +1,4 @@ -function [f] = forward_wavelet_transform(deg,lev,Lmin,Lmax,foo,params,blocks,t) +function [f] = forward_wavelet_transform(deg,lev,Lmin,Lmax,foo,dV,params,blocks,t) %% Decompose a 1D function into the multiwavelet basis @@ -27,7 +27,7 @@ % Get the function foo(x) at the quadrature points. - fxHere = foo(x, params, t); + fxHere = foo(x, params, t) .* dV(x); this_quad = (quad_w .* fxHere); diff --git a/gold/generated-inputs/adapt/continuity1_l4_d3_coarse.dat b/gold/generated-inputs/adapt/continuity1_l4_d3_coarse.dat new file mode 100644 index 00000000..60b740f6 --- /dev/null +++ b/gold/generated-inputs/adapt/continuity1_l4_d3_coarse.dat @@ -0,0 +1,20 @@ +# Created from matlab git hash aca3d9fe7ba23914a4fca9791dce9f33ba95f20e +# name: foo +# type: matrix +# rows: 15 +# columns: 1 +0.001 +0 +0 +0.001 +0 +0 +0.001 +0 +0 +0.001 +0 +0 +1 +1 +1 diff --git a/gold/generated-inputs/adapt/continuity1_l4_d3_coarse_table.dat b/gold/generated-inputs/adapt/continuity1_l4_d3_coarse_table.dat new file mode 100644 index 00000000..fb428e66 --- /dev/null +++ b/gold/generated-inputs/adapt/continuity1_l4_d3_coarse_table.dat @@ -0,0 +1,10 @@ +# Created from matlab git hash aca3d9fe7ba23914a4fca9791dce9f33ba95f20e +# name: foo +# type: matrix +# rows: 5 +# columns: 2 +4 3 +4 6 +3 1 +2 0 +0 0 diff --git a/gold/generated-inputs/adapt/continuity1_l4_d3_orig.dat b/gold/generated-inputs/adapt/continuity1_l4_d3_orig.dat new file mode 100644 index 00000000..662dc6fc --- /dev/null +++ b/gold/generated-inputs/adapt/continuity1_l4_d3_orig.dat @@ -0,0 +1,53 @@ +# Created from matlab git hash aca3d9fe7ba23914a4fca9791dce9f33ba95f20e +# name: foo +# type: matrix +# rows: 48 +# columns: 1 +0 +0 +0 +0 +0 +0 +5e-06 +0 +0 +0.001 +0 +0 +5e-06 +0 +0 +0 +0 +0 +0.001 +0 +0 +0 +0 +0 +5e-06 +0 +0 +0.001 +0 +0 +5e-06 +0 +0 +0 +0 +0 +0.001 +0 +0 +0 +0 +0 +5e-06 +0 +0 +1 +1 +1 diff --git a/gold/generated-inputs/adapt/continuity1_l4_d3_refine.dat b/gold/generated-inputs/adapt/continuity1_l4_d3_refine.dat new file mode 100644 index 00000000..dd7c8bd3 --- /dev/null +++ b/gold/generated-inputs/adapt/continuity1_l4_d3_refine.dat @@ -0,0 +1,65 @@ +# Created from matlab git hash aca3d9fe7ba23914a4fca9791dce9f33ba95f20e +# name: foo +# type: matrix +# rows: 60 +# columns: 1 +0 +0 +0 +0 +0 +0 +5e-06 +0 +0 +0.001 +0 +0 +5e-06 +0 +0 +0 +0 +0 +0.001 +0 +0 +0 +0 +0 +5e-06 +0 +0 +0.001 +0 +0 +5e-06 +0 +0 +0 +0 +0 +0.001 +0 +0 +0 +0 +0 +5e-06 +0 +0 +1 +1 +1 +1e-15 +1e-15 +1e-15 +1e-15 +1e-15 +1e-15 +1e-15 +1e-15 +1e-15 +1e-15 +1e-15 +1e-15 diff --git a/gold/generated-inputs/adapt/continuity1_l4_d3_refine_table.dat b/gold/generated-inputs/adapt/continuity1_l4_d3_refine_table.dat new file mode 100644 index 00000000..3ac5b4a0 --- /dev/null +++ b/gold/generated-inputs/adapt/continuity1_l4_d3_refine_table.dat @@ -0,0 +1,25 @@ +# Created from matlab git hash aca3d9fe7ba23914a4fca9791dce9f33ba95f20e +# name: foo +# type: matrix +# rows: 20 +# columns: 2 +4 0 +4 1 +4 2 +4 3 +4 4 +4 5 +4 6 +4 7 +3 0 +3 1 +3 2 +3 3 +2 0 +2 1 +1 0 +0 0 +5 6 +5 7 +5 12 +5 13 diff --git a/gold/generated-inputs/adapt/continuity2_l5_d2_coarse.dat b/gold/generated-inputs/adapt/continuity2_l5_d2_coarse.dat new file mode 100644 index 00000000..7979381e --- /dev/null +++ b/gold/generated-inputs/adapt/continuity2_l5_d2_coarse.dat @@ -0,0 +1,257 @@ +# Created from matlab git hash aca3d9fe7ba23914a4fca9791dce9f33ba95f20e +# name: foo +# type: matrix +# rows: 252 +# columns: 1 +0 +0 +0 +0 +0 +0 +0 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b/gold/generated-inputs/adapt/continuity2_l5_d2_coarse_table.dat @@ -0,0 +1,68 @@ +# Created from matlab git hash aca3d9fe7ba23914a4fca9791dce9f33ba95f20e +# name: foo +# type: matrix +# rows: 63 +# columns: 4 +5 0 0 0 +5 0 1 0 +5 0 2 0 +5 0 3 0 +5 0 4 0 +5 0 5 0 +5 0 6 0 +5 0 7 0 +5 0 8 0 +5 0 9 0 +5 0 10 0 +5 0 11 0 +5 0 12 0 +5 0 13 0 +5 0 14 0 +5 0 15 0 +0 5 0 0 +0 5 0 1 +0 5 0 2 +0 5 0 3 +0 5 0 4 +0 5 0 5 +0 5 0 6 +0 5 0 7 +0 5 0 8 +0 5 0 9 +0 5 0 10 +0 5 0 11 +0 5 0 12 +0 5 0 13 +0 5 0 14 +0 5 0 15 +4 0 0 0 +4 0 1 0 +4 0 2 0 +4 0 3 0 +4 0 4 0 +4 0 5 0 +4 0 6 0 +4 0 7 0 +0 4 0 0 +0 4 0 1 +0 4 0 2 +0 4 0 3 +0 4 0 4 +0 4 0 5 +0 4 0 6 +0 4 0 7 +3 0 0 0 +3 0 1 0 +3 0 2 0 +3 0 3 0 +0 3 0 0 +0 3 0 1 +0 3 0 2 +0 3 0 3 +2 0 0 0 +2 0 1 0 +0 2 0 0 +0 2 0 1 +1 0 0 0 +0 1 0 0 +0 0 0 0 diff --git a/gold/generated-inputs/adapt/continuity2_l5_d2_orig.dat b/gold/generated-inputs/adapt/continuity2_l5_d2_orig.dat new file mode 100644 index 00000000..e679380c --- /dev/null +++ b/gold/generated-inputs/adapt/continuity2_l5_d2_orig.dat @@ -0,0 +1,453 @@ +# Created from matlab git hash aca3d9fe7ba23914a4fca9791dce9f33ba95f20e +# name: foo +# type: matrix +# rows: 448 +# columns: 1 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 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columns: 6 +4 0 0 0 0 0 +4 0 0 1 0 0 +4 0 0 2 0 0 +4 0 0 3 0 0 +4 0 0 4 0 0 +4 0 0 5 0 0 +4 0 0 6 0 0 +4 0 0 7 0 0 +3 1 0 0 0 0 +3 1 0 1 0 0 +3 1 0 2 0 0 +3 1 0 3 0 0 +2 2 0 0 0 0 +2 2 0 1 0 0 +2 2 0 0 1 0 +2 2 0 1 1 0 +1 3 0 0 0 0 +1 3 0 0 1 0 +1 3 0 0 2 0 +1 3 0 0 3 0 +0 4 0 0 0 0 +0 4 0 0 1 0 +0 4 0 0 2 0 +0 4 0 0 3 0 +0 4 0 0 4 0 +0 4 0 0 5 0 +0 4 0 0 6 0 +0 4 0 0 7 0 +3 0 1 0 0 0 +3 0 1 1 0 0 +3 0 1 2 0 0 +3 0 1 3 0 0 +2 1 1 0 0 0 +2 1 1 1 0 0 +1 2 1 0 0 0 +1 2 1 0 1 0 +0 3 1 0 0 0 +0 3 1 0 1 0 +0 3 1 0 2 0 +0 3 1 0 3 0 +2 0 2 0 0 0 +2 0 2 1 0 0 +2 0 2 0 0 1 +2 0 2 1 0 1 +1 1 2 0 0 0 +1 1 2 0 0 1 +0 2 2 0 0 0 +0 2 2 0 1 0 +0 2 2 0 0 1 +0 2 2 0 1 1 +1 0 3 0 0 0 +1 0 3 0 0 1 +1 0 3 0 0 2 +1 0 3 0 0 3 +0 1 3 0 0 0 +0 1 3 0 0 1 +0 1 3 0 0 2 +0 1 3 0 0 3 +0 0 4 0 0 0 +0 0 4 0 0 1 +0 0 4 0 0 2 +0 0 4 0 0 3 +0 0 4 0 0 4 +0 0 4 0 0 5 +0 0 4 0 0 6 +0 0 4 0 0 7 +3 0 0 0 0 0 +3 0 0 1 0 0 +3 0 0 2 0 0 +3 0 0 3 0 0 +2 1 0 0 0 0 +2 1 0 1 0 0 +1 2 0 0 0 0 +1 2 0 0 1 0 +0 3 0 0 0 0 +0 3 0 0 1 0 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a/gold/generated-inputs/adapt/diffusion2_l2_d3_initial.dat b/gold/generated-inputs/adapt/diffusion2_l2_d3_initial.dat new file mode 100644 index 00000000..1c7417f4 --- /dev/null +++ b/gold/generated-inputs/adapt/diffusion2_l2_d3_initial.dat @@ -0,0 +1,437 @@ +# Created from matlab git hash 5ce0b4d10cd8ad0d4f665011571398caa8b7d3d1 +# name: foo +# type: matrix +# rows: 432 +# columns: 1 +0 +-0.003053896742084584 +0 +0 +-0.0003578408201700921 +0 +0 +0.002751876141017713 +0 +0 +-0.003053896742084597 +0 +0 +0.0003578408201701035 +0 +0 +0.002751876141017703 +0 +0.003869518802344462 +0 +-0.0035696813276062 +0 +0 +0 +-0.0035696813276062 +0 +0.003293077364797883 +0 +0 +0 +-0.003053896742084584 +-0.0003578408201700921 +0.002751876141017713 +0 +0 +0 +0 +0 +0 +-0.003053896742084597 +0.0003578408201701035 +0.002751876141017703 +0 +0 +0 +0 +-0.04366659759167969 +0 +0 +0 +0 +0 +0.04028300313947845 +0 +0 +0 +0 +-0.04366659759167969 +0 +0.04028300313947845 +0 +0 +0 +0 +0 +0 +0 +0.492767148224842 +0 +0 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a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l2_3_d3_1_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l2_3_d3_1_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 12 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l2_3_d3_2_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l2_3_d3_2_1.dat index 94eccfe3..bb505be7 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l2_3_d3_2_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l2_3_d3_2_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 12 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l2_3_d3_3_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l2_3_d3_3_1.dat index a61a51b2..6b204878 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l2_3_d3_3_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l2_3_d3_3_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 12 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l2_3_d3_4_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l2_3_d3_4_1.dat index 0d79fb31..0b72fadc 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l2_3_d3_4_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l2_3_d3_4_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 12 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l2_3_d3_5_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l2_3_d3_5_1.dat index 1ebcdab0..2a0f8808 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l2_3_d3_5_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l2_3_d3_5_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 12 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l2_3_d3_5_2.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l2_3_d3_5_2.dat index 79da5c3a..5af04151 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l2_3_d3_5_2.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l2_3_d3_5_2.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash ac92b7161918ea19d81ea25fb565944eac86e28c +# Created from matlab git hash 7a85cb21101a410cc7fef3124c6f52da775c291f # name: foo # type: matrix # rows: 24 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l2_3_d3_6_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l2_3_d3_6_1.dat index 911cc7ec..a6a9d929 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l2_3_d3_6_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l2_3_d3_6_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 12 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l2_3_d3_7_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l2_3_d3_7_1.dat index 6972eaa3..54d70164 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l2_3_d3_7_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l2_3_d3_7_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 12 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_1_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_1_1.dat index fa20c50d..4a5a21d5 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_1_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_1_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 24 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_2_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_2_1.dat index 77599a33..a42a8a32 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_2_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_2_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 24 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_3_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_3_1.dat index 5176c40b..5e741518 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_3_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_3_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 24 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_4_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_4_1.dat index 7c323a75..643c6448 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_4_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_4_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 24 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_5_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_5_1.dat index 0a6b5a59..2370018c 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_5_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_5_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 24 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_5_2.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_5_2.dat index 79da5c3a..5af04151 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_5_2.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_5_2.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash ac92b7161918ea19d81ea25fb565944eac86e28c +# Created from matlab git hash 7a85cb21101a410cc7fef3124c6f52da775c291f # name: foo # type: matrix # rows: 24 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_6_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_6_1.dat index 9913921f..6b2be06a 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_6_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_6_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 24 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_7_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_7_1.dat index 95823822..8aaf4632 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_7_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l3_3_d3_7_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 24 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_1_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_1_1.dat index d0728ddb..8e76f4df 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_1_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_1_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 64 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_2_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_2_1.dat index 7483bc7e..17417d1e 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_2_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_2_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 64 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_3_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_3_1.dat index ed5c4d7a..8cdbdaa3 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_3_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_3_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 64 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_4_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_4_1.dat index 64809843..abfd8248 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_4_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_4_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 64 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_5_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_5_1.dat index 27cb10e5..ecd20b11 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_5_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_5_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 64 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_5_2.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_5_2.dat index b984d82d..5e746f19 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_5_2.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_5_2.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash ac92b7161918ea19d81ea25fb565944eac86e28c +# Created from matlab git hash 7a85cb21101a410cc7fef3124c6f52da775c291f # name: foo # type: matrix # rows: 16 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_6_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_6_1.dat index 750d7284..8ee105d9 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_6_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_6_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 64 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_7_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_7_1.dat index 803522e2..02860847 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_7_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_2_d4_7_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 64 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_1_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_1_1.dat index d0728ddb..8e76f4df 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_1_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_1_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 64 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_2_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_2_1.dat index 7483bc7e..17417d1e 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_2_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_2_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 64 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_3_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_3_1.dat index ed5c4d7a..8cdbdaa3 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_3_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_3_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 64 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_4_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_4_1.dat index 64809843..abfd8248 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_4_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_4_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 64 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_5_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_5_1.dat index 27cb10e5..ecd20b11 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_5_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_5_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 64 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_5_2.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_5_2.dat index f13a08b1..873a15ab 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_5_2.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_5_2.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash ac92b7161918ea19d81ea25fb565944eac86e28c +# Created from matlab git hash 7a85cb21101a410cc7fef3124c6f52da775c291f # name: foo # type: matrix # rows: 64 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_6_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_6_1.dat index 750d7284..8ee105d9 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_6_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_6_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 64 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_7_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_7_1.dat index 803522e2..02860847 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_7_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_l4_4_d4_7_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 64 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_1_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_1_1.dat index 061f6240..561d8715 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_1_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_1_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 12 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_2_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_2_1.dat index bb120ee9..7c251e43 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_2_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_2_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 12 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_3_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_3_1.dat index 8c3bf6d8..47a10ca6 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_3_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_3_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 12 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_4_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_4_1.dat index 1d34cd95..7e2519dd 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_4_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_4_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 12 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_5_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_5_1.dat index d64d2d36..26a34ac5 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_5_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_5_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 12 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_5_2.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_5_2.dat index 48c59846..bdac1179 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_5_2.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_5_2.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash ac92b7161918ea19d81ea25fb565944eac86e28c +# Created from matlab git hash 7a85cb21101a410cc7fef3124c6f52da775c291f # name: foo # type: matrix # rows: 24 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_6_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_6_1.dat index abbe3269..064ef635 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_6_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_6_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 12 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_7_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_7_1.dat index cdcd9b4c..c36da1ca 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_7_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l2_3_d3_7_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 12 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_1_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_1_1.dat index d5780140..cf387d65 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_1_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_1_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 24 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_2_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_2_1.dat index 299b512f..e92435eb 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_2_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_2_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 24 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_3_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_3_1.dat index c7ce2919..384e2c44 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_3_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_3_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 24 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_4_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_4_1.dat index eef4d026..d860599e 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_4_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_4_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 24 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_5_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_5_1.dat index 913fef55..2f482393 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_5_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_5_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 24 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_5_2.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_5_2.dat index 48c59846..bdac1179 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_5_2.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_5_2.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash ac92b7161918ea19d81ea25fb565944eac86e28c +# Created from matlab git hash 7a85cb21101a410cc7fef3124c6f52da775c291f # name: foo # type: matrix # rows: 24 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_6_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_6_1.dat index 5d808919..2a57d31d 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_6_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_6_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 24 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_7_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_7_1.dat index 0b824911..2dd44bbe 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_7_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l3_3_d3_7_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 24 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_1_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_1_1.dat index 3c05d88b..6c0a3921 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_1_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_1_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 64 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_2_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_2_1.dat index 9d106a6b..a22e1041 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_2_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_2_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 64 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_3_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_3_1.dat index 24d47fda..6357cbf6 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_3_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_3_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 64 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_4_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_4_1.dat index 455543da..44af7923 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_4_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_4_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 64 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_5_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_5_1.dat index 62bbb416..b9e328f0 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_5_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_5_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 64 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_5_2.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_5_2.dat index 928c52e3..78fc76d1 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_5_2.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_5_2.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash ac92b7161918ea19d81ea25fb565944eac86e28c +# Created from matlab git hash 7a85cb21101a410cc7fef3124c6f52da775c291f # name: foo # type: matrix # rows: 16 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_6_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_6_1.dat index 116c8347..ee1d8750 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_6_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_6_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 64 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_7_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_7_1.dat index feb32f1d..3ff4f60a 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_7_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_2_d4_7_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 64 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_1_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_1_1.dat index 3c05d88b..6c0a3921 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_1_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_1_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 64 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_2_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_2_1.dat index 9d106a6b..a22e1041 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_2_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_2_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 64 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_3_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_3_1.dat index 24d47fda..6357cbf6 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_3_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_3_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 64 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_4_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_4_1.dat index 455543da..44af7923 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_4_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_4_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 64 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_5_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_5_1.dat index 62bbb416..b9e328f0 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_5_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_5_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 64 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_5_2.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_5_2.dat index ec0e1433..4f10b93a 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_5_2.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_5_2.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash ac92b7161918ea19d81ea25fb565944eac86e28c +# Created from matlab git hash 7a85cb21101a410cc7fef3124c6f52da775c291f # name: foo # type: matrix # rows: 64 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_6_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_6_1.dat index 116c8347..ee1d8750 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_6_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_6_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 64 diff --git a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_7_1.dat b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_7_1.dat index feb32f1d..3ff4f60a 100644 --- a/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_7_1.dat +++ b/gold/generated-inputs/coefficients/fokkerplanck2_complete_coefficients_norotate_l4_4_d4_7_1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 64 diff --git a/gold/generated-inputs/pde/advection_1_dt.dat b/gold/generated-inputs/pde/advection_1_dt.dat index 083eb719..c492dddc 100644 --- a/gold/generated-inputs/pde/advection_1_dt.dat +++ b/gold/generated-inputs/pde/advection_1_dt.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash 0fe7719bac1c5c6b1e5cd966dd854d769c845b91 +# Created from matlab git hash 20448e62cfb796cbc50ba721cc04821105301e56 # name: foo # type: scalar 0.3926990816987241 diff --git a/gold/generated-inputs/pde/advection_1_exact_dim0.dat b/gold/generated-inputs/pde/advection_1_exact_dim0.dat index da087df4..96b18484 100644 --- a/gold/generated-inputs/pde/advection_1_exact_dim0.dat +++ b/gold/generated-inputs/pde/advection_1_exact_dim0.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash 55f07601599aa9d35871cff328c82f83eb5a38bf +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar --0.4902608213406994 +# type: matrix +# rows: 1 +# columns: 5 +0.9950041652780257 0.9800665778412416 0.955336489125606 0.9210609940028851 0.8775825618903728 diff --git a/gold/generated-inputs/pde/advection_1_exact_time.dat b/gold/generated-inputs/pde/advection_1_exact_time.dat index 71b15be0..b2423e7f 100644 --- a/gold/generated-inputs/pde/advection_1_exact_time.dat +++ b/gold/generated-inputs/pde/advection_1_exact_time.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash 55f07601599aa9d35871cff328c82f83eb5a38bf +# Created from matlab git hash 7a85cb21101a410cc7fef3124c6f52da775c291f # name: foo # type: scalar 1 diff --git a/gold/generated-inputs/pde/advection_1_initial_dim0.dat b/gold/generated-inputs/pde/advection_1_initial_dim0.dat index da087df4..96b18484 100644 --- a/gold/generated-inputs/pde/advection_1_initial_dim0.dat +++ b/gold/generated-inputs/pde/advection_1_initial_dim0.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash 55f07601599aa9d35871cff328c82f83eb5a38bf +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar --0.4902608213406994 +# type: matrix +# rows: 1 +# columns: 5 +0.9950041652780257 0.9800665778412416 0.955336489125606 0.9210609940028851 0.8775825618903728 diff --git a/gold/generated-inputs/pde/advection_1_source0_dim0.dat b/gold/generated-inputs/pde/advection_1_source0_dim0.dat index 144b515f..a47227eb 100644 --- a/gold/generated-inputs/pde/advection_1_source0_dim0.dat +++ b/gold/generated-inputs/pde/advection_1_source0_dim0.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash 55f07601599aa9d35871cff328c82f83eb5a38bf +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -1.743151544827176 +# type: matrix +# rows: 1 +# columns: 5 +-0.1996668332936563 -0.3973386615901224 -0.5910404133226791 -0.778836684617301 -0.958851077208406 diff --git a/gold/generated-inputs/pde/advection_1_source0_time.dat b/gold/generated-inputs/pde/advection_1_source0_time.dat index 71b15be0..3247baef 100644 --- a/gold/generated-inputs/pde/advection_1_source0_time.dat +++ b/gold/generated-inputs/pde/advection_1_source0_time.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash 55f07601599aa9d35871cff328c82f83eb5a38bf +# Created from matlab git hash 20448e62cfb796cbc50ba721cc04821105301e56 # name: foo # type: scalar 1 diff --git a/gold/generated-inputs/pde/continuity2_dt.dat b/gold/generated-inputs/pde/continuity2_dt.dat new file mode 100644 index 00000000..b0162a84 --- /dev/null +++ b/gold/generated-inputs/pde/continuity2_dt.dat @@ -0,0 +1,4 @@ +# Created from matlab git hash 20448e62cfb796cbc50ba721cc04821105301e56 +# name: foo +# type: scalar +0.0625 diff --git a/gold/generated-inputs/pde/continuity2_exact_dim0.dat b/gold/generated-inputs/pde/continuity2_exact_dim0.dat new file mode 100644 index 00000000..6960025d --- /dev/null +++ b/gold/generated-inputs/pde/continuity2_exact_dim0.dat @@ -0,0 +1,6 @@ +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc +# name: foo +# type: matrix +# rows: 1 +# columns: 5 +0.9510565162951535 0.8090169943749475 0.5877852522924731 0.3090169943749475 6.123233995736766e-17 diff --git a/gold/generated-inputs/pde/continuity2_exact_dim1.dat b/gold/generated-inputs/pde/continuity2_exact_dim1.dat new file mode 100644 index 00000000..698ea835 --- /dev/null +++ b/gold/generated-inputs/pde/continuity2_exact_dim1.dat @@ -0,0 +1,6 @@ +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc +# name: foo +# type: matrix +# rows: 1 +# columns: 5 +0.5877852522924731 0.9510565162951535 0.9510565162951536 0.5877852522924732 1.224646799147353e-16 diff --git a/gold/generated-inputs/pde/continuity2_exact_time.dat b/gold/generated-inputs/pde/continuity2_exact_time.dat new file mode 100644 index 00000000..245036e5 --- /dev/null +++ b/gold/generated-inputs/pde/continuity2_exact_time.dat @@ -0,0 +1,4 @@ +# Created from matlab git hash 7a85cb21101a410cc7fef3124c6f52da775c291f +# name: foo +# type: scalar +-0.5440211108893698 diff --git a/gold/generated-inputs/pde/continuity2_initial_dim0.dat b/gold/generated-inputs/pde/continuity2_initial_dim0.dat new file mode 100644 index 00000000..6960025d --- /dev/null +++ b/gold/generated-inputs/pde/continuity2_initial_dim0.dat @@ -0,0 +1,6 @@ +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc +# name: foo +# type: matrix +# rows: 1 +# columns: 5 +0.9510565162951535 0.8090169943749475 0.5877852522924731 0.3090169943749475 6.123233995736766e-17 diff --git a/gold/generated-inputs/pde/continuity2_initial_dim1.dat b/gold/generated-inputs/pde/continuity2_initial_dim1.dat new file mode 100644 index 00000000..698ea835 --- /dev/null +++ b/gold/generated-inputs/pde/continuity2_initial_dim1.dat @@ -0,0 +1,6 @@ +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc +# name: foo +# type: matrix +# rows: 1 +# columns: 5 +0.5877852522924731 0.9510565162951535 0.9510565162951536 0.5877852522924732 1.224646799147353e-16 diff --git a/gold/generated-inputs/pde/continuity2_source0_dim0.dat b/gold/generated-inputs/pde/continuity2_source0_dim0.dat new file mode 100644 index 00000000..6960025d --- /dev/null +++ b/gold/generated-inputs/pde/continuity2_source0_dim0.dat @@ -0,0 +1,6 @@ +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc +# name: foo +# type: matrix +# rows: 1 +# columns: 5 +0.9510565162951535 0.8090169943749475 0.5877852522924731 0.3090169943749475 6.123233995736766e-17 diff --git a/gold/generated-inputs/pde/continuity2_source0_dim1.dat b/gold/generated-inputs/pde/continuity2_source0_dim1.dat new file mode 100644 index 00000000..698ea835 --- /dev/null +++ b/gold/generated-inputs/pde/continuity2_source0_dim1.dat @@ -0,0 +1,6 @@ +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc +# name: foo +# type: matrix +# rows: 1 +# columns: 5 +0.5877852522924731 0.9510565162951535 0.9510565162951536 0.5877852522924732 1.224646799147353e-16 diff --git a/gold/generated-inputs/pde/continuity2_source0_time.dat b/gold/generated-inputs/pde/continuity2_source0_time.dat new file mode 100644 index 00000000..05d555d9 --- /dev/null +++ b/gold/generated-inputs/pde/continuity2_source0_time.dat @@ -0,0 +1,4 @@ +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc +# name: foo +# type: scalar +-1.678143058152905 diff --git a/gold/generated-inputs/pde/continuity2_source1_dim0.dat b/gold/generated-inputs/pde/continuity2_source1_dim0.dat new file mode 100644 index 00000000..6960025d --- /dev/null +++ b/gold/generated-inputs/pde/continuity2_source1_dim0.dat @@ -0,0 +1,6 @@ +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc +# name: foo +# type: matrix +# rows: 1 +# columns: 5 +0.9510565162951535 0.8090169943749475 0.5877852522924731 0.3090169943749475 6.123233995736766e-17 diff --git a/gold/generated-inputs/pde/continuity2_source1_dim1.dat b/gold/generated-inputs/pde/continuity2_source1_dim1.dat new file mode 100644 index 00000000..ab28c317 --- /dev/null +++ b/gold/generated-inputs/pde/continuity2_source1_dim1.dat @@ -0,0 +1,6 @@ +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc +# name: foo +# type: matrix +# rows: 1 +# columns: 5 +0.8090169943749475 0.3090169943749475 -0.3090169943749473 -0.8090169943749473 -1 diff --git a/gold/generated-inputs/pde/continuity2_source1_time.dat b/gold/generated-inputs/pde/continuity2_source1_time.dat new file mode 100644 index 00000000..7cbfb6ee --- /dev/null +++ b/gold/generated-inputs/pde/continuity2_source1_time.dat @@ -0,0 +1,4 @@ +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc +# name: foo +# type: scalar +-3.418185450735605 diff --git a/gold/generated-inputs/pde/continuity2_source2_dim0.dat b/gold/generated-inputs/pde/continuity2_source2_dim0.dat new file mode 100644 index 00000000..6f9885a2 --- /dev/null +++ b/gold/generated-inputs/pde/continuity2_source2_dim0.dat @@ -0,0 +1,6 @@ +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc +# name: foo +# type: matrix +# rows: 1 +# columns: 5 +0.3090169943749474 0.5877852522924731 0.8090169943749475 0.9510565162951535 1 diff --git a/gold/generated-inputs/pde/continuity2_source2_dim1.dat b/gold/generated-inputs/pde/continuity2_source2_dim1.dat new file mode 100644 index 00000000..698ea835 --- /dev/null +++ b/gold/generated-inputs/pde/continuity2_source2_dim1.dat @@ -0,0 +1,6 @@ +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc +# name: foo +# type: matrix +# rows: 1 +# columns: 5 +0.5877852522924731 0.9510565162951535 0.9510565162951536 0.5877852522924732 1.224646799147353e-16 diff --git a/gold/generated-inputs/pde/continuity2_source2_time.dat b/gold/generated-inputs/pde/continuity2_source2_time.dat new file mode 100644 index 00000000..569e2b32 --- /dev/null +++ b/gold/generated-inputs/pde/continuity2_source2_time.dat @@ -0,0 +1,4 @@ +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc +# name: foo +# type: scalar +1.709092725367802 diff --git a/gold/generated-inputs/pde/continuity_1_dt.dat b/gold/generated-inputs/pde/continuity_1_dt.dat index 1f481aa3..9e6f1775 100644 --- a/gold/generated-inputs/pde/continuity_1_dt.dat +++ b/gold/generated-inputs/pde/continuity_1_dt.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 20448e62cfb796cbc50ba721cc04821105301e56 # name: foo # type: scalar 0.5 diff --git a/gold/generated-inputs/pde/continuity_1_exact_dim0.dat b/gold/generated-inputs/pde/continuity_1_exact_dim0.dat index bd7b04b0..ab28c317 100644 --- a/gold/generated-inputs/pde/continuity_1_exact_dim0.dat +++ b/gold/generated-inputs/pde/continuity_1_exact_dim0.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.8090169943749471 +# type: matrix +# rows: 1 +# columns: 5 +0.8090169943749475 0.3090169943749475 -0.3090169943749473 -0.8090169943749473 -1 diff --git a/gold/generated-inputs/pde/continuity_1_exact_time.dat b/gold/generated-inputs/pde/continuity_1_exact_time.dat index 51104bb6..992ebf46 100644 --- a/gold/generated-inputs/pde/continuity_1_exact_time.dat +++ b/gold/generated-inputs/pde/continuity_1_exact_time.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 7a85cb21101a410cc7fef3124c6f52da775c291f # name: foo # type: scalar -0.8912073600614354 +-0.9589242746631385 diff --git a/gold/generated-inputs/pde/continuity_1_initial_dim0.dat b/gold/generated-inputs/pde/continuity_1_initial_dim0.dat index ecc9d53e..ea4f771c 100644 --- a/gold/generated-inputs/pde/continuity_1_initial_dim0.dat +++ b/gold/generated-inputs/pde/continuity_1_initial_dim0.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0 +# type: matrix +# rows: 1 +# columns: 5 +0 0 0 0 0 diff --git a/gold/generated-inputs/pde/continuity_1_source0_dim0.dat b/gold/generated-inputs/pde/continuity_1_source0_dim0.dat index bd7b04b0..ab28c317 100644 --- a/gold/generated-inputs/pde/continuity_1_source0_dim0.dat +++ b/gold/generated-inputs/pde/continuity_1_source0_dim0.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.8090169943749471 +# type: matrix +# rows: 1 +# columns: 5 +0.8090169943749475 0.3090169943749475 -0.3090169943749473 -0.8090169943749473 -1 diff --git a/gold/generated-inputs/pde/continuity_1_source0_time.dat b/gold/generated-inputs/pde/continuity_1_source0_time.dat index d6bb40e7..56ebbe87 100644 --- a/gold/generated-inputs/pde/continuity_1_source0_time.dat +++ b/gold/generated-inputs/pde/continuity_1_source0_time.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo # type: scalar -0.4535961214255773 +0.2836621854632262 diff --git a/gold/generated-inputs/pde/continuity_1_source1_dim0.dat b/gold/generated-inputs/pde/continuity_1_source1_dim0.dat index f6d5be1a..698ea835 100644 --- a/gold/generated-inputs/pde/continuity_1_source1_dim0.dat +++ b/gold/generated-inputs/pde/continuity_1_source1_dim0.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.5877852522924736 +# type: matrix +# rows: 1 +# columns: 5 +0.5877852522924731 0.9510565162951535 0.9510565162951536 0.5877852522924732 1.224646799147353e-16 diff --git a/gold/generated-inputs/pde/continuity_1_source1_time.dat b/gold/generated-inputs/pde/continuity_1_source1_time.dat index ffafc471..bf634707 100644 --- a/gold/generated-inputs/pde/continuity_1_source1_time.dat +++ b/gold/generated-inputs/pde/continuity_1_source1_time.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo # type: scalar --5.599620990388318 +6.025098913261274 diff --git a/gold/generated-inputs/pde/continuity_2_dt.dat b/gold/generated-inputs/pde/continuity_2_dt.dat deleted file mode 100644 index 1f481aa3..00000000 --- a/gold/generated-inputs/pde/continuity_2_dt.dat +++ /dev/null @@ -1,4 +0,0 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c -# name: foo -# type: scalar -0.5 diff --git a/gold/generated-inputs/pde/continuity_2_exact_dim0.dat b/gold/generated-inputs/pde/continuity_2_exact_dim0.dat deleted file mode 100644 index bd7b04b0..00000000 --- a/gold/generated-inputs/pde/continuity_2_exact_dim0.dat +++ /dev/null @@ -1,4 +0,0 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c -# name: foo -# type: scalar -0.8090169943749471 diff --git a/gold/generated-inputs/pde/continuity_2_exact_dim1.dat b/gold/generated-inputs/pde/continuity_2_exact_dim1.dat deleted file mode 100644 index 47054191..00000000 --- a/gold/generated-inputs/pde/continuity_2_exact_dim1.dat +++ /dev/null @@ -1,4 +0,0 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c -# name: foo -# type: scalar -0.951056516295154 diff --git a/gold/generated-inputs/pde/continuity_2_exact_time.dat b/gold/generated-inputs/pde/continuity_2_exact_time.dat deleted file mode 100644 index e298bf1a..00000000 --- a/gold/generated-inputs/pde/continuity_2_exact_time.dat +++ /dev/null @@ -1,4 +0,0 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c -# name: foo -# type: scalar --0.9516020738895161 diff --git a/gold/generated-inputs/pde/continuity_2_initial_dim0.dat b/gold/generated-inputs/pde/continuity_2_initial_dim0.dat deleted file mode 100644 index ecc9d53e..00000000 --- a/gold/generated-inputs/pde/continuity_2_initial_dim0.dat +++ /dev/null @@ -1,4 +0,0 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c -# name: foo -# type: scalar -0 diff --git a/gold/generated-inputs/pde/continuity_2_initial_dim1.dat b/gold/generated-inputs/pde/continuity_2_initial_dim1.dat deleted file mode 100644 index ecc9d53e..00000000 --- a/gold/generated-inputs/pde/continuity_2_initial_dim1.dat +++ /dev/null @@ -1,4 +0,0 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c -# name: foo -# type: scalar -0 diff --git a/gold/generated-inputs/pde/continuity_2_source0_dim0.dat b/gold/generated-inputs/pde/continuity_2_source0_dim0.dat deleted file mode 100644 index bd7b04b0..00000000 --- a/gold/generated-inputs/pde/continuity_2_source0_dim0.dat +++ /dev/null @@ -1,4 +0,0 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c -# name: foo -# type: scalar -0.8090169943749471 diff --git a/gold/generated-inputs/pde/continuity_2_source0_dim1.dat b/gold/generated-inputs/pde/continuity_2_source0_dim1.dat deleted file mode 100644 index 47054191..00000000 --- a/gold/generated-inputs/pde/continuity_2_source0_dim1.dat +++ /dev/null @@ -1,4 +0,0 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c -# name: foo -# type: scalar -0.951056516295154 diff --git a/gold/generated-inputs/pde/continuity_2_source0_time.dat b/gold/generated-inputs/pde/continuity_2_source0_time.dat deleted file mode 100644 index 79affb0b..00000000 --- a/gold/generated-inputs/pde/continuity_2_source0_time.dat +++ /dev/null @@ -1,4 +0,0 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c -# name: foo -# type: scalar --0.6146657399568387 diff --git a/gold/generated-inputs/pde/continuity_2_source1_dim0.dat b/gold/generated-inputs/pde/continuity_2_source1_dim0.dat deleted file mode 100644 index bd7b04b0..00000000 --- a/gold/generated-inputs/pde/continuity_2_source1_dim0.dat +++ /dev/null @@ -1,4 +0,0 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c -# name: foo -# type: scalar -0.8090169943749471 diff --git a/gold/generated-inputs/pde/continuity_2_source1_dim1.dat b/gold/generated-inputs/pde/continuity_2_source1_dim1.dat deleted file mode 100644 index 23d5485f..00000000 --- a/gold/generated-inputs/pde/continuity_2_source1_dim1.dat +++ /dev/null @@ -1,4 +0,0 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c -# name: foo -# type: scalar -0.3090169943749462 diff --git a/gold/generated-inputs/pde/continuity_2_source1_time.dat b/gold/generated-inputs/pde/continuity_2_source1_time.dat deleted file mode 100644 index 13ee7dda..00000000 --- a/gold/generated-inputs/pde/continuity_2_source1_time.dat +++ /dev/null @@ -1,4 +0,0 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c -# name: foo -# type: scalar --5.979092168944231 diff --git a/gold/generated-inputs/pde/continuity_2_source2_dim0.dat b/gold/generated-inputs/pde/continuity_2_source2_dim0.dat deleted file mode 100644 index f6d5be1a..00000000 --- a/gold/generated-inputs/pde/continuity_2_source2_dim0.dat +++ /dev/null @@ -1,4 +0,0 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c -# name: foo -# type: scalar -0.5877852522924736 diff --git a/gold/generated-inputs/pde/continuity_2_source2_dim1.dat b/gold/generated-inputs/pde/continuity_2_source2_dim1.dat deleted file mode 100644 index 47054191..00000000 --- a/gold/generated-inputs/pde/continuity_2_source2_dim1.dat +++ /dev/null @@ -1,4 +0,0 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c -# name: foo -# type: scalar -0.951056516295154 diff --git a/gold/generated-inputs/pde/continuity_2_source2_time.dat b/gold/generated-inputs/pde/continuity_2_source2_time.dat deleted file mode 100644 index 2c8fe66a..00000000 --- a/gold/generated-inputs/pde/continuity_2_source2_time.dat +++ /dev/null @@ -1,4 +0,0 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c -# name: foo -# type: scalar -2.989546084472115 diff --git a/gold/generated-inputs/pde/continuity_3_dt.dat b/gold/generated-inputs/pde/continuity_3_dt.dat index 1f481aa3..813244a3 100644 --- a/gold/generated-inputs/pde/continuity_3_dt.dat +++ b/gold/generated-inputs/pde/continuity_3_dt.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 7a85cb21101a410cc7fef3124c6f52da775c291f # name: foo # type: scalar -0.5 +0.0625 diff --git a/gold/generated-inputs/pde/continuity_3_exact_dim0.dat b/gold/generated-inputs/pde/continuity_3_exact_dim0.dat index 936e703b..6960025d 100644 --- a/gold/generated-inputs/pde/continuity_3_exact_dim0.dat +++ b/gold/generated-inputs/pde/continuity_3_exact_dim0.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar --0.5877852522924735 +# type: matrix +# rows: 1 +# columns: 5 +0.9510565162951535 0.8090169943749475 0.5877852522924731 0.3090169943749475 6.123233995736766e-17 diff --git a/gold/generated-inputs/pde/continuity_3_exact_dim1.dat b/gold/generated-inputs/pde/continuity_3_exact_dim1.dat index 72744cec..698ea835 100644 --- a/gold/generated-inputs/pde/continuity_3_exact_dim1.dat +++ b/gold/generated-inputs/pde/continuity_3_exact_dim1.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.9510565162951539 +# type: matrix +# rows: 1 +# columns: 5 +0.5877852522924731 0.9510565162951535 0.9510565162951536 0.5877852522924732 1.224646799147353e-16 diff --git a/gold/generated-inputs/pde/continuity_3_exact_dim2.dat b/gold/generated-inputs/pde/continuity_3_exact_dim2.dat index 32ce9cbf..2aef659d 100644 --- a/gold/generated-inputs/pde/continuity_3_exact_dim2.dat +++ b/gold/generated-inputs/pde/continuity_3_exact_dim2.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.8090169943749476 +# type: matrix +# rows: 1 +# columns: 5 +0.9781476007338057 0.9135454576426009 0.8090169943749475 0.6691306063588582 0.5000000000000001 diff --git a/gold/generated-inputs/pde/continuity_3_exact_time.dat b/gold/generated-inputs/pde/continuity_3_exact_time.dat index eba4d005..245036e5 100644 --- a/gold/generated-inputs/pde/continuity_3_exact_time.dat +++ b/gold/generated-inputs/pde/continuity_3_exact_time.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 7a85cb21101a410cc7fef3124c6f52da775c291f # name: foo # type: scalar -0.3115413635133779 +-0.5440211108893698 diff --git a/gold/generated-inputs/pde/continuity_3_initial_dim0.dat b/gold/generated-inputs/pde/continuity_3_initial_dim0.dat index ecc9d53e..f9a203e4 100644 --- a/gold/generated-inputs/pde/continuity_3_initial_dim0.dat +++ b/gold/generated-inputs/pde/continuity_3_initial_dim0.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 7a85cb21101a410cc7fef3124c6f52da775c291f # name: foo -# type: scalar -0 +# type: matrix +# rows: 1 +# columns: 5 +0 0 0 0 0 diff --git a/gold/generated-inputs/pde/continuity_3_initial_dim1.dat b/gold/generated-inputs/pde/continuity_3_initial_dim1.dat index ecc9d53e..f9a203e4 100644 --- a/gold/generated-inputs/pde/continuity_3_initial_dim1.dat +++ b/gold/generated-inputs/pde/continuity_3_initial_dim1.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 7a85cb21101a410cc7fef3124c6f52da775c291f # name: foo -# type: scalar -0 +# type: matrix +# rows: 1 +# columns: 5 +0 0 0 0 0 diff --git a/gold/generated-inputs/pde/continuity_3_initial_dim2.dat b/gold/generated-inputs/pde/continuity_3_initial_dim2.dat index ecc9d53e..f9a203e4 100644 --- a/gold/generated-inputs/pde/continuity_3_initial_dim2.dat +++ b/gold/generated-inputs/pde/continuity_3_initial_dim2.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 7a85cb21101a410cc7fef3124c6f52da775c291f # name: foo -# type: scalar -0 +# type: matrix +# rows: 1 +# columns: 5 +0 0 0 0 0 diff --git a/gold/generated-inputs/pde/continuity_3_source0_dim0.dat b/gold/generated-inputs/pde/continuity_3_source0_dim0.dat index 936e703b..6960025d 100644 --- a/gold/generated-inputs/pde/continuity_3_source0_dim0.dat +++ b/gold/generated-inputs/pde/continuity_3_source0_dim0.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar --0.5877852522924735 +# type: matrix +# rows: 1 +# columns: 5 +0.9510565162951535 0.8090169943749475 0.5877852522924731 0.3090169943749475 6.123233995736766e-17 diff --git a/gold/generated-inputs/pde/continuity_3_source0_dim1.dat b/gold/generated-inputs/pde/continuity_3_source0_dim1.dat index 72744cec..698ea835 100644 --- a/gold/generated-inputs/pde/continuity_3_source0_dim1.dat +++ b/gold/generated-inputs/pde/continuity_3_source0_dim1.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.9510565162951539 +# type: matrix +# rows: 1 +# columns: 5 +0.5877852522924731 0.9510565162951535 0.9510565162951536 0.5877852522924732 1.224646799147353e-16 diff --git a/gold/generated-inputs/pde/continuity_3_source0_dim2.dat b/gold/generated-inputs/pde/continuity_3_source0_dim2.dat index 32ce9cbf..2aef659d 100644 --- a/gold/generated-inputs/pde/continuity_3_source0_dim2.dat +++ b/gold/generated-inputs/pde/continuity_3_source0_dim2.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.8090169943749476 +# type: matrix +# rows: 1 +# columns: 5 +0.9781476007338057 0.9135454576426009 0.8090169943749475 0.6691306063588582 0.5000000000000001 diff --git a/gold/generated-inputs/pde/continuity_3_source0_time.dat b/gold/generated-inputs/pde/continuity_3_source0_time.dat index 2376929a..05d555d9 100644 --- a/gold/generated-inputs/pde/continuity_3_source0_time.dat +++ b/gold/generated-inputs/pde/continuity_3_source0_time.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo # type: scalar -1.900465183917059 +-1.678143058152905 diff --git a/gold/generated-inputs/pde/continuity_3_source1_dim0.dat b/gold/generated-inputs/pde/continuity_3_source1_dim0.dat index 936e703b..6960025d 100644 --- a/gold/generated-inputs/pde/continuity_3_source1_dim0.dat +++ b/gold/generated-inputs/pde/continuity_3_source1_dim0.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar --0.5877852522924735 +# type: matrix +# rows: 1 +# columns: 5 +0.9510565162951535 0.8090169943749475 0.5877852522924731 0.3090169943749475 6.123233995736766e-17 diff --git a/gold/generated-inputs/pde/continuity_3_source1_dim1.dat b/gold/generated-inputs/pde/continuity_3_source1_dim1.dat index 4b01e92f..ab28c317 100644 --- a/gold/generated-inputs/pde/continuity_3_source1_dim1.dat +++ b/gold/generated-inputs/pde/continuity_3_source1_dim1.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar --0.3090169943749467 +# type: matrix +# rows: 1 +# columns: 5 +0.8090169943749475 0.3090169943749475 -0.3090169943749473 -0.8090169943749473 -1 diff --git a/gold/generated-inputs/pde/continuity_3_source1_dim2.dat b/gold/generated-inputs/pde/continuity_3_source1_dim2.dat index 32ce9cbf..2aef659d 100644 --- a/gold/generated-inputs/pde/continuity_3_source1_dim2.dat +++ b/gold/generated-inputs/pde/continuity_3_source1_dim2.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.8090169943749476 +# type: matrix +# rows: 1 +# columns: 5 +0.9781476007338057 0.9135454576426009 0.8090169943749475 0.6691306063588582 0.5000000000000001 diff --git a/gold/generated-inputs/pde/continuity_3_source1_time.dat b/gold/generated-inputs/pde/continuity_3_source1_time.dat index 3148d32f..7cbfb6ee 100644 --- a/gold/generated-inputs/pde/continuity_3_source1_time.dat +++ b/gold/generated-inputs/pde/continuity_3_source1_time.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo # type: scalar -1.95747211780595 +-3.418185450735605 diff --git a/gold/generated-inputs/pde/continuity_3_source2_dim0.dat b/gold/generated-inputs/pde/continuity_3_source2_dim0.dat index 1abe96d6..6f9885a2 100644 --- a/gold/generated-inputs/pde/continuity_3_source2_dim0.dat +++ b/gold/generated-inputs/pde/continuity_3_source2_dim0.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar --0.8090169943749472 +# type: matrix +# rows: 1 +# columns: 5 +0.3090169943749474 0.5877852522924731 0.8090169943749475 0.9510565162951535 1 diff --git a/gold/generated-inputs/pde/continuity_3_source2_dim1.dat b/gold/generated-inputs/pde/continuity_3_source2_dim1.dat index 72744cec..698ea835 100644 --- a/gold/generated-inputs/pde/continuity_3_source2_dim1.dat +++ b/gold/generated-inputs/pde/continuity_3_source2_dim1.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.9510565162951539 +# type: matrix +# rows: 1 +# columns: 5 +0.5877852522924731 0.9510565162951535 0.9510565162951536 0.5877852522924732 1.224646799147353e-16 diff --git a/gold/generated-inputs/pde/continuity_3_source2_dim2.dat b/gold/generated-inputs/pde/continuity_3_source2_dim2.dat index 32ce9cbf..2aef659d 100644 --- a/gold/generated-inputs/pde/continuity_3_source2_dim2.dat +++ b/gold/generated-inputs/pde/continuity_3_source2_dim2.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.8090169943749476 +# type: matrix +# rows: 1 +# columns: 5 +0.9781476007338057 0.9135454576426009 0.8090169943749475 0.6691306063588582 0.5000000000000001 diff --git a/gold/generated-inputs/pde/continuity_3_source2_time.dat b/gold/generated-inputs/pde/continuity_3_source2_time.dat index 9e2a6f9d..569e2b32 100644 --- a/gold/generated-inputs/pde/continuity_3_source2_time.dat +++ b/gold/generated-inputs/pde/continuity_3_source2_time.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo # type: scalar --0.9787360589029751 +1.709092725367802 diff --git a/gold/generated-inputs/pde/continuity_3_source3_dim0.dat b/gold/generated-inputs/pde/continuity_3_source3_dim0.dat index 936e703b..6960025d 100644 --- a/gold/generated-inputs/pde/continuity_3_source3_dim0.dat +++ b/gold/generated-inputs/pde/continuity_3_source3_dim0.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar --0.5877852522924735 +# type: matrix +# rows: 1 +# columns: 5 +0.9510565162951535 0.8090169943749475 0.5877852522924731 0.3090169943749475 6.123233995736766e-17 diff --git a/gold/generated-inputs/pde/continuity_3_source3_dim1.dat b/gold/generated-inputs/pde/continuity_3_source3_dim1.dat index 72744cec..698ea835 100644 --- a/gold/generated-inputs/pde/continuity_3_source3_dim1.dat +++ b/gold/generated-inputs/pde/continuity_3_source3_dim1.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.9510565162951539 +# type: matrix +# rows: 1 +# columns: 5 +0.5877852522924731 0.9510565162951535 0.9510565162951536 0.5877852522924732 1.224646799147353e-16 diff --git a/gold/generated-inputs/pde/continuity_3_source3_dim2.dat b/gold/generated-inputs/pde/continuity_3_source3_dim2.dat index 88f49f49..fa9a0985 100644 --- a/gold/generated-inputs/pde/continuity_3_source3_dim2.dat +++ b/gold/generated-inputs/pde/continuity_3_source3_dim2.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.5877852522924729 +# type: matrix +# rows: 1 +# columns: 5 +0.2079116908177593 0.4067366430758002 0.5877852522924731 0.7431448254773942 0.8660254037844386 diff --git a/gold/generated-inputs/pde/continuity_3_source3_time.dat b/gold/generated-inputs/pde/continuity_3_source3_time.dat index 8248a539..d58f9a9d 100644 --- a/gold/generated-inputs/pde/continuity_3_source3_time.dat +++ b/gold/generated-inputs/pde/continuity_3_source3_time.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo # type: scalar --0.6524907059353167 +1.139395150245202 diff --git a/gold/generated-inputs/pde/continuity_6_dt.dat b/gold/generated-inputs/pde/continuity_6_dt.dat index 1f481aa3..1fe6ce5f 100644 --- a/gold/generated-inputs/pde/continuity_6_dt.dat +++ b/gold/generated-inputs/pde/continuity_6_dt.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 20448e62cfb796cbc50ba721cc04821105301e56 # name: foo # type: scalar -0.5 +0.25 diff --git a/gold/generated-inputs/pde/continuity_6_exact_dim0.dat b/gold/generated-inputs/pde/continuity_6_exact_dim0.dat index 4b01e92f..6960025d 100644 --- a/gold/generated-inputs/pde/continuity_6_exact_dim0.dat +++ b/gold/generated-inputs/pde/continuity_6_exact_dim0.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar --0.3090169943749467 +# type: matrix +# rows: 1 +# columns: 5 +0.9510565162951535 0.8090169943749475 0.5877852522924731 0.3090169943749475 6.123233995736766e-17 diff --git a/gold/generated-inputs/pde/continuity_6_exact_dim1.dat b/gold/generated-inputs/pde/continuity_6_exact_dim1.dat index 1abe96d6..951cfc81 100644 --- a/gold/generated-inputs/pde/continuity_6_exact_dim1.dat +++ b/gold/generated-inputs/pde/continuity_6_exact_dim1.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar --0.8090169943749472 +# type: matrix +# rows: 1 +# columns: 5 +0.1564344650402309 0.3090169943749474 0.4539904997395467 0.5877852522924731 0.7071067811865475 diff --git a/gold/generated-inputs/pde/continuity_6_exact_dim2.dat b/gold/generated-inputs/pde/continuity_6_exact_dim2.dat index 2452eabc..14ec2ced 100644 --- a/gold/generated-inputs/pde/continuity_6_exact_dim2.dat +++ b/gold/generated-inputs/pde/continuity_6_exact_dim2.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.8090169943749481 +# type: matrix +# rows: 1 +# columns: 5 +0.9945218953682733 0.9781476007338057 0.9510565162951536 0.9135454576426009 0.8660254037844387 diff --git a/gold/generated-inputs/pde/continuity_6_exact_dim3.dat b/gold/generated-inputs/pde/continuity_6_exact_dim3.dat index c1c57946..85bb35d4 100644 --- a/gold/generated-inputs/pde/continuity_6_exact_dim3.dat +++ b/gold/generated-inputs/pde/continuity_6_exact_dim3.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar --0.481753674101715 +# type: matrix +# rows: 1 +# columns: 5 +0.9995065603657316 0.9980267284282716 0.99556196460308 0.9921147013144779 0.9876883405951378 diff --git a/gold/generated-inputs/pde/continuity_6_exact_dim4.dat b/gold/generated-inputs/pde/continuity_6_exact_dim4.dat index 4134e47a..435e842a 100644 --- a/gold/generated-inputs/pde/continuity_6_exact_dim4.dat +++ b/gold/generated-inputs/pde/continuity_6_exact_dim4.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.8607420270039435 +# type: matrix +# rows: 1 +# columns: 5 +0.01570731731182068 0.03141075907812829 0.04710645070964266 0.06279051952931337 0.07845909572784494 diff --git a/gold/generated-inputs/pde/continuity_6_exact_dim5.dat b/gold/generated-inputs/pde/continuity_6_exact_dim5.dat index 58a1166e..41c01c05 100644 --- a/gold/generated-inputs/pde/continuity_6_exact_dim5.dat +++ b/gold/generated-inputs/pde/continuity_6_exact_dim5.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.7705132427757893 +# type: matrix +# rows: 1 +# columns: 5 +0.9999451693655121 0.9997806834748455 0.9995065603657316 0.9991228300988584 0.9986295347545738 diff --git a/gold/generated-inputs/pde/continuity_6_exact_time.dat b/gold/generated-inputs/pde/continuity_6_exact_time.dat index b84414ee..245036e5 100644 --- a/gold/generated-inputs/pde/continuity_6_exact_time.dat +++ b/gold/generated-inputs/pde/continuity_6_exact_time.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 7a85cb21101a410cc7fef3124c6f52da775c291f # name: foo # type: scalar -0.592073514707223 +-0.5440211108893698 diff --git a/gold/generated-inputs/pde/continuity_6_initial_dim0.dat b/gold/generated-inputs/pde/continuity_6_initial_dim0.dat index ecc9d53e..f9a203e4 100644 --- a/gold/generated-inputs/pde/continuity_6_initial_dim0.dat +++ b/gold/generated-inputs/pde/continuity_6_initial_dim0.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 7a85cb21101a410cc7fef3124c6f52da775c291f # name: foo -# type: scalar -0 +# type: matrix +# rows: 1 +# columns: 5 +0 0 0 0 0 diff --git a/gold/generated-inputs/pde/continuity_6_initial_dim1.dat b/gold/generated-inputs/pde/continuity_6_initial_dim1.dat index ecc9d53e..f9a203e4 100644 --- a/gold/generated-inputs/pde/continuity_6_initial_dim1.dat +++ b/gold/generated-inputs/pde/continuity_6_initial_dim1.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 7a85cb21101a410cc7fef3124c6f52da775c291f # name: foo -# type: scalar -0 +# type: matrix +# rows: 1 +# columns: 5 +0 0 0 0 0 diff --git a/gold/generated-inputs/pde/continuity_6_initial_dim2.dat b/gold/generated-inputs/pde/continuity_6_initial_dim2.dat index ecc9d53e..f9a203e4 100644 --- a/gold/generated-inputs/pde/continuity_6_initial_dim2.dat +++ b/gold/generated-inputs/pde/continuity_6_initial_dim2.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 7a85cb21101a410cc7fef3124c6f52da775c291f # name: foo -# type: scalar -0 +# type: matrix +# rows: 1 +# columns: 5 +0 0 0 0 0 diff --git a/gold/generated-inputs/pde/continuity_6_initial_dim3.dat b/gold/generated-inputs/pde/continuity_6_initial_dim3.dat index ecc9d53e..f9a203e4 100644 --- a/gold/generated-inputs/pde/continuity_6_initial_dim3.dat +++ b/gold/generated-inputs/pde/continuity_6_initial_dim3.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 7a85cb21101a410cc7fef3124c6f52da775c291f # name: foo -# type: scalar -0 +# type: matrix +# rows: 1 +# columns: 5 +0 0 0 0 0 diff --git a/gold/generated-inputs/pde/continuity_6_initial_dim4.dat b/gold/generated-inputs/pde/continuity_6_initial_dim4.dat index ecc9d53e..f9a203e4 100644 --- a/gold/generated-inputs/pde/continuity_6_initial_dim4.dat +++ b/gold/generated-inputs/pde/continuity_6_initial_dim4.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 7a85cb21101a410cc7fef3124c6f52da775c291f # name: foo -# type: scalar -0 +# type: matrix +# rows: 1 +# columns: 5 +0 0 0 0 0 diff --git a/gold/generated-inputs/pde/continuity_6_initial_dim5.dat b/gold/generated-inputs/pde/continuity_6_initial_dim5.dat index ecc9d53e..f9a203e4 100644 --- a/gold/generated-inputs/pde/continuity_6_initial_dim5.dat +++ b/gold/generated-inputs/pde/continuity_6_initial_dim5.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 7a85cb21101a410cc7fef3124c6f52da775c291f # name: foo -# type: scalar -0 +# type: matrix +# rows: 1 +# columns: 5 +0 0 0 0 0 diff --git a/gold/generated-inputs/pde/continuity_6_source0_dim0.dat b/gold/generated-inputs/pde/continuity_6_source0_dim0.dat index 4b01e92f..6960025d 100644 --- a/gold/generated-inputs/pde/continuity_6_source0_dim0.dat +++ b/gold/generated-inputs/pde/continuity_6_source0_dim0.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar --0.3090169943749467 +# type: matrix +# rows: 1 +# columns: 5 +0.9510565162951535 0.8090169943749475 0.5877852522924731 0.3090169943749475 6.123233995736766e-17 diff --git a/gold/generated-inputs/pde/continuity_6_source0_dim1.dat b/gold/generated-inputs/pde/continuity_6_source0_dim1.dat index 1abe96d6..951cfc81 100644 --- a/gold/generated-inputs/pde/continuity_6_source0_dim1.dat +++ b/gold/generated-inputs/pde/continuity_6_source0_dim1.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar --0.8090169943749472 +# type: matrix +# rows: 1 +# columns: 5 +0.1564344650402309 0.3090169943749474 0.4539904997395467 0.5877852522924731 0.7071067811865475 diff --git a/gold/generated-inputs/pde/continuity_6_source0_dim2.dat b/gold/generated-inputs/pde/continuity_6_source0_dim2.dat index 2452eabc..14ec2ced 100644 --- a/gold/generated-inputs/pde/continuity_6_source0_dim2.dat +++ b/gold/generated-inputs/pde/continuity_6_source0_dim2.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.8090169943749481 +# type: matrix +# rows: 1 +# columns: 5 +0.9945218953682733 0.9781476007338057 0.9510565162951536 0.9135454576426009 0.8660254037844387 diff --git a/gold/generated-inputs/pde/continuity_6_source0_dim3.dat b/gold/generated-inputs/pde/continuity_6_source0_dim3.dat index c1c57946..85bb35d4 100644 --- a/gold/generated-inputs/pde/continuity_6_source0_dim3.dat +++ b/gold/generated-inputs/pde/continuity_6_source0_dim3.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar --0.481753674101715 +# type: matrix +# rows: 1 +# columns: 5 +0.9995065603657316 0.9980267284282716 0.99556196460308 0.9921147013144779 0.9876883405951378 diff --git a/gold/generated-inputs/pde/continuity_6_source0_dim4.dat b/gold/generated-inputs/pde/continuity_6_source0_dim4.dat index 4134e47a..435e842a 100644 --- a/gold/generated-inputs/pde/continuity_6_source0_dim4.dat +++ b/gold/generated-inputs/pde/continuity_6_source0_dim4.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.8607420270039435 +# type: matrix +# rows: 1 +# columns: 5 +0.01570731731182068 0.03141075907812829 0.04710645070964266 0.06279051952931337 0.07845909572784494 diff --git a/gold/generated-inputs/pde/continuity_6_source0_dim5.dat b/gold/generated-inputs/pde/continuity_6_source0_dim5.dat index 58a1166e..41c01c05 100644 --- a/gold/generated-inputs/pde/continuity_6_source0_dim5.dat +++ b/gold/generated-inputs/pde/continuity_6_source0_dim5.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.7705132427757893 +# type: matrix +# rows: 1 +# columns: 5 +0.9999451693655121 0.9997806834748455 0.9995065603657316 0.9991228300988584 0.9986295347545738 diff --git a/gold/generated-inputs/pde/continuity_6_source0_time.dat b/gold/generated-inputs/pde/continuity_6_source0_time.dat index 8e86e308..05d555d9 100644 --- a/gold/generated-inputs/pde/continuity_6_source0_time.dat +++ b/gold/generated-inputs/pde/continuity_6_source0_time.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo # type: scalar -1.611767915280901 +-1.678143058152905 diff --git a/gold/generated-inputs/pde/continuity_6_source1_dim0.dat b/gold/generated-inputs/pde/continuity_6_source1_dim0.dat index 4b01e92f..6960025d 100644 --- a/gold/generated-inputs/pde/continuity_6_source1_dim0.dat +++ b/gold/generated-inputs/pde/continuity_6_source1_dim0.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar --0.3090169943749467 +# type: matrix +# rows: 1 +# columns: 5 +0.9510565162951535 0.8090169943749475 0.5877852522924731 0.3090169943749475 6.123233995736766e-17 diff --git a/gold/generated-inputs/pde/continuity_6_source1_dim1.dat b/gold/generated-inputs/pde/continuity_6_source1_dim1.dat index 936e703b..9bbb6190 100644 --- a/gold/generated-inputs/pde/continuity_6_source1_dim1.dat +++ b/gold/generated-inputs/pde/continuity_6_source1_dim1.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar --0.5877852522924735 +# type: matrix +# rows: 1 +# columns: 5 +0.9876883405951378 0.9510565162951535 0.8910065241883679 0.8090169943749475 0.7071067811865476 diff --git a/gold/generated-inputs/pde/continuity_6_source1_dim2.dat b/gold/generated-inputs/pde/continuity_6_source1_dim2.dat index 2452eabc..14ec2ced 100644 --- a/gold/generated-inputs/pde/continuity_6_source1_dim2.dat +++ b/gold/generated-inputs/pde/continuity_6_source1_dim2.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.8090169943749481 +# type: matrix +# rows: 1 +# columns: 5 +0.9945218953682733 0.9781476007338057 0.9510565162951536 0.9135454576426009 0.8660254037844387 diff --git a/gold/generated-inputs/pde/continuity_6_source1_dim3.dat b/gold/generated-inputs/pde/continuity_6_source1_dim3.dat index c1c57946..85bb35d4 100644 --- a/gold/generated-inputs/pde/continuity_6_source1_dim3.dat +++ b/gold/generated-inputs/pde/continuity_6_source1_dim3.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar --0.481753674101715 +# type: matrix +# rows: 1 +# columns: 5 +0.9995065603657316 0.9980267284282716 0.99556196460308 0.9921147013144779 0.9876883405951378 diff --git a/gold/generated-inputs/pde/continuity_6_source1_dim4.dat b/gold/generated-inputs/pde/continuity_6_source1_dim4.dat index 4134e47a..435e842a 100644 --- a/gold/generated-inputs/pde/continuity_6_source1_dim4.dat +++ b/gold/generated-inputs/pde/continuity_6_source1_dim4.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.8607420270039435 +# type: matrix +# rows: 1 +# columns: 5 +0.01570731731182068 0.03141075907812829 0.04710645070964266 0.06279051952931337 0.07845909572784494 diff --git a/gold/generated-inputs/pde/continuity_6_source1_dim5.dat b/gold/generated-inputs/pde/continuity_6_source1_dim5.dat index 58a1166e..41c01c05 100644 --- a/gold/generated-inputs/pde/continuity_6_source1_dim5.dat +++ b/gold/generated-inputs/pde/continuity_6_source1_dim5.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.7705132427757893 +# type: matrix +# rows: 1 +# columns: 5 +0.9999451693655121 0.9997806834748455 0.9995065603657316 0.9991228300988584 0.9986295347545738 diff --git a/gold/generated-inputs/pde/continuity_6_source1_time.dat b/gold/generated-inputs/pde/continuity_6_source1_time.dat index 01cf2c25..e6d8c5fd 100644 --- a/gold/generated-inputs/pde/continuity_6_source1_time.dat +++ b/gold/generated-inputs/pde/continuity_6_source1_time.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo # type: scalar -0.9300269020946501 +-0.8545463626839012 diff --git a/gold/generated-inputs/pde/continuity_6_source2_dim0.dat b/gold/generated-inputs/pde/continuity_6_source2_dim0.dat index 72744cec..6f9885a2 100644 --- a/gold/generated-inputs/pde/continuity_6_source2_dim0.dat +++ b/gold/generated-inputs/pde/continuity_6_source2_dim0.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.9510565162951539 +# type: matrix +# rows: 1 +# columns: 5 +0.3090169943749474 0.5877852522924731 0.8090169943749475 0.9510565162951535 1 diff --git a/gold/generated-inputs/pde/continuity_6_source2_dim1.dat b/gold/generated-inputs/pde/continuity_6_source2_dim1.dat index 1abe96d6..951cfc81 100644 --- a/gold/generated-inputs/pde/continuity_6_source2_dim1.dat +++ b/gold/generated-inputs/pde/continuity_6_source2_dim1.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar --0.8090169943749472 +# type: matrix +# rows: 1 +# columns: 5 +0.1564344650402309 0.3090169943749474 0.4539904997395467 0.5877852522924731 0.7071067811865475 diff --git a/gold/generated-inputs/pde/continuity_6_source2_dim2.dat b/gold/generated-inputs/pde/continuity_6_source2_dim2.dat index 2452eabc..14ec2ced 100644 --- a/gold/generated-inputs/pde/continuity_6_source2_dim2.dat +++ b/gold/generated-inputs/pde/continuity_6_source2_dim2.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.8090169943749481 +# type: matrix +# rows: 1 +# columns: 5 +0.9945218953682733 0.9781476007338057 0.9510565162951536 0.9135454576426009 0.8660254037844387 diff --git a/gold/generated-inputs/pde/continuity_6_source2_dim3.dat b/gold/generated-inputs/pde/continuity_6_source2_dim3.dat index c1c57946..85bb35d4 100644 --- a/gold/generated-inputs/pde/continuity_6_source2_dim3.dat +++ b/gold/generated-inputs/pde/continuity_6_source2_dim3.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar --0.481753674101715 +# type: matrix +# rows: 1 +# columns: 5 +0.9995065603657316 0.9980267284282716 0.99556196460308 0.9921147013144779 0.9876883405951378 diff --git a/gold/generated-inputs/pde/continuity_6_source2_dim4.dat b/gold/generated-inputs/pde/continuity_6_source2_dim4.dat index 4134e47a..435e842a 100644 --- a/gold/generated-inputs/pde/continuity_6_source2_dim4.dat +++ b/gold/generated-inputs/pde/continuity_6_source2_dim4.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.8607420270039435 +# type: matrix +# rows: 1 +# columns: 5 +0.01570731731182068 0.03141075907812829 0.04710645070964266 0.06279051952931337 0.07845909572784494 diff --git a/gold/generated-inputs/pde/continuity_6_source2_dim5.dat b/gold/generated-inputs/pde/continuity_6_source2_dim5.dat index 58a1166e..41c01c05 100644 --- a/gold/generated-inputs/pde/continuity_6_source2_dim5.dat +++ b/gold/generated-inputs/pde/continuity_6_source2_dim5.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.7705132427757893 +# type: matrix +# rows: 1 +# columns: 5 +0.9999451693655121 0.9997806834748455 0.9995065603657316 0.9991228300988584 0.9986295347545738 diff --git a/gold/generated-inputs/pde/continuity_6_source2_time.dat b/gold/generated-inputs/pde/continuity_6_source2_time.dat index 479779e0..569e2b32 100644 --- a/gold/generated-inputs/pde/continuity_6_source2_time.dat +++ b/gold/generated-inputs/pde/continuity_6_source2_time.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo # type: scalar --1.8600538041893 +1.709092725367802 diff --git a/gold/generated-inputs/pde/continuity_6_source3_dim0.dat b/gold/generated-inputs/pde/continuity_6_source3_dim0.dat index 4b01e92f..6960025d 100644 --- a/gold/generated-inputs/pde/continuity_6_source3_dim0.dat +++ b/gold/generated-inputs/pde/continuity_6_source3_dim0.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar --0.3090169943749467 +# type: matrix +# rows: 1 +# columns: 5 +0.9510565162951535 0.8090169943749475 0.5877852522924731 0.3090169943749475 6.123233995736766e-17 diff --git a/gold/generated-inputs/pde/continuity_6_source3_dim1.dat b/gold/generated-inputs/pde/continuity_6_source3_dim1.dat index 1abe96d6..951cfc81 100644 --- a/gold/generated-inputs/pde/continuity_6_source3_dim1.dat +++ b/gold/generated-inputs/pde/continuity_6_source3_dim1.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar --0.8090169943749472 +# type: matrix +# rows: 1 +# columns: 5 +0.1564344650402309 0.3090169943749474 0.4539904997395467 0.5877852522924731 0.7071067811865475 diff --git a/gold/generated-inputs/pde/continuity_6_source3_dim2.dat b/gold/generated-inputs/pde/continuity_6_source3_dim2.dat index c6869307..614f1e8e 100644 --- a/gold/generated-inputs/pde/continuity_6_source3_dim2.dat +++ b/gold/generated-inputs/pde/continuity_6_source3_dim2.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.5877852522924722 +# type: matrix +# rows: 1 +# columns: 5 +0.1045284632676535 0.2079116908177593 0.3090169943749473 0.4067366430758002 0.4999999999999999 diff --git a/gold/generated-inputs/pde/continuity_6_source3_dim3.dat b/gold/generated-inputs/pde/continuity_6_source3_dim3.dat index c1c57946..85bb35d4 100644 --- a/gold/generated-inputs/pde/continuity_6_source3_dim3.dat +++ b/gold/generated-inputs/pde/continuity_6_source3_dim3.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar --0.481753674101715 +# type: matrix +# rows: 1 +# columns: 5 +0.9995065603657316 0.9980267284282716 0.99556196460308 0.9921147013144779 0.9876883405951378 diff --git a/gold/generated-inputs/pde/continuity_6_source3_dim4.dat b/gold/generated-inputs/pde/continuity_6_source3_dim4.dat index 4134e47a..435e842a 100644 --- a/gold/generated-inputs/pde/continuity_6_source3_dim4.dat +++ b/gold/generated-inputs/pde/continuity_6_source3_dim4.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.8607420270039435 +# type: matrix +# rows: 1 +# columns: 5 +0.01570731731182068 0.03141075907812829 0.04710645070964266 0.06279051952931337 0.07845909572784494 diff --git a/gold/generated-inputs/pde/continuity_6_source3_dim5.dat b/gold/generated-inputs/pde/continuity_6_source3_dim5.dat index 58a1166e..41c01c05 100644 --- a/gold/generated-inputs/pde/continuity_6_source3_dim5.dat +++ b/gold/generated-inputs/pde/continuity_6_source3_dim5.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.7705132427757893 +# type: matrix +# rows: 1 +# columns: 5 +0.9999451693655121 0.9997806834748455 0.9995065603657316 0.9991228300988584 0.9986295347545738 diff --git a/gold/generated-inputs/pde/continuity_6_source3_time.dat b/gold/generated-inputs/pde/continuity_6_source3_time.dat index 479779e0..569e2b32 100644 --- a/gold/generated-inputs/pde/continuity_6_source3_time.dat +++ b/gold/generated-inputs/pde/continuity_6_source3_time.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo # type: scalar --1.8600538041893 +1.709092725367802 diff --git a/gold/generated-inputs/pde/continuity_6_source4_dim0.dat b/gold/generated-inputs/pde/continuity_6_source4_dim0.dat index 4b01e92f..6960025d 100644 --- a/gold/generated-inputs/pde/continuity_6_source4_dim0.dat +++ b/gold/generated-inputs/pde/continuity_6_source4_dim0.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar --0.3090169943749467 +# type: matrix +# rows: 1 +# columns: 5 +0.9510565162951535 0.8090169943749475 0.5877852522924731 0.3090169943749475 6.123233995736766e-17 diff --git a/gold/generated-inputs/pde/continuity_6_source4_dim1.dat b/gold/generated-inputs/pde/continuity_6_source4_dim1.dat index 1abe96d6..951cfc81 100644 --- a/gold/generated-inputs/pde/continuity_6_source4_dim1.dat +++ b/gold/generated-inputs/pde/continuity_6_source4_dim1.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar --0.8090169943749472 +# type: matrix +# rows: 1 +# columns: 5 +0.1564344650402309 0.3090169943749474 0.4539904997395467 0.5877852522924731 0.7071067811865475 diff --git a/gold/generated-inputs/pde/continuity_6_source4_dim2.dat b/gold/generated-inputs/pde/continuity_6_source4_dim2.dat index 2452eabc..14ec2ced 100644 --- a/gold/generated-inputs/pde/continuity_6_source4_dim2.dat +++ b/gold/generated-inputs/pde/continuity_6_source4_dim2.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.8090169943749481 +# type: matrix +# rows: 1 +# columns: 5 +0.9945218953682733 0.9781476007338057 0.9510565162951536 0.9135454576426009 0.8660254037844387 diff --git a/gold/generated-inputs/pde/continuity_6_source4_dim3.dat b/gold/generated-inputs/pde/continuity_6_source4_dim3.dat index c1c57946..85bb35d4 100644 --- a/gold/generated-inputs/pde/continuity_6_source4_dim3.dat +++ b/gold/generated-inputs/pde/continuity_6_source4_dim3.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar --0.481753674101715 +# type: matrix +# rows: 1 +# columns: 5 +0.9995065603657316 0.9980267284282716 0.99556196460308 0.9921147013144779 0.9876883405951378 diff --git a/gold/generated-inputs/pde/continuity_6_source4_dim4.dat b/gold/generated-inputs/pde/continuity_6_source4_dim4.dat index 3075b982..952a3d16 100644 --- a/gold/generated-inputs/pde/continuity_6_source4_dim4.dat +++ b/gold/generated-inputs/pde/continuity_6_source4_dim4.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.5090414157503714 +# type: matrix +# rows: 1 +# columns: 5 +0.9998766324816606 0.9995065603657316 0.99888987496197 0.9980267284282716 0.996917333733128 diff --git a/gold/generated-inputs/pde/continuity_6_source4_dim5.dat b/gold/generated-inputs/pde/continuity_6_source4_dim5.dat index 58a1166e..41c01c05 100644 --- a/gold/generated-inputs/pde/continuity_6_source4_dim5.dat +++ b/gold/generated-inputs/pde/continuity_6_source4_dim5.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.7705132427757893 +# type: matrix +# rows: 1 +# columns: 5 +0.9999451693655121 0.9997806834748455 0.9995065603657316 0.9991228300988584 0.9986295347545738 diff --git a/gold/generated-inputs/pde/continuity_6_source4_time.dat b/gold/generated-inputs/pde/continuity_6_source4_time.dat index d52500da..e449a5ec 100644 --- a/gold/generated-inputs/pde/continuity_6_source4_time.dat +++ b/gold/generated-inputs/pde/continuity_6_source4_time.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo # type: scalar -0.2790080706283951 +-0.2563639088051703 diff --git a/gold/generated-inputs/pde/continuity_6_source5_dim0.dat b/gold/generated-inputs/pde/continuity_6_source5_dim0.dat index 4b01e92f..6960025d 100644 --- a/gold/generated-inputs/pde/continuity_6_source5_dim0.dat +++ b/gold/generated-inputs/pde/continuity_6_source5_dim0.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar --0.3090169943749467 +# type: matrix +# rows: 1 +# columns: 5 +0.9510565162951535 0.8090169943749475 0.5877852522924731 0.3090169943749475 6.123233995736766e-17 diff --git a/gold/generated-inputs/pde/continuity_6_source5_dim1.dat b/gold/generated-inputs/pde/continuity_6_source5_dim1.dat index 1abe96d6..951cfc81 100644 --- a/gold/generated-inputs/pde/continuity_6_source5_dim1.dat +++ b/gold/generated-inputs/pde/continuity_6_source5_dim1.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar --0.8090169943749472 +# type: matrix +# rows: 1 +# columns: 5 +0.1564344650402309 0.3090169943749474 0.4539904997395467 0.5877852522924731 0.7071067811865475 diff --git a/gold/generated-inputs/pde/continuity_6_source5_dim2.dat b/gold/generated-inputs/pde/continuity_6_source5_dim2.dat index 2452eabc..14ec2ced 100644 --- a/gold/generated-inputs/pde/continuity_6_source5_dim2.dat +++ b/gold/generated-inputs/pde/continuity_6_source5_dim2.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.8090169943749481 +# type: matrix +# rows: 1 +# columns: 5 +0.9945218953682733 0.9781476007338057 0.9510565162951536 0.9135454576426009 0.8660254037844387 diff --git a/gold/generated-inputs/pde/continuity_6_source5_dim3.dat b/gold/generated-inputs/pde/continuity_6_source5_dim3.dat index 56b8579d..52ea5bcc 100644 --- a/gold/generated-inputs/pde/continuity_6_source5_dim3.dat +++ b/gold/generated-inputs/pde/continuity_6_source5_dim3.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.8763066800438637 +# type: matrix +# rows: 1 +# columns: 5 +0.03141075907812829 0.06279051952931337 0.09410831331851431 0.1253332335643043 0.1564344650402309 diff --git a/gold/generated-inputs/pde/continuity_6_source5_dim4.dat b/gold/generated-inputs/pde/continuity_6_source5_dim4.dat index 4134e47a..435e842a 100644 --- a/gold/generated-inputs/pde/continuity_6_source5_dim4.dat +++ b/gold/generated-inputs/pde/continuity_6_source5_dim4.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.8607420270039435 +# type: matrix +# rows: 1 +# columns: 5 +0.01570731731182068 0.03141075907812829 0.04710645070964266 0.06279051952931337 0.07845909572784494 diff --git a/gold/generated-inputs/pde/continuity_6_source5_dim5.dat b/gold/generated-inputs/pde/continuity_6_source5_dim5.dat index 58a1166e..41c01c05 100644 --- a/gold/generated-inputs/pde/continuity_6_source5_dim5.dat +++ b/gold/generated-inputs/pde/continuity_6_source5_dim5.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.7705132427757893 +# type: matrix +# rows: 1 +# columns: 5 +0.9999451693655121 0.9997806834748455 0.9995065603657316 0.9991228300988584 0.9986295347545738 diff --git a/gold/generated-inputs/pde/continuity_6_source5_time.dat b/gold/generated-inputs/pde/continuity_6_source5_time.dat index da07e159..2fa6c16a 100644 --- a/gold/generated-inputs/pde/continuity_6_source5_time.dat +++ b/gold/generated-inputs/pde/continuity_6_source5_time.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo # type: scalar --0.7440215216757201 +0.6836370901471209 diff --git a/gold/generated-inputs/pde/continuity_6_source6_dim0.dat b/gold/generated-inputs/pde/continuity_6_source6_dim0.dat index 4b01e92f..6960025d 100644 --- a/gold/generated-inputs/pde/continuity_6_source6_dim0.dat +++ b/gold/generated-inputs/pde/continuity_6_source6_dim0.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar --0.3090169943749467 +# type: matrix +# rows: 1 +# columns: 5 +0.9510565162951535 0.8090169943749475 0.5877852522924731 0.3090169943749475 6.123233995736766e-17 diff --git a/gold/generated-inputs/pde/continuity_6_source6_dim1.dat b/gold/generated-inputs/pde/continuity_6_source6_dim1.dat index 1abe96d6..951cfc81 100644 --- a/gold/generated-inputs/pde/continuity_6_source6_dim1.dat +++ b/gold/generated-inputs/pde/continuity_6_source6_dim1.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar --0.8090169943749472 +# type: matrix +# rows: 1 +# columns: 5 +0.1564344650402309 0.3090169943749474 0.4539904997395467 0.5877852522924731 0.7071067811865475 diff --git a/gold/generated-inputs/pde/continuity_6_source6_dim2.dat b/gold/generated-inputs/pde/continuity_6_source6_dim2.dat index 2452eabc..14ec2ced 100644 --- a/gold/generated-inputs/pde/continuity_6_source6_dim2.dat +++ b/gold/generated-inputs/pde/continuity_6_source6_dim2.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.8090169943749481 +# type: matrix +# rows: 1 +# columns: 5 +0.9945218953682733 0.9781476007338057 0.9510565162951536 0.9135454576426009 0.8660254037844387 diff --git a/gold/generated-inputs/pde/continuity_6_source6_dim3.dat b/gold/generated-inputs/pde/continuity_6_source6_dim3.dat index c1c57946..85bb35d4 100644 --- a/gold/generated-inputs/pde/continuity_6_source6_dim3.dat +++ b/gold/generated-inputs/pde/continuity_6_source6_dim3.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar --0.481753674101715 +# type: matrix +# rows: 1 +# columns: 5 +0.9995065603657316 0.9980267284282716 0.99556196460308 0.9921147013144779 0.9876883405951378 diff --git a/gold/generated-inputs/pde/continuity_6_source6_dim4.dat b/gold/generated-inputs/pde/continuity_6_source6_dim4.dat index 4134e47a..435e842a 100644 --- a/gold/generated-inputs/pde/continuity_6_source6_dim4.dat +++ b/gold/generated-inputs/pde/continuity_6_source6_dim4.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.8607420270039435 +# type: matrix +# rows: 1 +# columns: 5 +0.01570731731182068 0.03141075907812829 0.04710645070964266 0.06279051952931337 0.07845909572784494 diff --git a/gold/generated-inputs/pde/continuity_6_source6_dim5.dat b/gold/generated-inputs/pde/continuity_6_source6_dim5.dat index 4febd00e..4220fef3 100644 --- a/gold/generated-inputs/pde/continuity_6_source6_dim5.dat +++ b/gold/generated-inputs/pde/continuity_6_source6_dim5.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.6374239897486896 +# type: matrix +# rows: 1 +# columns: 5 +0.01047178411624579 0.02094241988335696 0.03141075907812829 0.04187565372919963 0.05233595624294383 diff --git a/gold/generated-inputs/pde/continuity_6_source6_time.dat b/gold/generated-inputs/pde/continuity_6_source6_time.dat index 41a0a51e..d01268ab 100644 --- a/gold/generated-inputs/pde/continuity_6_source6_time.dat +++ b/gold/generated-inputs/pde/continuity_6_source6_time.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash d4591680ada8fa22940eade8d507cd43dc65ed5c +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo # type: scalar --0.1240035869459533 +0.1139395150245201 diff --git a/gold/generated-inputs/pde/diffusion_1_dt.dat b/gold/generated-inputs/pde/diffusion_1_dt.dat index 50c835d3..e292797c 100644 --- a/gold/generated-inputs/pde/diffusion_1_dt.dat +++ b/gold/generated-inputs/pde/diffusion_1_dt.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash 0fe7719bac1c5c6b1e5cd966dd854d769c845b91 +# Created from matlab git hash 20448e62cfb796cbc50ba721cc04821105301e56 # name: foo # type: scalar 0.015625 diff --git a/gold/generated-inputs/pde/diffusion_1_exact_dim0.dat b/gold/generated-inputs/pde/diffusion_1_exact_dim0.dat index 1dffc523..2fa2be55 100644 --- a/gold/generated-inputs/pde/diffusion_1_exact_dim0.dat +++ b/gold/generated-inputs/pde/diffusion_1_exact_dim0.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash 0fe7719bac1c5c6b1e5cd966dd854d769c845b91 +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.9991181296463766 +# type: matrix +# rows: 1 +# columns: 5 +0.9999995000000417 0.9999980000006666 0.999995500003375 0.9999920000106667 0.9999875000260416 diff --git a/gold/generated-inputs/pde/diffusion_1_exact_time.dat b/gold/generated-inputs/pde/diffusion_1_exact_time.dat index 80798ae3..9e87f3be 100644 --- a/gold/generated-inputs/pde/diffusion_1_exact_time.dat +++ b/gold/generated-inputs/pde/diffusion_1_exact_time.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash 0fe7719bac1c5c6b1e5cd966dd854d769c845b91 +# Created from matlab git hash 7a85cb21101a410cc7fef3124c6f52da775c291f # name: foo # type: scalar -0.9991603527012367 +0.999000499833375 diff --git a/gold/generated-inputs/pde/diffusion_1_initial_dim0.dat b/gold/generated-inputs/pde/diffusion_1_initial_dim0.dat index 1dffc523..2fa2be55 100644 --- a/gold/generated-inputs/pde/diffusion_1_initial_dim0.dat +++ b/gold/generated-inputs/pde/diffusion_1_initial_dim0.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash 0fe7719bac1c5c6b1e5cd966dd854d769c845b91 +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar -0.9991181296463766 +# type: matrix +# rows: 1 +# columns: 5 +0.9999995000000417 0.9999980000006666 0.999995500003375 0.9999920000106667 0.9999875000260416 diff --git a/gold/generated-inputs/pde/diffusion_1_source0_dim0.dat b/gold/generated-inputs/pde/diffusion_1_source0_dim0.dat index be6dbb3e..d8a05c7b 100644 --- a/gold/generated-inputs/pde/diffusion_1_source0_dim0.dat +++ b/gold/generated-inputs/pde/diffusion_1_source0_dim0.dat @@ -1,4 +1,6 @@ -# Created from matlab git hash 0fe7719bac1c5c6b1e5cd966dd854d769c845b91 +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo -# type: scalar --9.991181296463767e-05 +# type: matrix +# rows: 1 +# columns: 5 +-9.999995000000418e-05 -9.999980000006667e-05 -9.99995500003375e-05 -9.999920000106667e-05 -9.999875000260417e-05 diff --git a/gold/generated-inputs/pde/diffusion_1_source0_time.dat b/gold/generated-inputs/pde/diffusion_1_source0_time.dat index 80798ae3..dabf798b 100644 --- a/gold/generated-inputs/pde/diffusion_1_source0_time.dat +++ b/gold/generated-inputs/pde/diffusion_1_source0_time.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash 0fe7719bac1c5c6b1e5cd966dd854d769c845b91 +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc # name: foo # type: scalar -0.9991603527012367 +0.999000499833375 diff --git a/gold/generated-inputs/pde/diffusion_2_dt.dat b/gold/generated-inputs/pde/diffusion_2_dt.dat new file mode 100644 index 00000000..e292797c --- /dev/null +++ b/gold/generated-inputs/pde/diffusion_2_dt.dat @@ -0,0 +1,4 @@ +# Created from matlab git hash 20448e62cfb796cbc50ba721cc04821105301e56 +# name: foo +# type: scalar +0.015625 diff --git a/gold/generated-inputs/pde/diffusion_2_exact_dim0.dat b/gold/generated-inputs/pde/diffusion_2_exact_dim0.dat new file mode 100644 index 00000000..6960025d --- /dev/null +++ b/gold/generated-inputs/pde/diffusion_2_exact_dim0.dat @@ -0,0 +1,6 @@ +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc +# name: foo +# type: matrix +# rows: 1 +# columns: 5 +0.9510565162951535 0.8090169943749475 0.5877852522924731 0.3090169943749475 6.123233995736766e-17 diff --git a/gold/generated-inputs/pde/diffusion_2_exact_dim1.dat b/gold/generated-inputs/pde/diffusion_2_exact_dim1.dat new file mode 100644 index 00000000..6960025d --- /dev/null +++ b/gold/generated-inputs/pde/diffusion_2_exact_dim1.dat @@ -0,0 +1,6 @@ +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc +# name: foo +# type: matrix +# rows: 1 +# columns: 5 +0.9510565162951535 0.8090169943749475 0.5877852522924731 0.3090169943749475 6.123233995736766e-17 diff --git a/gold/generated-inputs/pde/diffusion_2_exact_time.dat b/gold/generated-inputs/pde/diffusion_2_exact_time.dat new file mode 100644 index 00000000..cdb27602 --- /dev/null +++ b/gold/generated-inputs/pde/diffusion_2_exact_time.dat @@ -0,0 +1,4 @@ +# Created from matlab git hash 7a85cb21101a410cc7fef3124c6f52da775c291f +# name: foo +# type: scalar +1.370416883188896e-43 diff --git a/gold/generated-inputs/pde/diffusion_2_initial_dim0.dat b/gold/generated-inputs/pde/diffusion_2_initial_dim0.dat new file mode 100644 index 00000000..6960025d --- /dev/null +++ b/gold/generated-inputs/pde/diffusion_2_initial_dim0.dat @@ -0,0 +1,6 @@ +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc +# name: foo +# type: matrix +# rows: 1 +# columns: 5 +0.9510565162951535 0.8090169943749475 0.5877852522924731 0.3090169943749475 6.123233995736766e-17 diff --git a/gold/generated-inputs/pde/diffusion_2_initial_dim1.dat b/gold/generated-inputs/pde/diffusion_2_initial_dim1.dat new file mode 100644 index 00000000..6960025d --- /dev/null +++ b/gold/generated-inputs/pde/diffusion_2_initial_dim1.dat @@ -0,0 +1,6 @@ +# Created from matlab git hash 08b9e829d2a8ebd3fc4d0eff5f059930d7b7e8fc +# name: foo +# type: matrix +# rows: 1 +# columns: 5 +0.9510565162951535 0.8090169943749475 0.5877852522924731 0.3090169943749475 6.123233995736766e-17 diff --git a/gold/generated-inputs/pde/fokkerplanck2_complete_dt.dat b/gold/generated-inputs/pde/fokkerplanck2_complete_dt.dat index c8bbf4c7..1b293eb9 100644 --- a/gold/generated-inputs/pde/fokkerplanck2_complete_dt.dat +++ b/gold/generated-inputs/pde/fokkerplanck2_complete_dt.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash 0fe7719bac1c5c6b1e5cd966dd854d769c845b91 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: scalar -0.625 +0.59375 diff --git a/gold/generated-inputs/pde/fokkerplanck2_complete_exact_dim0.dat b/gold/generated-inputs/pde/fokkerplanck2_complete_exact_dim0.dat deleted file mode 100644 index 66cc0f17..00000000 --- a/gold/generated-inputs/pde/fokkerplanck2_complete_exact_dim0.dat +++ /dev/null @@ -1,6 +0,0 @@ -# Created from matlab git hash 0fe7719bac1c5c6b1e5cd966dd854d769c845b91 -# name: foo -# type: matrix -# rows: 1 -# columns: 5 -1.117151606788937 1.084134787104863 1.031260909618963 0.9615412988393078 0.8787825789354448 diff --git a/gold/generated-inputs/pde/fokkerplanck2_complete_exact_dim1.dat b/gold/generated-inputs/pde/fokkerplanck2_complete_exact_dim1.dat deleted file mode 100644 index 048fe5fe..00000000 --- a/gold/generated-inputs/pde/fokkerplanck2_complete_exact_dim1.dat +++ /dev/null @@ -1,6 +0,0 @@ -# Created from matlab git hash 0fe7719bac1c5c6b1e5cd966dd854d769c845b91 -# name: foo -# type: matrix -# rows: 1 -# columns: 5 -1 1 1 1 1 diff --git a/gold/generated-inputs/pde/fokkerplanck2_complete_exact_time.dat b/gold/generated-inputs/pde/fokkerplanck2_complete_exact_time.dat deleted file mode 100644 index 6a1d864f..00000000 --- a/gold/generated-inputs/pde/fokkerplanck2_complete_exact_time.dat +++ /dev/null @@ -1,4 +0,0 @@ -# Created from matlab git hash 0fe7719bac1c5c6b1e5cd966dd854d769c845b91 -# name: foo -# type: scalar -1 diff --git a/gold/generated-inputs/pde/fokkerplanck2_complete_initial_dim0.dat b/gold/generated-inputs/pde/fokkerplanck2_complete_initial_dim0.dat index 711c008e..bb192388 100644 --- a/gold/generated-inputs/pde/fokkerplanck2_complete_initial_dim0.dat +++ b/gold/generated-inputs/pde/fokkerplanck2_complete_initial_dim0.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash 0fe7719bac1c5c6b1e5cd966dd854d769c845b91 +# Created from matlab git hash 7a85cb21101a410cc7fef3124c6f52da775c291f # name: foo # type: matrix # rows: 1 diff --git a/gold/generated-inputs/pde/fokkerplanck2_complete_initial_dim1.dat b/gold/generated-inputs/pde/fokkerplanck2_complete_initial_dim1.dat index 048fe5fe..a472871f 100644 --- a/gold/generated-inputs/pde/fokkerplanck2_complete_initial_dim1.dat +++ b/gold/generated-inputs/pde/fokkerplanck2_complete_initial_dim1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash 0fe7719bac1c5c6b1e5cd966dd854d769c845b91 +# Created from matlab git hash 20448e62cfb796cbc50ba721cc04821105301e56 # name: foo # type: matrix # rows: 1 diff --git a/gold/generated-inputs/time_advance/continuity2_ad_sg_l3_d4_t0.dat b/gold/generated-inputs/time_advance/continuity2_ad_sg_l3_d4_t0.dat new file mode 100644 index 00000000..b677177e --- /dev/null +++ b/gold/generated-inputs/time_advance/continuity2_ad_sg_l3_d4_t0.dat @@ -0,0 +1,1797 @@ +# Created from matlab git hash 5ce0b4d10cd8ad0d4f665011571398caa8b7d3d1 +# name: foo +# type: matrix +# rows: 1792 +# columns: 1 +-2.387438553207452e-26 +3.976043007481444e-07 +-2.197311796746333e-12 +5.49659212378544e-07 +-1.884468327148999e-25 +-4.634029684522869e-08 +5.358800769477936e-12 +-6.406211154587234e-08 +1.10617714795842e-25 +-7.017704996485931e-07 +1.43847238665426e-12 +-9.701470013836856e-07 +-5.896387275945608e-26 +3.699657809596586e-08 +2.301532719607139e-12 +5.114509560984046e-08 +-3.436442861782582e-26 +-4.003275473988777e-07 +-2.197311796039898e-12 +-5.534239040755618e-07 +2.015180812618591e-25 +-5.298173005744824e-08 +-5.358800792996242e-12 +-7.324341300974995e-08 +1.042467051223654e-25 +7.03553283050345e-07 +1.438472388384678e-12 +9.726115706002461e-07 +5.81086731440136e-26 +3.414417108794248e-08 +-2.301532741890463e-12 +4.720184905423168e-08 +2.38742552639062e-26 +-3.976043007579455e-07 +2.197311771834961e-12 +-5.496592123935142e-07 +1.884468524831334e-25 +4.634029683556006e-08 +-5.358800792834396e-12 +6.406211153110134e-08 +-1.106176711464719e-25 +7.017704996406968e-07 +-1.438472406128165e-12 +9.701470013716217e-07 +5.896390212873609e-26 +-3.699657810668421e-08 +-2.301532746111257e-12 +-5.114509562622297e-08 +3.436429938361311e-26 +4.003275473891003e-07 +2.19731177097562e-12 +5.534239040606235e-07 +-2.015180926275739e-25 +5.298173004787904e-08 +5.358800769472102e-12 +7.32434129951333e-08 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+-2.027591271270423e-09 +1.279347019708993e-08 +9.667370076270263e-10 +-6.446518328495691e-08 +3.428384706255174e-08 +1.171164711333587e-07 +-1.601395876452556e-08 +1.219414349908686e-08 +2.600094539558956e-09 +-2.446111482870628e-08 +-1.159262447248639e-09 +4.667167699698845e-08 +-2.500181347894317e-08 +-8.434941591106628e-08 +1.168545794567024e-08 +-1.133096359274661e-08 +-2.084863734756693e-09 +1.690374220483656e-08 +7.853025004100609e-10 +-6.557021077879244e-08 +3.431578378427863e-08 +1.178432915074554e-07 +-1.606749377177039e-08 +1.6304996245678e-08 +2.637969805405835e-09 +-2.715633625084851e-08 +-1.040506490522069e-09 +4.673231335330057e-08 +-2.502009989954514e-08 +-8.439034843364445e-08 +1.169661548637244e-08 +1.133096538854499e-08 +2.084865652992083e-09 +-1.690374044132824e-08 +-7.853001766939555e-10 +6.557021268187734e-08 +-3.431578180776334e-08 +-1.178432896899509e-07 +1.606749611837036e-08 +-1.630499447438595e-08 +-2.637967921785879e-09 +2.715633798658088e-08 +1.040508644599091e-09 +-4.673231129875898e-08 +2.502010198442926e-08 +8.4390350344065e-08 +-1.169661298317348e-08 diff --git a/gold/generated-inputs/time_advance/diffusion1_ad_sg_l3_d3_t0.dat b/gold/generated-inputs/time_advance/diffusion1_ad_sg_l3_d3_t0.dat new file mode 100644 index 00000000..2294ce30 --- /dev/null +++ b/gold/generated-inputs/time_advance/diffusion1_ad_sg_l3_d3_t0.dat @@ -0,0 +1,11 @@ +# Created from matlab git hash 5ce0b4d10cd8ad0d4f665011571398caa8b7d3d1 +# name: foo +# type: matrix +# rows: 6 +# columns: 1 +0.9999833021671835 +-1.44336599214678e-05 +-3.726726615492545e-06 +2.902378699466127e-14 +1.671127487369021e-14 +-2.813084358875386e-13 diff --git a/gold/generated-inputs/time_advance/diffusion1_ad_sg_l3_d3_t1.dat b/gold/generated-inputs/time_advance/diffusion1_ad_sg_l3_d3_t1.dat new file mode 100644 index 00000000..7dc0493c --- /dev/null +++ b/gold/generated-inputs/time_advance/diffusion1_ad_sg_l3_d3_t1.dat @@ -0,0 +1,11 @@ +# Created from matlab git hash 5ce0b4d10cd8ad0d4f665011571398caa8b7d3d1 +# name: foo +# type: matrix +# rows: 6 +# columns: 1 +0.9999832709177028 +-1.443365933989967e-05 +-3.726726505870419e-06 +2.907763281135559e-14 +1.672899218279152e-14 +-2.79578060785075e-13 diff --git a/gold/generated-inputs/time_advance/diffusion1_ad_sg_l3_d3_t2.dat b/gold/generated-inputs/time_advance/diffusion1_ad_sg_l3_d3_t2.dat new file mode 100644 index 00000000..7a165b38 --- /dev/null +++ b/gold/generated-inputs/time_advance/diffusion1_ad_sg_l3_d3_t2.dat @@ -0,0 +1,11 @@ +# Created from matlab git hash 5ce0b4d10cd8ad0d4f665011571398caa8b7d3d1 +# name: foo +# type: matrix +# rows: 6 +# columns: 1 +0.9999832396682231 +-1.443365876026362e-05 +-3.726726396104889e-06 +2.913018336785451e-14 +1.674643193613667e-14 +-2.778731282935923e-13 diff --git a/gold/generated-inputs/time_advance/diffusion1_ad_sg_l3_d3_t3.dat b/gold/generated-inputs/time_advance/diffusion1_ad_sg_l3_d3_t3.dat new file mode 100644 index 00000000..68bf61d4 --- /dev/null +++ b/gold/generated-inputs/time_advance/diffusion1_ad_sg_l3_d3_t3.dat @@ -0,0 +1,11 @@ +# Created from matlab git hash 5ce0b4d10cd8ad0d4f665011571398caa8b7d3d1 +# name: foo +# type: matrix +# rows: 6 +# columns: 1 +0.9999832084187444 +-1.443365818253115e-05 +-3.726726286197991e-06 +2.918245636859728e-14 +1.676350161514029e-14 +-2.76194933673286e-13 diff --git a/gold/generated-inputs/time_advance/diffusion1_ad_sg_l3_d3_t4.dat b/gold/generated-inputs/time_advance/diffusion1_ad_sg_l3_d3_t4.dat new file mode 100644 index 00000000..1791de68 --- /dev/null +++ b/gold/generated-inputs/time_advance/diffusion1_ad_sg_l3_d3_t4.dat @@ -0,0 +1,11 @@ +# Created from matlab git hash 5ce0b4d10cd8ad0d4f665011571398caa8b7d3d1 +# name: foo +# type: matrix +# rows: 6 +# columns: 1 +0.9999831771692669 +-1.44336576066739e-05 +-3.726726176152499e-06 +2.92331565533885e-14 +1.678043251626582e-14 +-2.745416265524483e-13 diff --git a/gold/generated-inputs/time_advance/diffusion2_ad_implicit_sg_l3_d4_t0.dat b/gold/generated-inputs/time_advance/diffusion2_ad_implicit_sg_l3_d4_t0.dat new file mode 100644 index 00000000..d23907c1 --- /dev/null +++ b/gold/generated-inputs/time_advance/diffusion2_ad_implicit_sg_l3_d4_t0.dat @@ -0,0 +1,245 @@ +# Created from matlab git hash 5ce0b4d10cd8ad0d4f665011571398caa8b7d3d1 +# name: foo +# type: matrix +# rows: 240 +# columns: 1 +-3.368955815645968e-11 +-1.156156176980755e-05 +-7.53325941444072e-11 +1.377076305457556e-06 +-1.539176584153012e-10 +7.769587230031008e-07 +-3.448425494853416e-10 +-8.756865090854785e-08 +4.376301323755741e-10 +2.097920488228633e-05 +9.810834314675814e-10 +-2.585830656101811e-06 +-2.662414951723239e-10 +1.914929730352847e-08 +-5.962852950511137e-10 +4.171429931283037e-08 +-7.255974686292758e-14 +-5.170701340832147e-06 +-1.620049924609503e-13 +6.291665752661925e-07 +5.707851962536625e-14 +1.137358071245246e-06 +1.274288991788065e-13 +-1.515652182703303e-07 +5.97907308637288e-14 +8.822506274253199e-06 +1.335284626103444e-13 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+2.304931241247514e-09 +0.007202666590826511 diff --git a/gold/generated-inputs/time_advance/diffusion2_ad_implicit_sg_l3_d4_t1.dat b/gold/generated-inputs/time_advance/diffusion2_ad_implicit_sg_l3_d4_t1.dat new file mode 100644 index 00000000..bb70cd68 --- /dev/null +++ b/gold/generated-inputs/time_advance/diffusion2_ad_implicit_sg_l3_d4_t1.dat @@ -0,0 +1,245 @@ +# Created from matlab git hash 5ce0b4d10cd8ad0d4f665011571398caa8b7d3d1 +# name: foo +# type: matrix +# rows: 240 +# columns: 1 +-3.235758213795446e-11 +-1.13884896923694e-05 +-7.22467393732896e-11 +1.33355383129901e-06 +-2.669564155610608e-10 +9.20694788681087e-07 +-5.986787454687147e-10 +-1.016656076363772e-07 +8.704661130084802e-10 +2.084827767941866e-05 +1.953173245098188e-09 +-2.611023304041533e-06 +-4.318384253871715e-10 +1.839300149636939e-08 +-9.675761591570787e-10 +7.812923952399347e-08 +-1.961708596979098e-14 +-5.210283334921934e-06 +-4.311882826056857e-14 +6.363235578548074e-07 +1.2777864160283e-14 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from matlab git hash 5ce0b4d10cd8ad0d4f665011571398caa8b7d3d1 +# name: foo +# type: matrix +# rows: 240 +# columns: 1 +6.395160591147193e-08 +-4.124470081427497e-05 +1.428698416055869e-07 +1.037724399789429e-07 +8.369373946810152e-08 +-3.313510141269013e-05 +1.869730720989719e-07 +-1.399043495173917e-06 +-1.429168359420141e-08 +2.232186346776476e-05 +-3.192346996411964e-08 +-2.226934785748435e-06 +1.143822026893386e-07 +-3.678667565719727e-05 +2.55530979572652e-07 +-1.047755635259999e-06 +-8.969872108020277e-10 +8.662248025998066e-06 +-2.004357438021239e-09 +1.849789129396108e-06 +7.745892002215503e-10 +-2.733655346063083e-05 +1.730868634480769e-09 +-2.741388007382987e-06 +5.67005771970847e-10 +-7.15399641437759e-06 +1.26698835212916e-09 +-2.465095042619976e-06 +-3.277855133282699e-10 +-5.962187296764323e-06 +-7.324409889222962e-10 +-4.492724964429612e-07 +-3.869308247615601e-12 +1.893342592521643e-05 +-8.648992350195915e-12 +7.512321021648142e-07 +-2.500915181281455e-12 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b/gold/generated-inputs/time_advance/diffusion2_ad_sg_l3_d4_t2.dat @@ -0,0 +1,245 @@ +# Created from matlab git hash 5ce0b4d10cd8ad0d4f665011571398caa8b7d3d1 +# name: foo +# type: matrix +# rows: 240 +# columns: 1 +-1.311541967097307e-06 +0.000267832707734855 +-2.928259583627614e-06 +5.19398613146403e-05 +-1.663021670098077e-06 +0.0003205943874942185 +-3.713113713154097e-06 +5.72618013075807e-05 +9.383589239305046e-08 +1.216397131721624e-05 +2.099472507812573e-07 +-7.471435426593409e-06 +-2.182147345977873e-06 +0.0003488208152032288 +-4.872347471635009e-06 +6.087569640854002e-05 +4.017351437471536e-08 +-0.0001253577434688045 +8.968629644392067e-08 +-2.606161507535182e-05 +-3.586164064230433e-08 +0.0002493602553269679 +-8.006087021694961e-08 +5.614363674059415e-05 +-2.513526577249283e-08 +0.0001469361065125023 +-5.611397366255078e-08 +3.023717948142551e-05 +1.395148693557104e-08 +4.693067453074847e-05 +3.114591227346522e-08 +1.138321897709858e-05 +3.112345675634049e-10 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b/gold/generated-inputs/time_advance/diffusion2_ad_sg_l3_d4_t3.dat new file mode 100644 index 00000000..15740110 --- /dev/null +++ b/gold/generated-inputs/time_advance/diffusion2_ad_sg_l3_d4_t3.dat @@ -0,0 +1,245 @@ +# Created from matlab git hash 5ce0b4d10cd8ad0d4f665011571398caa8b7d3d1 +# name: foo +# type: matrix +# rows: 240 +# columns: 1 +2.081461601046734e-05 +-0.002664445494716943 +4.645071900063354e-05 +-0.000876072749083666 +2.603175197080439e-05 +-0.003050431771960827 +5.809566528314908e-05 +-0.001004786123609149 +-2.815251007150334e-07 +6.952418823140322e-05 +-6.365445722764899e-07 +3.967964132103465e-05 +3.355453162899888e-05 +-0.00336517028583596 +7.488787238806476e-05 +-0.001094682860567686 +-9.446833919973427e-07 +0.00106076585761284 +-2.107509243524575e-06 +0.0003885032088627897 +8.694667141136113e-07 +-0.00219526333095102 +1.939709841085943e-06 +-0.0008148861894679881 +5.946031658579935e-07 +-0.001215871610146273 +1.326515907601701e-06 +-0.0004537808272466674 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a/gold/generated-inputs/time_advance/diffusion2_ad_sg_l3_d4_t4.dat b/gold/generated-inputs/time_advance/diffusion2_ad_sg_l3_d4_t4.dat new file mode 100644 index 00000000..bae938c2 --- /dev/null +++ b/gold/generated-inputs/time_advance/diffusion2_ad_sg_l3_d4_t4.dat @@ -0,0 +1,4437 @@ +# Created from matlab git hash 5ce0b4d10cd8ad0d4f665011571398caa8b7d3d1 +# name: foo +# type: matrix +# rows: 4432 +# columns: 1 +-80.57221182424685 +18675.28527150241 +-179.873545877178 +6858.655114821177 +-426.1022160076786 +57988.10681084723 +-950.9145703285454 +19917.14895845503 +38.73940650628712 +-10836.568159532 +86.49279982360362 +-4027.759030501034 +-364.7889079435712 +34038.10855063441 +-814.1678171054164 +11298.2345193869 +44.07530151793515 +-17299.70625018916 +98.35569311068133 +-6360.13653582678 +-41.2660664945654 +33470.52060830866 +-92.08275430597057 +12589.28606862498 +-28.59467879936354 +11812.15134379582 +-63.8100371411127 +4352.667999919374 +12.756947584886 +10037.21257715651 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+9.953021833842214e-16 +9.865232301417002e-16 diff --git a/gold/generated-inputs/time_advance/fokkerplanck1_4p1a_ad_sg_l4_d4_t1.dat b/gold/generated-inputs/time_advance/fokkerplanck1_4p1a_ad_sg_l4_d4_t1.dat new file mode 100644 index 00000000..d7357c09 --- /dev/null +++ b/gold/generated-inputs/time_advance/fokkerplanck1_4p1a_ad_sg_l4_d4_t1.dat @@ -0,0 +1,13 @@ +# Created from matlab git hash 5ce0b4d10cd8ad0d4f665011571398caa8b7d3d1 +# name: foo +# type: matrix +# rows: 8 +# columns: 1 +1.414213562373093 +0.004082479502571349 +7.905683856550809e-06 +1.336304473054458e-08 +9.135883309072302e-12 +2.025137840638742e-14 +-1.594618623078514e-11 +-6.740860660434073e-15 diff --git a/gold/generated-inputs/time_advance/fokkerplanck1_4p1a_ad_sg_l4_d4_t2.dat b/gold/generated-inputs/time_advance/fokkerplanck1_4p1a_ad_sg_l4_d4_t2.dat new file mode 100644 index 00000000..d3c12d40 --- /dev/null +++ b/gold/generated-inputs/time_advance/fokkerplanck1_4p1a_ad_sg_l4_d4_t2.dat @@ -0,0 +1,13 @@ +# Created from matlab git hash 5ce0b4d10cd8ad0d4f665011571398caa8b7d3d1 +# name: foo +# type: matrix +# rows: 8 +# columns: 1 +1.414213562373093 +0.006123712874994571 +1.778775448695545e-05 +4.510018694011361e-08 +4.176044338208758e-11 +1.165954622226789e-13 +-7.290026413870292e-11 +-4.541890303734372e-14 diff --git a/gold/generated-inputs/time_advance/fokkerplanck1_4p1a_ad_sg_l4_d4_t3.dat b/gold/generated-inputs/time_advance/fokkerplanck1_4p1a_ad_sg_l4_d4_t3.dat new file mode 100644 index 00000000..4643e88c --- /dev/null +++ b/gold/generated-inputs/time_advance/fokkerplanck1_4p1a_ad_sg_l4_d4_t3.dat @@ -0,0 +1,13 @@ +# Created from matlab git hash 5ce0b4d10cd8ad0d4f665011571398caa8b7d3d1 +# name: foo +# type: matrix +# rows: 8 +# columns: 1 +1.414213562373093 +0.008164938592815505 +3.162259131252932e-05 +1.069038912210505e-07 +1.135342546591953e-10 +3.477700642774887e-13 +-1.981988380174734e-10 +-1.382911972404805e-13 diff --git a/gold/generated-inputs/time_advance/fokkerplanck1_4p1a_ad_sg_l4_d4_t4.dat b/gold/generated-inputs/time_advance/fokkerplanck1_4p1a_ad_sg_l4_d4_t4.dat new file mode 100644 index 00000000..2fd5ef4a --- /dev/null +++ b/gold/generated-inputs/time_advance/fokkerplanck1_4p1a_ad_sg_l4_d4_t4.dat @@ -0,0 +1,13 @@ +# Created from matlab git hash 5ce0b4d10cd8ad0d4f665011571398caa8b7d3d1 +# name: foo +# type: matrix +# rows: 8 +# columns: 1 +1.414213562373093 +0.01020615410455353 +4.941013257081277e-05 +2.08796075468906e-07 +2.401166848458696e-10 +7.715389004370626e-13 +-4.191791213094816e-10 +-3.086010257639334e-13 diff --git a/gold/generated-inputs/time_advance/fokkerplanck1_pitch_E_case2_ad_sg_l4_d4_t0.dat b/gold/generated-inputs/time_advance/fokkerplanck1_pitch_E_case2_ad_sg_l4_d4_t0.dat new file mode 100644 index 00000000..bf88977d --- /dev/null +++ b/gold/generated-inputs/time_advance/fokkerplanck1_pitch_E_case2_ad_sg_l4_d4_t0.dat @@ -0,0 +1,149 @@ +# Created from matlab git hash 5b113ba64dceadce746223be59f9d5572723f7db +# name: foo +# type: matrix +# rows: 144 +# columns: 1 +2.756208736642233e-05 +1.755852287101041e-05 +-3.497535876461787e-05 +-1.132549260027526e-05 +-0.006186338885590969 +-0.001911231228218668 +0.01224583023307797 +0.001571145014085031 +-0.006288954388483419 +0.001711925013855724 +0.0126245284164832 +-0.001429686957675133 +3.066097966410449e-05 +-1.942035248578319e-05 +-3.916504125308e-05 +1.259132128880833e-05 +-0.009086744308259617 +-0.01481024776543643 +-0.005153994173800401 +0.008272315218536221 +-0.01052043852270412 +0.01598772888707519 +-0.003419965117879465 +-0.00916886951954944 +0.03694177640129082 +0.02188052719519528 +-0.05513339623051867 +-0.01746492410334381 +0.03603012375373815 +-0.02081447679147049 +-0.05540379747397672 +0.01713561891833646 +-0.1530728179304367 +-0.001329853168802239 +-0.2357688248406901 +-0.003558183067463886 +0.1253314137315488 +0.000269993579573449 +-0.1380222648577996 +-0.0006033210697105925 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+-3.560394136077327e-07 +1.528740682006163e-07 +2.696427401966215e-07 +-2.562635114346919e-07 +2.423127323083111e-07 +-2.765769995700588e-07 +-2.964893825155993e-07 +1.413268190730577e-07 +1.915201934422151e-07 +-1.234198240813065e-07 +-1.817146206313224e-07 +1.339760160938901e-07 +-5.074886852002881e-07 +3.962244259051228e-07 +5.040545687560193e-07 +-3.335974686605994e-07 +-4.240762171904132e-07 +2.153247311680702e-07 +3.383396126032845e-07 +-2.978074187335917e-07 diff --git a/gold/generated-inputs/time_advance/fokkerplanck1_pitch_E_case2_ad_sg_l4_d4_t1.dat b/gold/generated-inputs/time_advance/fokkerplanck1_pitch_E_case2_ad_sg_l4_d4_t1.dat new file mode 100644 index 00000000..3f102917 --- /dev/null +++ b/gold/generated-inputs/time_advance/fokkerplanck1_pitch_E_case2_ad_sg_l4_d4_t1.dat @@ -0,0 +1,149 @@ +# Created from matlab git hash 5b113ba64dceadce746223be59f9d5572723f7db +# name: foo +# type: matrix +# rows: 144 +# columns: 1 +2.61603582514842e-05 +1.672027548764736e-05 +-3.305980113180552e-05 +-1.075152387670291e-05 +-0.006126038351410647 +-0.00200261535992263 +0.01204079938168162 +0.001635616997728207 +-0.006330897807773101 +0.001604362294661164 +0.01279710099345189 +-0.00135235191121893 +3.241285284171519e-05 +-2.049677037297224e-05 +-4.148413465841942e-05 +1.329598692148508e-05 +-0.008381292362049075 +-0.01422325204228168 +-0.005980806556314422 +0.007831982562178352 +-0.01124733659316827 +0.01657672781483258 +-0.002513037194008669 +-0.009624422357019668 +0.03735090477789912 +0.02237413140782371 +-0.05496356420885044 +-0.01760865839064189 +0.03552712373247306 +-0.02024178240253831 +-0.05550342087251621 +0.01694971400946622 +-0.1530092405940495 +-0.002658430793963777 +-0.235730838127155 +-0.0071149056088708 +0.1253314137315488 +0.0005399863279469825 +-0.1380203333289884 +-0.001206630992305791 +7.163318863933629e-06 +3.002026877049401e-06 +-1.112624696544152e-05 +-1.949102396703476e-06 +7.12257919835814e-05 +-2.284864457947211e-05 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+-2.823169357287574e-08 +2.74182993208975e-07 +-2.01959324181001e-07 +-2.649515348772518e-07 +1.794446657214816e-07 +-5.073419963180926e-07 +3.943766699802004e-07 +5.028298242487638e-07 +-3.339506056062101e-07 +-7.442798832226384e-07 +4.970760835174608e-07 +6.840345073325609e-07 +-5.047228999979263e-07 diff --git a/gold/generated-inputs/time_advance/fokkerplanck1_pitch_E_case2_ad_sg_l4_d4_t2.dat b/gold/generated-inputs/time_advance/fokkerplanck1_pitch_E_case2_ad_sg_l4_d4_t2.dat new file mode 100644 index 00000000..239c234b --- /dev/null +++ b/gold/generated-inputs/time_advance/fokkerplanck1_pitch_E_case2_ad_sg_l4_d4_t2.dat @@ -0,0 +1,149 @@ +# Created from matlab git hash 5b113ba64dceadce746223be59f9d5572723f7db +# name: foo +# type: matrix +# rows: 144 +# columns: 1 +2.480681191864212e-05 +1.590387893820379e-05 +-3.122754571731178e-05 +-1.019685645213465e-05 +-0.006059978321762796 +-0.002088541567823247 +0.01182602336674259 +0.001695869311563505 +-0.006366352990680886 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+-3.464030130857194e-07 +-8.899937741555043e-07 +6.32268583975957e-07 +8.456772110165014e-07 +-5.972377982106631e-07 diff --git a/gold/generated-inputs/time_advance/fokkerplanck1_pitch_E_case2_ad_sg_l4_d4_t3.dat b/gold/generated-inputs/time_advance/fokkerplanck1_pitch_E_case2_ad_sg_l4_d4_t3.dat new file mode 100644 index 00000000..2311fdef --- /dev/null +++ b/gold/generated-inputs/time_advance/fokkerplanck1_pitch_E_case2_ad_sg_l4_d4_t3.dat @@ -0,0 +1,149 @@ +# Created from matlab git hash 5b113ba64dceadce746223be59f9d5572723f7db +# name: foo +# type: matrix +# rows: 144 +# columns: 1 +2.350199841649514e-05 +1.51105973964826e-05 +-2.947707313862308e-05 +-9.661825743993318e-06 +-0.005988377307866781 +-0.002169018066201891 +0.01160206756127879 +0.001751874361278707 +-0.006395157097706119 +0.0013738021540929 +0.0131058747512653 +-0.001184700444651773 +3.621350689880654e-05 +-2.282652871435025e-05 +-4.651771967900722e-05 +1.482100962828088e-05 +-0.006996230410858425 +-0.01305620012673912 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a/gold/generated-inputs/time_advance/fokkerplanck1_pitch_E_case2_ad_sg_l4_d4_t4.dat b/gold/generated-inputs/time_advance/fokkerplanck1_pitch_E_case2_ad_sg_l4_d4_t4.dat new file mode 100644 index 00000000..062246c8 --- /dev/null +++ b/gold/generated-inputs/time_advance/fokkerplanck1_pitch_E_case2_ad_sg_l4_d4_t4.dat @@ -0,0 +1,149 @@ +# Created from matlab git hash 5b113ba64dceadce746223be59f9d5572723f7db +# name: foo +# type: matrix +# rows: 144 +# columns: 1 +2.224618293340396e-05 +1.434144252759932e-05 +-2.780666490717171e-05 +-9.146635622661691e-06 +-0.005911457956976778 +-0.002244060710275745 +0.01136950194648037 +0.001803623309600477 +-0.006417146291132689 +0.001250875835630243 +0.01324099849599581 +-0.001094555775991016 +3.826507432375059e-05 +-2.407345307173574e-05 +-4.92416677852295e-05 +1.564851454385608e-05 +-0.00631777355044209 +-0.01247737271237314 +-0.008299490729221787 +0.006546498076836745 +-0.01345996283959532 +0.01833661907682318 +0.0003651313191311074 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+3.152773989876396e-10 +2.395641305272315e-10 +-1.354213878317463e-10 +1.111143786722505e-15 +9.635039775526388e-16 +7.35662863105567e-16 +1.001462844667831e-15 +-1.944205518337827e-10 +1.622751427784961e-10 +1.282652452708378e-10 +-7.563833444962848e-11 +-7.687618825128741e-07 +5.821662816891545e-07 +7.538260376352659e-07 +-5.078617284111246e-07 +-8.788913181568254e-07 +6.357178421599027e-07 +8.443848653688432e-07 +-5.868589813550686e-07 +-6.979566327353848e-08 +1.717969913038241e-08 +4.720085962951709e-08 +-5.256235928515987e-08 +4.169387150625173e-07 +-3.10035981523584e-07 +-4.053496808830236e-07 +2.740682289422417e-07 +-5.674264975057499e-07 +4.446756808701462e-07 +5.657091895038234e-07 +-3.732416849331695e-07 +-9.285916893734839e-07 +6.818766625790105e-07 +8.962840570649453e-07 +-6.179964949905716e-07 diff --git a/gold/generated-inputs/time_advance/fokkerplanck1_pitch_E_case2_sg_l2_d2_t0.dat b/gold/generated-inputs/time_advance/fokkerplanck1_pitch_E_case2_sg_l2_d2_t0.dat new file mode 100644 index 00000000..a1d1ec37 --- /dev/null +++ b/gold/generated-inputs/time_advance/fokkerplanck1_pitch_E_case2_sg_l2_d2_t0.dat @@ -0,0 +1,13 @@ +# Created from matlab git hash 5b113ba64dceadce746223be59f9d5572723f7db +# name: foo +# type: matrix +# rows: 8 +# columns: 1 +0.1168748916418945 +0.05836185255343701 +0.1207197879199593 +-0.05532831057752801 +-0.1925509638273807 +-0.006334234258172602 +0.1253313438903165 +0.00109999695443589 diff --git a/gold/generated-inputs/time_advance/fokkerplanck1_pitch_E_case2_sg_l2_d2_t1.dat b/gold/generated-inputs/time_advance/fokkerplanck1_pitch_E_case2_sg_l2_d2_t1.dat new file mode 100644 index 00000000..2a50d8b2 --- /dev/null +++ b/gold/generated-inputs/time_advance/fokkerplanck1_pitch_E_case2_sg_l2_d2_t1.dat @@ -0,0 +1,13 @@ +# Created from matlab git hash 5b113ba64dceadce746223be59f9d5572723f7db +# name: foo +# type: matrix +# rows: 8 +# columns: 1 +0.1149044241108874 +0.05808039857160729 +0.1223295762772874 +-0.05198524874796995 +-0.1924483431878547 +-0.01249023209023374 +0.1253313438903165 +0.002199928906717105 diff --git a/gold/generated-inputs/time_advance/fokkerplanck1_pitch_E_case2_sg_l2_d2_t2.dat b/gold/generated-inputs/time_advance/fokkerplanck1_pitch_E_case2_sg_l2_d2_t2.dat new file mode 100644 index 00000000..11b61e6f --- /dev/null +++ b/gold/generated-inputs/time_advance/fokkerplanck1_pitch_E_case2_sg_l2_d2_t2.dat @@ -0,0 +1,13 @@ +# Created from matlab git hash 5b113ba64dceadce746223be59f9d5572723f7db +# name: foo +# type: matrix +# rows: 8 +# columns: 1 +0.1129472756172172 +0.05777937741944458 +0.1236930875467798 +-0.04860341175419054 +-0.1922792148090441 +-0.01847051486835991 +0.1253313438903165 +0.003299731955507621 diff --git a/gold/generated-inputs/time_advance/fokkerplanck1_pitch_E_case2_sg_l2_d2_t3.dat b/gold/generated-inputs/time_advance/fokkerplanck1_pitch_E_case2_sg_l2_d2_t3.dat new file mode 100644 index 00000000..3f4a506d --- /dev/null +++ b/gold/generated-inputs/time_advance/fokkerplanck1_pitch_E_case2_sg_l2_d2_t3.dat @@ -0,0 +1,13 @@ +# Created from matlab git hash 5b113ba64dceadce746223be59f9d5572723f7db +# name: foo +# type: matrix +# rows: 8 +# columns: 1 +0.11100396437766 +0.05745966438050083 +0.1248159576896253 +-0.04519210947170434 +-0.1920451153194681 +-0.02427760389654312 +0.1253313438903165 +0.004399343350992554 diff --git a/gold/generated-inputs/time_advance/fokkerplanck1_pitch_E_case2_sg_l2_d2_t4.dat b/gold/generated-inputs/time_advance/fokkerplanck1_pitch_E_case2_sg_l2_d2_t4.dat new file mode 100644 index 00000000..963fda89 --- /dev/null +++ b/gold/generated-inputs/time_advance/fokkerplanck1_pitch_E_case2_sg_l2_d2_t4.dat @@ -0,0 +1,13 @@ +# Created from matlab git hash 5b113ba64dceadce746223be59f9d5572723f7db +# name: foo +# type: matrix +# rows: 8 +# columns: 1 +0.1090749824060101 +0.05712211215411938 +0.1257038624445272 +-0.04176021735899683 +-0.191747560898483 +-0.02991401919794937 +0.1253313438903165 +0.005498701436351021 diff --git a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l2_3_d3_t0.dat b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l2_3_d3_t0.dat index 1ecef820..50468999 100644 --- a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l2_3_d3_t0.dat +++ b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l2_3_d3_t0.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 144 diff --git a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l2_3_d3_t1.dat b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l2_3_d3_t1.dat index ce72c338..3216e39c 100644 --- a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l2_3_d3_t1.dat +++ b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l2_3_d3_t1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 144 diff --git a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l2_3_d3_t2.dat b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l2_3_d3_t2.dat index 04617067..13cbebaa 100644 --- a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l2_3_d3_t2.dat +++ b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l2_3_d3_t2.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 144 diff --git a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l2_3_d3_t3.dat b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l2_3_d3_t3.dat index 8e2d0ee0..c70351dc 100644 --- a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l2_3_d3_t3.dat +++ b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l2_3_d3_t3.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 144 diff --git a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l2_3_d3_t4.dat b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l2_3_d3_t4.dat index a9279d48..86fc3e23 100644 --- a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l2_3_d3_t4.dat +++ b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l2_3_d3_t4.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 144 diff --git a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l3_d3_t0.dat b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l3_d3_t0.dat index d74aa34b..93b3aa59 100644 --- a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l3_d3_t0.dat +++ b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l3_d3_t0.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 180 diff --git a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l3_d3_t1.dat b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l3_d3_t1.dat index 0393e30c..c1a0d2b4 100644 --- a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l3_d3_t1.dat +++ b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l3_d3_t1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 180 diff --git a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l3_d3_t2.dat b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l3_d3_t2.dat index 26c4ef2d..b3603fc7 100644 --- a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l3_d3_t2.dat +++ b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l3_d3_t2.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 180 diff --git a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l3_d3_t3.dat b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l3_d3_t3.dat index 1f6ad5df..52c3c06b 100644 --- a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l3_d3_t3.dat +++ b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l3_d3_t3.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 180 diff --git a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l3_d3_t4.dat b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l3_d3_t4.dat index 66659597..3ce5820e 100644 --- a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l3_d3_t4.dat +++ b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l3_d3_t4.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 180 diff --git a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l4_d3_t0.dat b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l4_d3_t0.dat index 40c2761b..2f73222b 100644 --- a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l4_d3_t0.dat +++ b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l4_d3_t0.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 432 diff --git a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l4_d3_t1.dat b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l4_d3_t1.dat index 52d2951d..c89dd0b1 100644 --- a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l4_d3_t1.dat +++ b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l4_d3_t1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 432 diff --git a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l4_d3_t2.dat b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l4_d3_t2.dat index c1d91f33..a44368d4 100644 --- a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l4_d3_t2.dat +++ b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l4_d3_t2.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 432 diff --git a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l4_d3_t3.dat b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l4_d3_t3.dat index 50cded52..661e784c 100644 --- a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l4_d3_t3.dat +++ b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l4_d3_t3.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 432 diff --git a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l4_d3_t4.dat b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l4_d3_t4.dat index 0deb3e8d..3f16ad40 100644 --- a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l4_d3_t4.dat +++ b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l4_d3_t4.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 432 diff --git a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l5_d3_t0.dat b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l5_d3_t0.dat index 0addcfa7..32fdba21 100644 --- a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l5_d3_t0.dat +++ b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l5_d3_t0.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 1008 diff --git a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l5_d3_t1.dat b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l5_d3_t1.dat index 14118a2f..0b9def33 100644 --- a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l5_d3_t1.dat +++ b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l5_d3_t1.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 1008 diff --git a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l5_d3_t2.dat b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l5_d3_t2.dat index 4e28a49a..fc7d2859 100644 --- a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l5_d3_t2.dat +++ b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l5_d3_t2.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 1008 diff --git a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l5_d3_t3.dat b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l5_d3_t3.dat index 9ca210b4..a6042d48 100644 --- a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l5_d3_t3.dat +++ b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l5_d3_t3.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 1008 diff --git a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l5_d3_t4.dat b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l5_d3_t4.dat index b8a12065..d9776cdd 100644 --- a/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l5_d3_t4.dat +++ b/gold/generated-inputs/time_advance/fokkerplanck2_complete_implicit_sg_l5_d3_t4.dat @@ -1,4 +1,4 @@ -# Created from matlab git hash aaec71a692d4b986a1c1618d4589a40968233168 +# Created from matlab git hash a929c55dab9a3b448d174e77795d9ba5a019c172 # name: foo # type: matrix # rows: 1008 diff --git a/gold/gold_adapt.m b/gold/gold_adapt.m new file mode 100644 index 00000000..c2a8774e --- /dev/null +++ b/gold/gold_adapt.m @@ -0,0 +1,160 @@ +% adaptivity functions +data_dir = "generated-inputs/adapt/"; +out_format = strcat(data_dir, 'continuity1_l4_d3_'); +run_adapt(@continuity1,@fval_gen_1, out_format, ... + 'lev',4,'deg',3,'grid_type','SG'); +out_format = strcat(data_dir, 'continuity2_l5_d2_'); +run_adapt(@continuity2,@fval_gen_zeroes, out_format, ... + 'lev',5,'deg',2,'grid_type','SG'); +out_format = strcat(data_dir, 'continuity3_l4_d4_'); +run_adapt(@continuity3,@fval_gen_2, out_format, ... + 'lev',4,'deg',4,'grid_type','SG'); + + +% initial condition adapt +out_string = strcat(data_dir, 'diffusion2_l2_d3_initial.dat'); +run_initial(@diffusion2,out_string, ... + 'lev',2,'deg',3,'grid_type','SG'); +out_string = strcat(data_dir, 'diffusion1_l3_d4_initial.dat'); +run_initial(@diffusion1,out_string, ... + 'lev',3,'deg',4,'grid_type','SG'); + +function [x] = fval_gen_1(num_entries, elem_size) + x = zeros(num_entries, 1); + num_elems = num_entries/elem_size; + for i=1:num_elems-1 + entry = (i*elem_size)+1; + if mod(i, 2) == 0 + x(entry) = 0.5e-5; % should be coarsened + end + if mod(i, 3) == 0 + x(entry) = 1e-3; % should be refined + end + end + x(num_entries-elem_size+1:num_entries) = 1.0; +end + +function [x] = fval_gen_2(num_entries, elem_size) + x = zeros(num_entries, 1); + num_elems = num_entries/elem_size; + for i=1:num_elems-1 + entry = (i*elem_size)+1; + if mod(i, 3) == 0 + x(entry) = 1e-5; % should be coarsened + x(entry + elem_size) = 1e-5; + end + if mod(i, 5) == 0 + x(entry) = 1; % should be refined + x(entry + elem_size) = 0.5; + end + end + x = x(1:num_entries); + x(num_entries-elem_size+1:num_entries) = 1.0; +end + +function [x] = fval_gen_zeroes(num_entries, elem_size) + x = zeros(num_entries, 1); + x(num_entries-elem_size+1:num_entries) = 1.0; +end + +function run_adapt(pde_handle, fval_gen, out_format, varargin) + + opts = OPTS(varargin); + opts.quiet = 1; + opts.adapt_threshold = 1e-4; + opts.max_lev_coeffs = 0; + + pde = pde_handle( opts ); + lev_vec = get_lev_vec(pde); + num_dims = length(lev_vec); + + [elements, elements_idx] = hash_table_sparse_nD (lev_vec, ... + opts.max_lev, opts.grid_type); + hash_table.elements = elements; + hash_table.elements_idx = elements_idx; + + hash_table_orig = hash_table; + + elem_size = opts.deg^num_dims; + fval_size = numel(hash_table.elements_idx)*elem_size; + fval_orig = fval_gen(fval_size, elem_size); + fval = fval_orig; + write_octave_like_output(strcat(out_format,'orig.dat'), fval_orig); + + % coarsen + coarsen = 1; + refine = 0; + [~,fval,hash_table,~,~,~,~,~,~,~,~,~] ... + = adapt(pde,opts,[],fval,hash_table_orig,[],[],[],[],[],coarsen,refine); + write_octave_like_output(strcat(out_format,'coarse.dat'), fval); + [~, ~, cell_val] = find(hash_table.elements.pos_p1); + num_entries = size(cell_val,1) / num_dims; + table = zeros(num_entries, num_dims * 2); + for j=1:num_entries + id = hash_table.elements_idx(j); + table(j, :) = horzcat(full(hash_table.elements.lev_p1(id,:)), ... + full(hash_table.elements.pos_p1(id,:))) - 1; + end + write_octave_like_output(strcat(out_format, 'coarse_table.dat'),table); + + + % refine + coarsen = 0; + refine = 1; + [~,fval,hash_table,~,~,~,~,~,~,~,~,~] ... + = adapt(pde,opts,[],fval_orig,hash_table_orig,[],[],[],[],[],coarsen,refine); + write_octave_like_output(strcat(out_format, 'refine.dat'), fval); + [~, ~, cell_val] = find(hash_table.elements.pos_p1); + num_entries = size(cell_val,1) / num_dims; + table = zeros(num_entries, num_dims * 2); + for j=1:num_entries + id = hash_table.elements_idx(j); + table(j, :) = horzcat(full(hash_table.elements.lev_p1(id,:)), ... + full(hash_table.elements.pos_p1(id,:))) - 1; + end + write_octave_like_output(strcat(out_format,'refine_table.dat'),table); +end + + +function run_initial(pde_handle, out_string, varargin) + opts = OPTS(varargin); + opts.quiet = 1; + opts.adapt_threshold = 1e-4; + opts.max_lev_coeffs = 1; + + pde = pde_handle( opts ); + t = 0; + TD = 0; + pde = get_coeff_mats(pde,opts,t,TD,opts.use_oldcoeffmat); + + lev_vec = get_lev_vec(pde); + + [elements, elements_idx] = hash_table_sparse_nD (lev_vec, ... + opts.max_lev, opts.grid_type); + hash_table.elements = elements; + hash_table.elements_idx = elements_idx; + + fval = initial_condition_vector(pde, opts, hash_table, t); + + keep_adapting_initial_condition = true; + while keep_adapting_initial_condition + num_pre_adapt = numel(fval); + % first refine + [pde,fval_tmp,hash_table,~,~,~,~,~,~,~,~,~] ... + = adapt(pde,opts,[],fval,hash_table,[],[],[],[], ... + [],0,1); + if num_pre_adapt == numel(fval_tmp) + keep_adapting_initial_condition = false; + end + clear fval_tmp; + % reproject initial condition onto refined basis + fval = initial_condition_vector(pde, opts, hash_table, t); + end + % coarsen + [pde,~,hash_table,~,~,~,~,~,~,~,~,~] ... + = adapt(pde,opts,[],fval,hash_table,[],[],[],[], ... + [],1,0); + % reproject onto coarsend basis + fval = initial_condition_vector(pde, opts, hash_table, t); + write_octave_like_output(out_string,fval); +end diff --git a/gold/gold_coefficients.m b/gold/gold_coefficients.m index f3ab9d76..01ef4a51 100644 --- a/gold/gold_coefficients.m +++ b/gold/gold_coefficients.m @@ -1,56 +1,59 @@ % uniform level +% note fp2 must be calculated with modified x domain [1,20] to avoid singularity problem levels = [3, 3]; -generate_data( fokkerplanck2_complete, levels, 'fokkerplanck2_complete', 'deg', 3 ); +generate_data( @fokkerplanck2_complete, levels, 'fokkerplanck2_complete', 'case', 4, 'deg', 3 ); levels = [4, 4]; -generate_data( fokkerplanck2_complete, levels, 'fokkerplanck2_complete', 'lev', 4, 'deg', 4 ); +generate_data( @fokkerplanck2_complete, levels, 'fokkerplanck2_complete', 'case', 4, 'lev', 4, 'deg', 4 ); levels = [2]; -generate_data( continuity1, levels, 'continuity1', 'deg', 2 ); +generate_data( @continuity1, levels, 'continuity1', 'deg', 2 ); levels = [4, 4]; -generate_data( continuity2, levels, 'continuity2', 'deg', 3 ); +generate_data( @continuity2, levels, 'continuity2', 'deg', 3 ); levels = [4, 4, 4]; -generate_data( continuity3, levels, 'continuity3', 'deg', 4 ); +generate_data( @continuity3, levels, 'continuity3', 'deg', 4 ); levels = [2, 2, 2, 2, 2, 2]; -generate_data( continuity6, levels, 'continuity6', 'deg', 4 ); +generate_data( @continuity6, levels, 'continuity6', 'deg', 4 ); levels = [5]; -generate_data( diffusion1, levels, 'diffusion1', 'deg', 6 ); +generate_data( @diffusion1, levels, 'diffusion1', 'deg', 6 ); levels = [3, 3]; -generate_data( diffusion2, levels, 'diffusion2', 'deg', 5 ); +generate_data( @diffusion2, levels, 'diffusion2', 'deg', 5 ); levels = [4]; -generate_data( fokkerplanck1_pitch_E(1), levels, 'fokkerplanck1_4p1a', 'deg', 3 ); +generate_data( @fokkerplanck1_pitch_E, levels, 'fokkerplanck1_4p1a', 'case', 1, 'deg', 3 ); +generate_data( @fokkerplanck1_pitch_E, levels, 'fokkerplanck1_pitch_E_case2', 'case', 2, 'deg', 3 ); levels = [5]; -generate_data( fokkerplanck1_pitch_C, levels, 'fokkerplanck1_4p2', 'deg', 2 ); +generate_data( @fokkerplanck1_pitch_C, levels, 'fokkerplanck1_4p2', 'deg', 2 ); levels = [2]; -generate_data( fokkerplanck1_4p3, levels, 'fokkerplanck1_4p3', 'deg', 5 ); +generate_data( @fokkerplanck1_pitch_R, levels, 'fokkerplanck1_4p3', 'deg', 5 ); levels = [5]; -generate_data( fokkerplanck1_4p4, levels, 'fokkerplanck1_4p4', 'deg', 3 ); +generate_data( @fokkerplanck1_pitch_CE, levels, 'fokkerplanck1_4p4', 'deg', 3 ); levels = [3]; -generate_data( fokkerplanck1_4p5, levels, 'fokkerplanck1_4p5', 'deg', 5 ); +generate_data( @fokkerplanck1_pitch_CER, levels, 'fokkerplanck1_4p5', 'deg', 5 ); % non-uniform level -levels = [2, 3]; -generate_data( fokkerplanck2_complete, levels, 'fokkerplanck2_complete', 'deg', 3 ); +% note fp2 must be calculated with modified x domain [1,20] to avoid singularity problem +levels = [2, 310]; +generate_data( @fokkerplanck2_complete, levels, 'fokkerplanck2_complete', 'case', 4, 'deg', 3 ); levels = [4, 2]; -generate_data( fokkerplanck2_complete, levels, 'fokkerplanck2_complete', 'lev', 4, 'deg', 4 ); +generate_data( @fokkerplanck2_complete, levels, 'fokkerplanck2_complete', 'case', 4, 'lev', 4, 'deg', 4 ); levels = [4, 5]; -generate_data( continuity2, levels, 'continuity2', 'deg', 3 ); +generate_data( @continuity2, levels, 'continuity2', 'deg', 3 ); levels = [2, 3, 2]; -generate_data( continuity3, levels, 'continuity3', 'deg', 4 ); +generate_data( @continuity3, levels, 'continuity3', 'deg', 4 ); levels = [2, 3, 3, 3, 2, 4]; -generate_data( continuity6, levels, 'continuity6', 'deg', 4 ); +generate_data( @continuity6, levels, 'continuity6', 'deg', 4 ); levels = [2, 3]; -generate_data( diffusion2, levels, 'diffusion2', 'deg', 5 ); +generate_data( @diffusion2, levels, 'diffusion2', 'deg', 5 ); -function generate_data(pde, lev_vec, pde_name, varargin) +function generate_data(pde_handle, lev_vec, pde_name, varargin) coeff_dir = "generated-inputs/coefficients/"; root = get_root_folder(); [~,~] = mkdir ([root,'/gold/',char(coeff_dir)]); -runtime_defaults - +opts = OPTS(varargin); +opts.quiet = 1; opts.use_oldcoeffmat = 0; opts.use_oldhash = 0; opts.max_lev_coeffs = 1; -pde = check_pde(pde, opts); +pde = pde_handle( opts ); for i=1:length(pde.dimensions) pde.dimensions{i}.lev = lev_vec(i); diff --git a/gold/gold_pde.m b/gold/gold_pde.m index 21646d3e..c5f40c85 100644 --- a/gold/gold_pde.m +++ b/gold/gold_pde.m @@ -3,157 +3,69 @@ root = get_root_folder(); [stat,msg] = mkdir ([root,'/gold/',char(data_dir)]); -out_format = strcat( data_dir, "diffusion_1_"); -run_pde(diffusion1, out_format, 4.2, 0, 'lev', 3, 'deg', 2, 'CFL', 1); - -out_format = strcat( data_dir, "advection_1_"); -run_pde(advection1, out_format, 4.2, 0, 'lev', 3, 'deg', 2, 'CFL', 1); - -out_format = strcat( data_dir, "fokkerplanck2_complete_" ); +t = 5; domain = [ 0.1, 0.2, 0.3, 0.4, 0.5 ]; -t = 0; -%Captain -run_pde( fokkerplanck2_complete, out_format, domain, t, 'lev', 5, 'deg', 4, 'CFL', 1 ) - -% continuity 1 -out_format = strcat(data_dir, "continuity_1_"); -pde = continuity1; -pde = check_pde(pde); -pde.CFL = 1.0; -dt = pde.set_dt(pde,pde.CFL); -x = 1.1; -y_init = pde.dimensions{1}.init_cond_fn(x); -y_source0_x = pde.sources{1}{1}(x); -y_source0_t = pde.sources{1}{2}(x); -y_source1_x = pde.sources{2}{1}(x); -y_source1_t = pde.sources{2}{2}(x); -y_exact_x = pde.analytic_solutions_1D{1}(x); -y_exact_time = pde.analytic_solutions_1D{2}(x); - -write_octave_like_output(strcat(out_format, 'dt.dat'), dt); -write_octave_like_output(strcat(out_format, 'initial_dim0.dat'), y_init); -write_octave_like_output(strcat(out_format, 'source0_dim0.dat'), y_source0_x); -write_octave_like_output(strcat(out_format, 'source0_time.dat'), y_source0_t); -write_octave_like_output(strcat(out_format, 'source1_dim0.dat'), y_source1_x); -write_octave_like_output(strcat(out_format, 'source1_time.dat'), y_source1_t); -write_octave_like_output(strcat(out_format, 'exact_dim0.dat'), y_exact_x); -write_octave_like_output(strcat(out_format, 'exact_time.dat'), y_exact_time); -% continuity 2 -out_format = strcat(data_dir, "continuity_2_"); -pde = continuity2; -pde = check_pde(pde); -x = 2.2; -for d=1:length(pde.dimensions) - y_init = pde.dimensions{d}.init_cond_fn(x); - write_octave_like_output(strcat(out_format, sprintf('initial_dim%d.dat', d-1)), y_init); - y_exact = pde.analytic_solutions_1D{d}(x); - write_octave_like_output(strcat(out_format, sprintf('exact_dim%d.dat', d-1)), y_exact); -end -y_exact_time = pde.analytic_solutions_1D{length(pde.analytic_solutions_1D)}(x); -write_octave_like_output(strcat(out_format, 'exact_time.dat'), y_exact_time); +out_format = strcat( data_dir, "diffusion_1_"); +run_pde(@diffusion1, out_format, domain, t, 'lev', 3, 'deg', 2, 'CFL', 1); -for s=1:length(pde.sources) - for d=1:length(pde.dimensions) - y_source = pde.sources{s}{d}(x); - write_octave_like_output(strcat(out_format, sprintf('source%d_dim%d.dat',s-1,d-1)), y_source); - y_source_t = pde.sources{s}{length(pde.sources{s})}(x); - write_octave_like_output(strcat(out_format, sprintf('source%d_time.dat',s-1)), y_source_t); - end -end -pde.CFL=1; -dt = pde.set_dt(pde,pde.CFL); -write_octave_like_output(strcat(out_format, 'dt.dat'), dt); +out_format = strcat( data_dir, "diffusion_2_"); +run_pde(@diffusion2, out_format, domain, t, 'lev', 3, 'deg', 2, 'CFL', 1); -% continuity 3 -out_format = strcat(data_dir, "continuity_3_"); -pde = continuity3; -pde = check_pde(pde); -pde.dimensions{1}.lev = 2; -pde.dimensions{2}.lev = 2; -pde.dimensions{3}.lev = 2; -x = 3.3; -for d=1:length(pde.dimensions) - y_init = pde.dimensions{d}.init_cond_fn(x); - write_octave_like_output(strcat(out_format, sprintf('initial_dim%d.dat', d-1)), y_init); - y_exact = pde.analytic_solutions_1D{d}(x); - write_octave_like_output(strcat(out_format, sprintf('exact_dim%d.dat', d-1)), y_exact); -end -y_exact_time = pde.analytic_solutions_1D{length(pde.analytic_solutions_1D)}(x); -write_octave_like_output(strcat(out_format, 'exact_time.dat'), y_exact_time); +out_format = strcat( data_dir, "advection_1_"); +run_pde(@advection1, out_format, domain, t, 'lev', 3, 'deg', 2, 'CFL', 1); -for s=1:length(pde.sources) - for d=1:length(pde.dimensions) - y_source = pde.sources{s}{d}(x); - write_octave_like_output(strcat(out_format, sprintf('source%d_dim%d.dat',s-1,d-1)), y_source); - y_source_t = pde.sources{s}{length(pde.sources{s})}(x); - write_octave_like_output(strcat(out_format, sprintf('source%d_time.dat',s-1)), y_source_t); - end -end +% note fp2 must be calculated with modified x domain [1, 20] to avoid +% singularity problem +out_format = strcat( data_dir, "fokkerplanck2_complete_" ); +run_pde(@fokkerplanck2_complete, out_format, domain, t, 'case', 4, 'lev', 5, 'deg', 4); -pde.CFL=1; -dt = pde.set_dt(pde,pde.CFL); -write_octave_like_output(strcat(out_format, 'dt.dat'), dt); +out_format = strcat( data_dir, "continuity_1_" ); +run_pde(@continuity1, out_format, domain, t, 'lev', 2, 'deg', 2); -% continuity 6 -out_format = strcat(data_dir, "continuity_6_"); -pde = check_pde(continuity6); -x = 6.6; -for d=1:length(pde.dimensions) - y_init = pde.dimensions{d}.init_cond_fn(x); - write_octave_like_output(strcat(out_format, sprintf('initial_dim%d.dat', d-1)), y_init); - y_exact = pde.analytic_solutions_1D{d}(x); - write_octave_like_output(strcat(out_format, sprintf('exact_dim%d.dat', d-1)), y_exact); -end -y_exact_time = pde.analytic_solutions_1D{length(pde.analytic_solutions_1D)}(x); -write_octave_like_output(strcat(out_format, 'exact_time.dat'), y_exact_time); +out_format = strcat( data_dir, "continuity2_" ); +run_pde(@continuity2, out_format, domain, t, 'lev', 5, 'deg', 4); -for s=1:length(pde.sources) - for d=1:length(pde.dimensions) - y_source = pde.sources{s}{d}(x); - write_octave_like_output(strcat(out_format, sprintf('source%d_dim%d.dat',s-1,d-1)), y_source); - y_source_t = pde.sources{s}{length(pde.sources{s})}(x); - write_octave_like_output(strcat(out_format, sprintf('source%d_time.dat',s-1)), y_source_t); - end -end -pde.CFL=1; -dt = pde.set_dt(pde,pde.CFL); -write_octave_like_output(strcat(out_format, 'dt.dat'), dt); +out_format = strcat( data_dir, "continuity_3_" ); +run_pde(@continuity3, out_format, domain, t, 'lev', 5, 'deg', 4); -% fokkerplanck2_complete -out_format = strcat(data_dir, "fokkerplanck2_complete_"); -pde = check_pde(fokkerplanck2_complete); -x = 0.5; -for d=1:length(pde.dimensions) - y_init = pde.dimensions{d}.init_cond_fn(x); - write_octave_like_output(strcat(out_format, sprintf('initial_dim%d.dat', d-1)), y_init); -end +out_format = strcat( data_dir, "continuity_6_" ); +run_pde(@continuity6, out_format, domain, t); -pde.CFL=1; -dt = pde.set_dt(pde,pde.CFL); -write_octave_like_output(strcat(out_format, 'dt.dat'), dt); -function run_pde(pde, out_format, x, t, varargin) +function run_pde(pde_handle, out_format, x, t, varargin) - runtime_defaults; - pde = check_pde( pde, opts ); - pde.CFL=1; - dt = pde.set_dt(pde,pde.CFL); + opts = OPTS(varargin); + opts.quiet = 1; + opts.CFL = 1; + pde = pde_handle( opts ); + dt = pde.set_dt(pde,opts.CFL); + write_octave_like_output(strcat(out_format, 'dt.dat'), dt); + for d=1:length(pde.dimensions) - y_init = pde.dimensions{d}.init_cond_fn(x, 0, t); + init_cond = pde.initial_conditions{1}{d}; + y_init = init_cond(x, pde.params, 0); write_octave_like_output(strcat(out_format, sprintf('initial_dim%d.dat', d-1)), y_init); - y_exact = pde.analytic_solutions_1D{d}(x, 0, 0); - write_octave_like_output(strcat(out_format, sprintf('exact_dim%d.dat', d-1)), y_exact); + + if ~isempty(pde.solutions) + exact_sol = pde.solutions{1}{d}; + y_exact = exact_sol(x, pde.params, t); + write_octave_like_output(strcat(out_format, sprintf('exact_dim%d.dat', d-1)), y_exact); + end + end + + if ~isempty(pde.solutions) + y_exact_time = pde.solutions{1}{length(pde.dimensions)+1}(t); + write_octave_like_output(strcat(out_format, 'exact_time.dat'), y_exact_time); end - y_exact_time = pde.analytic_solutions_1D{length(pde.analytic_solutions_1D)}(x); - write_octave_like_output(strcat(out_format, 'exact_time.dat'), y_exact_time); + for s=1:length(pde.sources) for d=1:length(pde.dimensions) y_source = pde.sources{s}{d}(x); write_octave_like_output(strcat(out_format, sprintf('source%d_dim%d.dat',s-1,d-1)), ... y_source); - y_source_t = pde.sources{s}{length(pde.sources{s})}(x); + y_source_t = pde.sources{s}{length(pde.sources{s})}(t); write_octave_like_output(strcat(out_format, sprintf('source%d_time.dat',s-1)), y_source_t); end end diff --git a/gold/gold_time_advance.m b/gold/gold_time_advance.m index 893c626b..751e394d 100644 --- a/gold/gold_time_advance.m +++ b/gold/gold_time_advance.m @@ -6,161 +6,195 @@ root = get_root_folder(); [stat,msg] = mkdir ([root,'/gold/',char(data_dir)]); +%% adaptive time advance testing +out_format = strcat(data_dir,'fokkerplanck1_pitch_E_case2_ad_sg_l4_d4_t%d.dat'); +run_time_advance(@fokkerplanck1_pitch_E,out_format, ... + 'CFL',0.01,'lev',4,'deg',4,'case', 2, 'grid_type','SG','timestep_method','RK3', 'adapt', true, ... + 'adapt_initial_condition', true, 'adapt_threshold', 1e-4); + +out_format = strcat(data_dir,'fokkerplanck1_4p1a_ad_sg_l4_d4_t%d.dat'); +run_time_advance(@fokkerplanck1_pitch_E,out_format, ... + 'CFL',0.01,'lev',4,'deg',4,'grid_type','SG','timestep_method','RK3', 'adapt', true, ... + 'adapt_initial_condition', true, 'adapt_threshold', 1e-4); + +out_format = strcat(data_dir,'continuity2_ad_sg_l3_d4_t%d.dat'); +run_time_advance(@continuity2,out_format, ... + 'CFL',0.01,'lev',3,'deg',4,'grid_type','SG','timestep_method','RK3', 'adapt', true, ... + 'adapt_initial_condition', true, 'adapt_threshold', 1e-3); + +out_format = strcat(data_dir,'diffusion2_ad_sg_l3_d4_t%d.dat'); +run_time_advance(@diffusion2,out_format, ... + 'CFL',0.01,'lev',3,'deg',4,'grid_type','SG','timestep_method','RK3', 'adapt', true, ... + 'adapt_initial_condition', true, 'adapt_threshold', 0.5e-1); + +out_format = strcat(data_dir,'diffusion2_ad_implicit_sg_l3_d4_t%d.dat'); +run_time_advance(@diffusion2,out_format, ... + 'CFL',0.01,'lev',3,'deg',4,'grid_type','SG','timestep_method','BE', 'adapt', true, ... + 'adapt_initial_condition', true, 'adapt_threshold', 0.5e-1); + +%% non-adaptive %% uniform level, explicit % diffusion2 l2d2 RK3 out_format = strcat(data_dir,'diffusion2_sg_l2_d2_t%d.dat'); -run_time_advance(diffusion2,out_format, ... +run_time_advance(@diffusion2,out_format, ... 'CFL',0.01,'lev',2,'deg',2,'grid_type','SG','timestep_method','RK3'); % diffusion2 l3d3 RK3 out_format = strcat(data_dir,'diffusion2_sg_l3_d3_t%d.dat'); -run_time_advance(diffusion2,out_format, ... +run_time_advance(@diffusion2,out_format, ... 'CFL',0.01,'lev',3,'deg',3,'grid_type','SG','timestep_method','RK3'); % diffusion2 l4d4 RK3 out_format = strcat(data_dir,'diffusion2_sg_l4_d4_t%d.dat'); -run_time_advance(diffusion2,out_format, ... +run_time_advance(@diffusion2,out_format, ... 'CFL',0.01,'lev',4,'deg',4,'grid_type','SG','timestep_method','RK3'); % diffusion1 l2d2 RK3 out_format = strcat(data_dir,'diffusion1_sg_l2_d2_t%d.dat'); -run_time_advance(diffusion1,out_format, ... +run_time_advance(@diffusion1,out_format, ... 'CFL',0.01,'lev',2,'deg',2,'grid_type','SG','timestep_method','RK3'); % diffusion1 l3d3 RK3 out_format = strcat(data_dir,'diffusion1_sg_l3_d3_t%d.dat'); -run_time_advance(diffusion1,out_format, ... +run_time_advance(@diffusion1,out_format, ... 'CFL',0.01,'lev',3,'deg',3,'grid_type','SG','timestep_method','RK3'); % diffusion1 l4d4 RK3 out_format = strcat(data_dir,'diffusion1_sg_l4_d4_t%d.dat'); -run_time_advance(diffusion1,out_format, ... +run_time_advance(@diffusion1,out_format, ... 'CFL',0.01,'lev',4,'deg',4,'grid_type','SG','timestep_method','RK3'); % continuity1 sg l2d2 out_format = strcat(data_dir, 'continuity1_sg_l2_d2_t%d.dat'); -run_time_advance(continuity1,out_format, ... +run_time_advance(@continuity1,out_format, ... 'CFL',0.01,'lev',2,'deg',2,'grid_type','SG','timestep_method','RK3'); % continuity1 fg l2d2 out_format = strcat(data_dir, 'continuity1_fg_l2_d2_t%d.dat'); -run_time_advance(continuity1,out_format, ... +run_time_advance(@continuity1,out_format, ... 'CFL',0.01,'lev',2,'deg',2,'grid_type','FG','timestep_method','RK3'); % continuity1 sg l4d3 out_format = strcat(data_dir, 'continuity1_sg_l4_d3_t%d.dat'); -run_time_advance(continuity1,out_format, ... +run_time_advance(@continuity1,out_format, ... 'CFL',0.01,'lev',4,'deg',3,'grid_type','SG','timestep_method','RK3'); % continuity2 sg l2d2 out_format = strcat(data_dir, 'continuity2_sg_l2_d2_t%d.dat'); -run_time_advance(continuity2,out_format, ... +run_time_advance(@continuity2,out_format, ... 'CFL',0.01,'lev',2,'deg',2,'grid_type','SG','timestep_method','RK3'); % continuity2 fg l2d2 out_format = strcat(data_dir, 'continuity2_fg_l2_d2_t%d.dat'); -run_time_advance(continuity2,out_format, ... +run_time_advance(@continuity2,out_format, ... 'CFL',0.01,'lev',2,'deg',2,'grid_type','FG','timestep_method','RK3'); % continuity2 sg l4d3 out_format = strcat(data_dir, 'continuity2_sg_l4_d3_t%d.dat'); -run_time_advance(continuity2,out_format, ... +run_time_advance(@continuity2,out_format, ... 'CFL',0.01,'lev',4,'deg',3,'grid_type','SG','timestep_method','RK3'); % continuity3 sg l2d2 out_format = strcat(data_dir,'continuity3_sg_l2_d2_t%d.dat'); -run_time_advance(continuity3,out_format, ... +run_time_advance(@continuity3,out_format, ... 'CFL',0.01,'lev',2,'deg',2,'grid_type','SG','timestep_method','RK3'); % continuity3 sg l4d3 out_format = strcat(data_dir,'continuity3_sg_l4_d3_t%d.dat'); -run_time_advance(continuity3,out_format, ... +run_time_advance(@continuity3,out_format, ... 'CFL',0.01,'lev',4,'deg',3,'grid_type','SG','timestep_method','RK3'); % continuity6 sg l2d2 out_format = strcat(data_dir, 'continuity6_sg_l2_d2_t%d.dat'); -run_time_advance(continuity6,out_format, ... +run_time_advance(@continuity6,out_format, ... 'CFL',0.01,'lev',2,'deg',2,'grid_type','SG','timestep_method','RK3'); % continuity6 sg l2d3 out_format = strcat(data_dir, 'continuity6_sg_l2_d3_t%d.dat'); -run_time_advance(continuity6,out_format, ... +run_time_advance(@continuity6,out_format, ... 'CFL',0.01,'lev',2,'deg',3,'grid_type','SG','timestep_method','RK3'); % fokkerplanck1_4p2 sg l2d2 out_format = strcat(data_dir,'fokkerplanck1_4p2_sg_l2_d2_t%d.dat'); -run_time_advance(fokkerplanck1_pitch_C,out_format, ... +run_time_advance(@fokkerplanck1_pitch_C,out_format, ... 'CFL',0.01,'lev',2,'deg',2,'grid_type','SG','timestep_method','RK3'); + % fokkerplanck1_4p2 fg l2d2 out_format = strcat(data_dir,'fokkerplanck1_4p2_fg_l2_d2_t%d.dat'); -run_time_advance(fokkerplanck1_pitch_C,out_format, ... +run_time_advance(@fokkerplanck1_pitch_C,out_format, ... 'CFL',0.01,'lev',2,'deg',2,'grid_type','FG','timestep_method','RK3'); % fokkerplanck1_4p1a sg l2d2 out_format = strcat(data_dir,'fokkerplanck1_4p1a_sg_l2_d2_t%d.dat'); -run_time_advance(fokkerplanck1_pitch_E(1),out_format, ... +run_time_advance(@fokkerplanck1_pitch_E,out_format, ... 'CFL',0.01,'lev',2,'deg',2,'grid_type','SG','timestep_method','RK3'); -% fokkerplanck1_4p3 sg l2d2 +% same, case 2 +out_format = strcat(data_dir,'fokkerplanck1_pitch_E_case2_sg_l2_d2_t%d.dat'); +run_time_advance(@fokkerplanck1_pitch_E,out_format, ... + 'CFL',0.01,'case', 2, 'lev',2,'deg',2,'grid_type','SG','timestep_method','RK3'); + +%fokkerplanck1_4p3 sg l2d2 out_format = strcat(data_dir,'fokkerplanck1_4p3_sg_l2_d2_t%d.dat'); -run_time_advance(fokkerplanck1_4p3,out_format, ... +run_time_advance(@fokkerplanck1_pitch_R,out_format, ... 'CFL',0.01,'lev',2,'deg',2,'grid_type','SG','timestep_method','RK3'); %% uniform level, implicit - +% note fp2 must be calculated with modified x domain [1, 20] to avoid +% singularity problem % fokkerplanck2_complete sg l3d3 out_format = strcat(data_dir,'fokkerplanck2_complete_implicit_sg_l3_d3_t%d.dat'); % any explicit timestep method will give diverging results -run_time_advance(fokkerplanck2_complete,out_format, ... - 'CFL',0.01,'lev',3,'deg',3,'grid_type','SG',... +run_time_advance(@fokkerplanck2_complete,out_format, ... + 'CFL',0.01,'lev',3,'deg',3,'grid_type','SG','case', 4,... 'timestep_method', 'BE'); out_format = strcat(data_dir,'fokkerplanck2_complete_implicit_sg_l4_d3_t%d.dat'); -run_time_advance(fokkerplanck2_complete,out_format, ... - 'CFL',0.01,'lev',4,'deg',3,'grid_type','SG',... +run_time_advance(@fokkerplanck2_complete,out_format, ... + 'CFL',0.01,'lev',4,'deg',3,'grid_type','SG','case', 4,... 'timestep_method', 'BE'); out_format = strcat(data_dir,'fokkerplanck2_complete_implicit_sg_l5_d3_t%d.dat'); -run_time_advance(fokkerplanck2_complete,out_format, ... - 'CFL',0.01,'lev',5,'deg',3,'grid_type','SG',... +run_time_advance(@fokkerplanck2_complete,out_format, ... + 'CFL',0.01,'lev',5,'deg',3,'grid_type','SG','case', 4,... 'timestep_method', 'BE'); % continuity1 sg l2d2 out_format = strcat(data_dir,'continuity1_implicit_l2_d2_t%d.dat'); -run_time_advance(continuity1,out_format, ... +run_time_advance(@continuity1,out_format, ... 'CFL',0.01,'lev',2,'deg',2,'grid_type','SG','timestep_method','BE'); % continuity1 sg l4d3 out_format = strcat(data_dir,'continuity1_implicit_l4_d3_t%d.dat'); -run_time_advance(continuity1,out_format, ... +run_time_advance(@continuity1,out_format, ... 'CFL',0.01,'lev',4,'deg',3,'grid_type','SG','timestep_method','BE'); % continuity2 sg l2d2 out_format = strcat(data_dir,'continuity2_implicit_l2_d2_t%d.dat'); -run_time_advance(continuity2,out_format, ... +run_time_advance(@continuity2,out_format, ... 'CFL',0.01,'lev',2,'deg',2,'grid_type','SG','timestep_method','BE'); % continuity2 sg l4d3 out_format = strcat(data_dir,'continuity2_implicit_l4_d3_t%d.dat'); -run_time_advance(continuity2,out_format, ... +run_time_advance(@continuity2,out_format, ... 'CFL',0.01,'lev',4,'deg',3,'grid_type','SG','timestep_method','BE'); % diffusion1 l4d4 BE out_format = strcat(data_dir,'diffusion1_implicit_sg_l4_d4_t%d.dat'); -run_time_advance(diffusion1,out_format, ... +run_time_advance(@diffusion1,out_format, ... 'CFL',0.01,'lev',4,'deg',4,'grid_type','SG','timestep_method','BE'); % diffusion 2 implicit out_format = strcat(data_dir,'diffusion2_implicit_sg_l3_d3_t%d.dat'); -run_time_advance(diffusion2,out_format, ... +run_time_advance(@diffusion2,out_format, ... 'CFL',0.01,'lev',3,'deg',3,'grid_type','SG',... 'timestep_method', 'BE'); out_format = strcat(data_dir,'diffusion2_implicit_sg_l4_d3_t%d.dat'); -run_time_advance(diffusion2,out_format, ... +run_time_advance(@diffusion2,out_format, ... 'CFL',0.01,'lev',4,'deg',3,'grid_type','SG',... 'timestep_method', 'BE'); out_format = strcat(data_dir,'diffusion2_implicit_sg_l5_d3_t%d.dat'); -run_time_advance(diffusion2,out_format, ... +run_time_advance(@diffusion2,out_format, ... 'CFL',0.01,'lev',5,'deg',3,'grid_type','SG',... 'timestep_method', 'BE'); % advection1 l4d4 implicit BE out_format = strcat(data_dir,'advection1_implicit_sg_l4_d4_t%d.dat'); -run_time_advance(advection1,out_format, ... +run_time_advance(@advection1,out_format, ... 'CFL',0.01,'lev',4,'deg',4,'grid_type','SG','timestep_method','BE'); @@ -169,26 +203,26 @@ % diffusion2 d2 out_format = strcat(data_dir,'diffusion2'); levels = [4, 5]; -run_time_advance(diffusion2,out_format, ... +run_time_advance(@diffusion2,out_format, ... 'CFL',0.01,'lev',levels,'deg',2,'grid_type','SG','timestep_method','RK3'); % continuity2 fg d3 out_format = strcat(data_dir, 'continuity2'); levels = [3, 4]; -run_time_advance(continuity2,out_format, ... +run_time_advance(@continuity2,out_format, ... 'CFL',0.01,'lev',levels,'deg',3,'grid_type','FG','timestep_method','RK3'); % continuity3 sg d4 out_format = strcat(data_dir,'continuity3'); levels = [3, 4, 2]; -run_time_advance(continuity3,out_format, ... +run_time_advance(@continuity3,out_format, ... 'CFL',0.01,'lev',levels,'deg',4,'grid_type','SG','timestep_method','RK3'); % continuity6 sg d2 out_format = strcat(data_dir, 'continuity6'); levels = [2, 3, 2, 3, 3, 2]; -run_time_advance(continuity6,out_format, ... +run_time_advance(@continuity6,out_format, ... 'CFL',0.01,'lev',levels,'deg',2,'grid_type','SG','timestep_method','RK3'); %% non-uniform level, implicit @@ -196,46 +230,48 @@ % diffusion2 sg d2 out_format = strcat(data_dir,'diffusion2_implicit'); levels = [4, 5]; -run_time_advance(diffusion2,out_format, ... +run_time_advance(@diffusion2,out_format, ... 'CFL',0.01,'lev',levels,'deg',2,'grid_type','SG','timestep_method','BE'); % continuity2 fg d3 out_format = strcat(data_dir, 'continuity2_implicit'); levels = [3, 4]; -run_time_advance(continuity2,out_format, ... +run_time_advance(@continuity2,out_format, ... 'CFL',0.01,'lev',levels,'deg',3,'grid_type','FG','timestep_method','BE'); % fokkerplanck2_complete sg d3 +% note fp2 must be calculated with modified x domain [1, 20] to avoid +% singularity problem out_format = strcat(data_dir,'fokkerplanck2_complete_implicit'); % any explicit timestep method will give diverging results levels = [2, 3]; -run_time_advance(fokkerplanck2_complete,out_format, ... - 'CFL',0.01,'lev',levels,'deg',3,'grid_type','SG',... +run_time_advance(@fokkerplanck2_complete,out_format, ... + 'CFL',0.01,'lev',levels,'deg',3,'grid_type','SG','case', 4,... 'timestep_method', 'BE'); +function run_time_advance(pde_handle, out_format, varargin) -function run_time_advance(pde, out_format, varargin) - - runtime_defaults - - pde = check_pde( pde, opts ); + opts = OPTS(varargin); + opts.quiet = 1; + pde = pde_handle( opts ); dt = pde.set_dt( pde, opts.CFL ); if length(pde.dimensions) > 3 opts.max_lev = 4; end opts.max_lev_coeffs = 1; + lev_vec = get_lev_vec(pde); % non-uniform case - if ~(length(unique(opts.lev_vec)) == 1) + if ~(length(unique(lev_vec)) == 1) lev_string = ""; for i=1:length(pde.dimensions) - lev_string = lev_string + int2str(opts.lev_vec(i)) + "_"; + lev_string = lev_string + int2str(lev_vec(i)) + "_"; end out_format = strcat(out_format, '_', lower(opts.grid_type),... '_l', lev_string, 'd', int2str(opts.deg), '_t%d.dat'); end - [elements, elements_idx] = hash_table_sparse_nD (opts.lev_vec, ... + [elements, elements_idx] = hash_table_sparse_nD (lev_vec, ... opts.max_lev, opts.grid_type); hash_table.elements = elements; hash_table.elements_idx = elements_idx; @@ -248,13 +284,81 @@ function run_time_advance(pde, out_format, varargin) A_data = global_matrix(pde,opts,hash_table); - Vmax = 0; - Emax = 0; - out = initial_condition_vector(pde,opts,hash_table,0); + fval = initial_condition_vector(pde,opts,hash_table,0); + + %% Check to see if initial resolution meets requested accuracy +if opts.adapt + if opts.adapt_initial_condition + keep_adapting_initial_condition = true; + while keep_adapting_initial_condition + num_pre_adapt = numel(fval); + % first refine + [pde,fval_tmp,hash_table,~,~,~,~,~,~,~,~,~] ... + = adapt(pde,opts,[],fval,hash_table,[],[],[],[], ... + [],0,1); + if num_pre_adapt == numel(fval_tmp) + keep_adapting_initial_condition = false; + end + clear fval_tmp; + % reproject initial condition onto refined basis + fval = initial_condition_vector(pde, opts, hash_table, t); + end + % coarsen + [pde,~,hash_table,A_data,~,~,~,~,~,~] ... + = adapt(pde,opts,[],fval,hash_table,[],[],[],[], ... + [],1,0); + % reproject onto coarsend basis + fval = initial_condition_vector(pde, opts, hash_table, t); + end +end + + for i=0:4 - time = i*dt; - out = time_advance(pde,opts,A_data,out,time,dt,opts.deg,hash_table,Vmax,Emax); - write_octave_like_output(sprintf(out_format,i), out); + t = i*dt; + % Coarsen Grid + if opts.adapt + [pde,fval,hash_table,A_data,~,~,~,~,~,~] ... + = adapt(pde,opts,[],fval,hash_table,[],[],[],[],[],1,0); + end + + needs_adapting = true; + while needs_adapting + + + % construct the TD coeff_mats. + TD = 1; + pde = get_coeff_mats(pde,opts,t,TD); + + + fval_unstepped = fval; + fval = time_advance(pde,opts,A_data,fval,t,dt,opts.deg,hash_table,[],[]); + + %% + % Refine Grid - determine which elements to add, but reset fval to + % fval_previous with those new elements added and time_advance + % again + if opts.adapt + + num_elements_0 = numel(fval); + + [pde,~,hash_table,A_data,~,~,~,~,~,~,fval_unstepped_adapted] ... + = adapt(pde,opts,[],fval,hash_table,[],[],[],[], ... + [],0,1,fval_unstepped); + + num_elements_adapted = numel(fval_unstepped_adapted); + + if num_elements_0 == num_elements_adapted + needs_adapting = false; + fval = time_advance(pde,opts,A_data,fval_unstepped_adapted,t,dt,opts.deg,hash_table,[],[]); + else + fval = fval_unstepped_adapted; + end + else + needs_adapting = false; + end + + end + write_octave_like_output(sprintf(out_format,i), fval); end end diff --git a/initial_condition_vector_test.m b/initial_condition_vector_test.m index d3e50837..b7bd1d0d 100644 --- a/initial_condition_vector_test.m +++ b/initial_condition_vector_test.m @@ -20,6 +20,8 @@ function sane_1D_function_test(testCase) pde.dimensions{1}.max = 2*pi; pde.dimensions{1}.init_cond_fn = @(x,p,t) my_func(x); +pde = compute_dimension_mass_mat(opts,pde); + [elements, elements_idx] = hash_table_sparse_nD (pde.get_lev_vec, opts.max_lev, opts.grid_type); hash_table.elements = elements; hash_table.elements_idx = elements_idx; diff --git a/matrix_plot_D.m b/matrix_plot_D.m index 2d88836f..da82de6e 100755 --- a/matrix_plot_D.m +++ b/matrix_plot_D.m @@ -144,6 +144,7 @@ if user_provided_nodes assert(numel(nodes_count)==numel(input_nodes)); + assert(numel(Meval(:,1))==sum(nodes_count)); end %% % Transform back to real space from wavelet space diff --git a/md_eval_function.m b/md_eval_function.m index 409db27f..cb459634 100644 --- a/md_eval_function.m +++ b/md_eval_function.m @@ -16,7 +16,9 @@ for d=1:num_dims fList{d} = forward_wavelet_transform(deg,dims{d}.lev, ... dims{d}.min,dims{d}.max, ... - md_func{d},params, blocks, t); + md_func{d},dims{d}.moment_dV,params, blocks, t); + N = numel(fList{d}); + fList{d} = dims{d}.mass_mat(1:N,1:N) \ fList{d}; end time_multiplier = md_funcs{s}{num_dims+1}(t); diff --git a/moment_integral_test.m b/moment_integral_test.m index a0d973a9..963bcdb2 100644 --- a/moment_integral_test.m +++ b/moment_integral_test.m @@ -10,21 +10,34 @@ function test_moment_2D_spherical(testCase) num_dims = numel(pde.dimensions); +v_th = 0.2; + function ans = my_func_v(v) - v_th = 0.2; ans = exp(-v.^2./v_th^2); end function ans = my_func_z(z) - ans = z.*+1; + ans = z; end pde.dimensions{1}.min = 0; pde.dimensions{1}.max = 1; -pde.dimensions{1}.jacobian = @(v,p,t) v.^2; + pde.dimensions{2}.min = 0; pde.dimensions{2}.max = pi; -pde.dimensions{2}.jacobian = @(z,p,t) sin(z); + +% with jacobian +pde.dimensions{1}.jacobian = @(v,p,t) v; +pde.dimensions{2}.jacobian = @(z,p,t) z.*0+1; + + + + + + + + + % overwrite the initial conditions for this test @@ -44,7 +57,8 @@ function test_moment_2D_spherical(testCase) t = 0; fval = initial_condition_vector(pde,opts,hash_table,t); -fval_realspace = wavelet_to_realspace(pde,opts,Meval,fval,hash_table); +fval_realspace = wavelet_to_realspace(pde,opts,Meval,fval,hash_table); +f = singleD_to_multiD(num_dims,fval_realspace,nodes); do_plot = 0; if do_plot @@ -62,8 +76,8 @@ function test_moment_2D_spherical(testCase) end moment_func_nD = {@mass_func_v,@mass_func_z}; -mass = moment_integral(opts.lev, opts.deg, coord, fval_realspace, moment_func_nD, pde.dimensions); -mass_analytic = 0.0111367; +mass = moment_integral(opts.lev, opts.deg, f, moment_func_nD, pde.dimensions,nodes,[1,2]); +mass_analytic = 0.098696; diff1 = abs(mass-mass_analytic); verifyLessThan(testCase, diff1, 1e-6); @@ -73,8 +87,8 @@ function test_moment_2D_spherical(testCase) end moment_func_nD = {@energy_func_v,@mass_func_z}; -energy = moment_integral(opts.lev, opts.deg, coord, fval_realspace, moment_func_nD, pde.dimensions); -energy_analytic = 0.000668199; +energy = moment_integral(opts.lev, opts.deg, f, moment_func_nD, pde.dimensions,nodes,[1,2]); +energy_analytic = 0.00394784; diff2 = abs(energy-energy_analytic); verifyLessThan(testCase, diff2, 1e-6); @@ -87,9 +101,52 @@ function test_moment_2D_spherical(testCase) end moment_func_nD = {@random_func_v,@random_func_z}; -moment = moment_integral(opts.lev, opts.deg, coord, fval_realspace, moment_func_nD, pde.dimensions); -moment_analytic = 0.00258567; +moment = moment_integral(opts.lev, opts.deg, f, moment_func_nD, pde.dimensions,nodes,[1,2]); +moment_analytic = 0.0194818; diff3 = abs(moment-moment_analytic); verifyLessThan(testCase, diff3, 1e-6); +% check the 1D mass moment of a 2D function, i.e., give back a vector + +% with jacobian but over z only +moment_func_nD = {@mass_func_v,@mass_func_z}; +moment = moment_integral(opts.lev, opts.deg, f, moment_func_nD, pde.dimensions,nodes,[2]); +moment_analytic_fn = @(v) 1/2*exp(-v.^2./v_th^2).*pi^2; +moment_analytic = moment_analytic_fn(nodes{1}); +moment_analytic = reshape(moment_analytic,size(moment)); +diff5 = norm(moment-moment_analytic); +plot(nodes{1},moment) +hold on +plot(nodes{1},moment_analytic,'o') +hold off +verifyLessThan(testCase, diff5, 2e-5); + +% with jacobian but over v only +moment_func_nD = {@mass_func_v,@mass_func_z}; +moment = moment_integral(opts.lev, opts.deg, f, moment_func_nD, pde.dimensions,nodes,[1]); +moment_analytic_fn = @(z) 1/2 * (1-exp(-1/v_th^2))*v_th^2.*z; +moment_analytic = moment_analytic_fn(nodes{2}); +moment_analytic = reshape(moment_analytic,size(moment)); +diff6 = norm(moment-moment_analytic); +plot(nodes{2},moment) +hold on +plot(nodes{2},moment_analytic,'o') +hold off +verifyLessThan(testCase, diff6, 2e-5); + +% no jacobian and over z only +pde.dimensions{1}.jacobian = @(v,p,t) v.*0+1; +pde.dimensions{2}.jacobian = @(v,p,t) v.*0+1; +moment_func_nD = {@mass_func_v,@mass_func_z}; +moment = moment_integral(opts.lev, opts.deg, f, moment_func_nD, pde.dimensions,nodes,[2]); +moment_analytic_fn = @(v) 1/2*exp(-v.^2./v_th^2).*pi^2; +moment_analytic = moment_analytic_fn(nodes{1}); +moment_analytic = reshape(moment_analytic,size(moment)); +diff4 = norm(moment-moment_analytic); +plot(nodes{1},moment) +hold on +plot(nodes{1},moment_analytic,'o') +hold off +verifyLessThan(testCase, diff4, 2e-5); + end diff --git a/moment_integral_test.nb b/moment_integral_test.nb new file mode 100644 index 00000000..366152e7 --- /dev/null +++ b/moment_integral_test.nb @@ -0,0 +1,835 @@ +(* Content-type: application/vnd.wolfram.mathematica *) + +(*** Wolfram Notebook File ***) +(* http://www.wolfram.com/nb *) + +(* CreatedBy='Mathematica 12.1' *) + +(*CacheID: 234*) +(* Internal cache information: +NotebookFileLineBreakTest +NotebookFileLineBreakTest +NotebookDataPosition[ 158, 7] +NotebookDataLength[ 41447, 827] +NotebookOptionsPosition[ 40079, 799] +NotebookOutlinePosition[ 40475, 815] +CellTagsIndexPosition[ 40432, 812] +WindowFrame->Normal*) + +(* Beginning of Notebook Content *) +Notebook[{ +Cell["\<\ +2D test case with no Jacobian, i.e., the line elements are simply 1\ +\>", "Text", + CellChangeTimes->{{3.8201063597653503`*^9, + 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operators. + +dV = @(x,p,t,dat) 0*x+1; % -2*df/dx g1 = @(x,p,t,dat) x.*0-2; -pterm1 = GRAD(num_dims,g1,-1,'D','D', BCL_fList, BCR_fList); +pterm1 = DIV(num_dims,g1,'',-1,'D','N', BCL_fList, '','',dV); term1_x = SD_TERM({pterm1}); term1 = MD_TERM(num_dims,{term1_x}); diff --git a/pdes/advection1_bidirectional_flow.m b/pdes/advection1_bidirectional_flow.m index 353435f6..715134ec 100644 --- a/pdes/advection1_bidirectional_flow.m +++ b/pdes/advection1_bidirectional_flow.m @@ -12,6 +12,7 @@ %% Define dimensions dim_x = DIMENSION(-pi,+pi); +dim_x.moment_dV = @(x,p,t,dat) 0*x+1; dimensions = {dim_x}; num_dims = numel(dimensions); @@ -26,16 +27,13 @@ ic1 = sol1; initial_conditions = {ic1}; -%% Define boundary conditions - -BCL = sol1; -BCR = sol1; - %% Define PDE terms + +dV = @(x,p,t,dat) 0*x+1; % -d/dx (x*f) g1 = @(x,p,t,dat) -x; -pterm1 = GRAD(num_dims,g1,-1,'D','D', BCL, BCR); +pterm1 = DIV(num_dims,g1,'',-1,'N','N','','','',dV); term1_x = SD_TERM({pterm1}); term1 = MD_TERM(num_dims,{term1_x}); diff --git a/pdes/advection1_reverse_flow.m b/pdes/advection1_reverse_flow.m index 0575f146..10e10f2a 100644 --- a/pdes/advection1_reverse_flow.m +++ b/pdes/advection1_reverse_flow.m @@ -17,7 +17,7 @@ %% Define dimensions dim_x = DIMENSION(0,pi); -dim_x.init_cond_fn = @(x,p,t) cos(x); +dim_x.moment_dV = @(x,p,t,dat) 0*x+1; dimensions = {dim_x}; num_dims = numel(dimensions); @@ -47,9 +47,10 @@ %% Define PDE terms % Here the term is df/dx, which is opposite the direction in advection1.m -g1 = @(x,p,t,dat) x.*0 + 2; -pterm = GRAD(num_dims,g1,-1,'D','D', BCL_fList, BCR_fList); +dV = @(x,p,t,dat) 0*x+1; +g1 = @(x,p,t,dat) x.*0 + 2; +pterm = DIV(num_dims,g1,'',-1,'N','D', '', BCR_fList,'',dV); term_x = SD_TERM({pterm}); term1 = MD_TERM(num_dims, {term_x}); diff --git a/pdes/advection1_spherical.m b/pdes/advection1_spherical.m index c4943234..f1946338 100644 --- a/pdes/advection1_spherical.m +++ b/pdes/advection1_spherical.m @@ -1,9 +1,9 @@ function pde = advection1_spherical(opts) % 1D test case using continuity equation, i.e., % -% r^2 * df/dt == -d/dr(r^2 * v * r * f(r,t)) +% df/dt == -1/r^2*d/dr(r^2 * v * r * f(r,t)) % -% so this is just pure advection in spherical coordinates with flux=v*r +% so this is just pure advection in spherical coordinates with flux=v*r*f % % f(r,0) == cos(r) % @@ -14,14 +14,8 @@ % % Run with % -% asgard(@advection1_spherical,'timestep_method','BE','dt',0.001,'num_steps',20,'case',1) +% asgard(@advection1_spherical,'timestep_method','BE','dt',0.001,'num_steps',20) % -% case = 1 % the standard approach, i.e., no jacobian application -% (working but minor difference near p=0) -% case = 2 % apply p^2 jacobian to LHS, volume, trace and BC evaluations using g_funcs. -% (does not seem to work?) -% case = 3 % apply p^2 jacobian to LHS, volume, trace and BC evaluations using dim.jacobian. -% (does not seem to work?) %% Define paramaters @@ -30,17 +24,7 @@ %% Define dimensions dim_x = DIMENSION(0,2*pi); - -switch opts.case_ - case 1 % no jacobian applied - dim_x.jacobian = @(x,p,t,d) x.*0+1; - case 2 % jacobian applied withing g_funcs - dim_x.jacobian = @(x,p,t,d) x.*0+1; - case 3 % jacobian applied within dim.jacobian - dim_x.jacobian = @(x,p,t,d) x.^2; - case 4 % jacobian applied within dim.jacobian - dim_x.jacobian = @(x,p,t,d) x.^2; -end +dim_x.moment_dV = @(x,p,t,dat) x.^2; dimensions = {dim_x}; num_dims = numel(dimensions); @@ -56,48 +40,16 @@ BCL = sol1; BCR = sol1; -%% Define LHS PDE terms (only on the d/dt) -switch opts.case_ - case 1 % no jacobian applied - g1 = @(x,p,t,dat) x.^2; - case 2 % jacobian defined within g funcs (weak form before coordinate choice) - g1 = @(x,p,t,dat) x.^2; - case 3 % jacobian defined within dim.jacobian (weak form before coordinate choice) - g1 = @(x,p,t,dat) x.*0+1; - case 4 % weak form AFTER coordinate choice - g1 = @(x,p,t,dat) x.^2; -end -pterm1 = MASS(g1); -LHS_term_x = SD_TERM({pterm1}); -LHS_term = MD_TERM(num_dims,{LHS_term_x}); -LHS_terms = {LHS_term}; % still have to include this even if it is I to allow for the jacobian application +%% Define PDE terms (all other non d/dt terms) -%% Define RHS PDE terms (all other non d/dt terms) -switch opts.case_ - case 1 % no jacobian applied - % -d/dr (r^2 * v * r * f) - g1 = @(x,p,t,dat) -x.^2 .* p.v .* x; - case 2 % jacobian defined within g funcs - % -int(g*J dr) = -int(v*r * r^2 dr) - g1 = @(x,p,t,dat) -p.v .* x .* x.^2; - case 3 % jacobian defined within dim.jacobian - % -int(g*J dr) = -int(v*r * J dr) - g1 = @(x,p,t,dat) -p.v .* x; -end +dV = @(x,p,t,dat) x.^2; -switch opts.case_ - case {1,2,3} - pterm1 = GRAD(num_dims,g1,-1,'D','N',BCL); - term1_x = SD_TERM({pterm1}); - term1 = MD_TERM(num_dims,{term1_x}); - case 4 - g = @(x,p,t,d) x.*0-1; - pterm1 = MASS(g); - g = @(x,p,t,d) x.^2 .* x .* p.v; - pterm2 = GRAD(num_dims,g,-1,'D','N',BCL); - term1_x = SD_TERM({pterm1,pterm2}); - term1 = MD_TERM(num_dims,{term1_x}); -end +g1 = @(x,p,t,dat) -p.v*x; +pterm1 = DIV(num_dims,g1,'',-1,'D','N','','','',dV); + %Note left BC does not matter since jacobian is zero there. + %Right BC is free since flow is going to the right +term1_x = SD_TERM({pterm1}); +term1 = MD_TERM(num_dims,{term1_x}); terms = {term1}; @@ -116,6 +68,6 @@ end %% Construct PDE -pde = PDE(opts,dimensions,terms,LHS_terms,sources,params,@set_dt,[],initial_conditions,solutions); +pde = PDE(opts,dimensions,terms,[],sources,params,@set_dt,[],initial_conditions,solutions); end diff --git a/pdes/advection1_velocity.m b/pdes/advection1_velocity.m index 976856f7..241733b3 100644 --- a/pdes/advection1_velocity.m +++ b/pdes/advection1_velocity.m @@ -22,6 +22,7 @@ %% Define dimensions dim_v = DIMENSION(0.01,10^2); +dim_v.moment_dV = @(x,p,t) x.^2; dim_v.init_cond_fn = @(v,p,t) soln(v,p,t); BCFunc_R = @(v,p,t) soln(v,p,t); @@ -61,12 +62,12 @@ % term V1 == g(v) q(v) [mass, g(v) = 1/v^2, BC N/A] % q(v) == d/dv(g2(v)f(v)) [grad, g2(v) = v^3, BCL= N, BCR=N] -g1 = @(v,p,t,dat) 1./v.^2; -g2 = @(v,p,t,dat) (m_a*nu_s/(m_a + m_b))*v.^3; +dV = @(x,p,t,dat) x.^2; -pterm1 = MASS(g1); -pterm2 = GRAD(num_dims,g2,-1,'N','D', BCL_fList, BCR_fList); -termV_s = SD_TERM({pterm1,pterm2}); +g1 = @(v,p,t,dat) (m_a*nu_s/(m_a + m_b))*v; + +pterm1 = DIV(num_dims,g1,'',-1,'N','D', '', BCR_fList,'',dV); +termV_s = SD_TERM({pterm1}); termV1 = MD_TERM(num_dims,{termV_s}); terms = {termV1}; @@ -106,3 +107,4 @@ pde = PDE(opts,dimensions,terms,[],sources,params,@set_dt,[],initial_conditions,solutions); end + diff --git a/pdes/continuity1.m b/pdes/continuity1.m index e2e5ba32..1e7d6b54 100644 --- a/pdes/continuity1.m +++ b/pdes/continuity1.m @@ -6,16 +6,15 @@ % Run with % % explicit -% asgard(@continuity1) % asgard(@continuity1,'lev',4,'deg',3) % % implicit % asgard(@continuity1,'timestep_method','CN') -% asgard(@continuity1,'timestep_method','CN','CFL',0.1) %% Define the dimensions dim_x = DIMENSION(-1,+1); +dim_x.moment_dV = @(x,p,t,dat) 0*x+1; dimensions = {dim_x}; num_dims = numel(dimensions); @@ -29,9 +28,7 @@ %% Define the initial conditions -ic_x = @(x,p,t) x.*0; -ic1 = new_md_func(num_dims,{ic_x}); -initial_conditions = {ic1}; +initial_conditions = {sol1}; %% Define the terms of the PDE % @@ -40,8 +37,10 @@ %% % -df/dx +dV = @(x,p,t,dat) 0*x+1; + g1 = @(x,p,t,dat) x.*0-1; -pterm1 = GRAD(num_dims,g1,0,'P','P'); +pterm1 = DIV(num_dims,g1,'',-1,'P','P','','','',dV); term1_x = SD_TERM({pterm1}); term1 = MD_TERM(num_dims,{term1_x}); @@ -63,13 +62,17 @@ % Source 1 s1x = @(x,p,t) cos(2*pi*x); s1t = @(t,p) cos(t); -source1 = {s1x,s1t}; +source1 = new_md_func(num_dims,{s1x,s1t}); %% % Source 2 s2x = @(x,p,t) sin(2*pi*x); s2t = @(t,p) -2*pi*sin(t); -source2 = {s2x,s2t}; +source2 = new_md_func(num_dims,{s2x,s2t}); + +s3x = @(x,p,t) cos(1/2*pi*x); +s3t = @(t,p) sin(2*pi*0.1*t); +source3 = new_md_func(num_dims,{s3x,s3t}); sources = {source1,source2}; diff --git a/pdes/continuity2.m b/pdes/continuity2.m index 4e7f9b17..ec615c99 100644 --- a/pdes/continuity2.m +++ b/pdes/continuity2.m @@ -25,7 +25,9 @@ % Here we setup a 2D problem (x,y) dim_x = DIMENSION(-1,+1); +dim_x.moment_dV = @(x,p,t,dat) 0*x+1; dim_y = DIMENSION(-2,+2); +dim_y.moment_dV = @(y,p,t,dat) 0*y+1; dimensions = {dim_x,dim_y}; num_dims = numel(dimensions); @@ -37,15 +39,22 @@ % % Here we have 2 terms, having only nDims=2 (x,y) operators. +dV = @(x,p,t,dat) 0*x+1; + %% % -df/dx which is % % d/dx g1(x) f(x,y) [grad,g1(x)=-1, BCL=P, BCR=P] g1 = @(x,p,t,dat) x*0-1; -pterm1 = GRAD(num_dims,g1,0,'P','P'); +pterm1 = DIV(num_dims,g1,'',-1,'P','P','','','',dV); term1_x = SD_TERM({pterm1}); -term1 = MD_TERM(num_dims,{term1_x,[]}); + +g1 = @(x,p,t,dat) 0*x+1; +pterm1 = MASS(g1,'','',dV); +term1_y = SD_TERM({pterm1}); + +term1 = MD_TERM(num_dims,{term1_x,term1_y}); %% % -df/dy which is @@ -53,7 +62,7 @@ % d/dy g1(y) f(x,y) [grad,g1(y)=-1, BCL=P, BCR=P] g1 = @(y,p,t,dat) y*0-1; -pterm1 = GRAD(num_dims,g1,0,'P','P'); +pterm1 = DIV(num_dims,g1,'',-1,'P','P','','','',dV); term2_y = SD_TERM({pterm1}); term2 = MD_TERM(num_dims,{[],term2_y}); diff --git a/pdes/continuity3.m b/pdes/continuity3.m index 4a18af92..b8193988 100644 --- a/pdes/continuity3.m +++ b/pdes/continuity3.m @@ -23,33 +23,38 @@ dim_x = DIMENSION(-1,+1); dim_x.name = 'x'; +dim_x.moment_dV = @(x,p,t,dat) 0*x+1; dim_x.lev = 5; dim_y = DIMENSION(-2,+2); dim_y.name = 'y'; +dim_y.moment_dV = @(x,p,t,dat) 0*x+1; dim_y.lev = 4; dim_z = DIMENSION(-3,+3); dim_z.name = 'z'; +dim_z.moment_dV = @(x,p,t,dat) 0*x+1; dim_z.lev = 3; dimensions = {dim_x,dim_y,dim_z}; num_dims = numel(dimensions); %% Initial conditions - -ic1 = new_md_func(num_dims); % set to all zero +ic_x = @(x,p,t) x.*0; +ic1 = new_md_func(num_dims,{ic_x,ic_x,ic_x}); % set to all zero initial_conditions = {ic1}; %% Define the terms of the PDE % % Here we have 3 terms, having only nDims=3 (x,y,z) operators. +dV = @(x,p,t,dat) 0*x+1; + %% % -df/dx g1 = @(x,p,t,dat) x.*0-1; -pterm1 = GRAD(num_dims,g1,0,'P','P'); +pterm1 = DIV(num_dims,g1,'',-1,'P','P','','','',dV); term1_x = SD_TERM({pterm1}); term1 = MD_TERM(num_dims,{term1_x,[],[]}); @@ -57,7 +62,7 @@ % -df/fy g1 = @(y,p,t,dat) y.*0-1; -pterm1 = GRAD(num_dims,g1,0,'P','P'); +pterm1 = DIV(num_dims,g1,'',-1,'P','P','','','',dV); term2_y = SD_TERM({pterm1}); term2 = MD_TERM(num_dims,{[],term2_y,[]}); @@ -65,7 +70,7 @@ % -df/dz g1 = @(z,p,t,dat) z*0-1; -pterm1 = GRAD(num_dims,g1,0,'P','P'); +pterm1 = DIV(num_dims,g1,'',-1,'P','P','','','',dV); term3_z = SD_TERM({pterm1}); term3 = MD_TERM(num_dims,{[],[],term3_z}); @@ -144,3 +149,4 @@ end + diff --git a/pdes/continuity6.m b/pdes/continuity6.m index f4c9eec5..d5f6466b 100644 --- a/pdes/continuity6.m +++ b/pdes/continuity6.m @@ -26,25 +26,34 @@ % Here we setup a 6D problem (x,y,z,vx,vy,vz) dim_x = DIMENSION(-1,+1); +dim_x.moment_dV = @(x,p,t,dat) 0*x+1; dim_y = DIMENSION(-2,+2); +dim_y.moment_dV = @(x,p,t,dat) 0*x+1; dim_z = DIMENSION(-3,+3); +dim_z.moment_dV = @(x,p,t,dat) 0*x+1; dim_vx = DIMENSION(-10,+10); +dim_vx.moment_dV = @(x,p,t,dat) 0*x+1; dim_vy = DIMENSION(-20,+20); +dim_vy.moment_dV = @(x,p,t,dat) 0*x+1; dim_vz = DIMENSION(-30,+30); +dim_vz.moment_dV = @(x,p,t,dat) 0*x+1; dimensions = {dim_x,dim_y,dim_z,dim_vx,dim_vy,dim_vz}; num_dims = numel(dimensions); %% Initial conditions -ic1 = new_md_func(num_dims); % all zero +ic_x = @(x,p,t) x.*0; +ic1 = new_md_func(num_dims,{ic_x,ic_x,ic_x,ic_x,ic_x,ic_x}); % set to all zero initial_conditions = {ic1}; %% Define the terms of the PDE % % Here we have 6 terms, having only nDims=6 (x,y,z,vx,vy,vz) operators. +dV = @(x,p,t,dat) 0*x+1; + %% % -bx*df/dx @@ -53,7 +62,7 @@ % term2 = term_fill({term2_x,[],[],[],[],[]}); g1 = @(x,p,t,dat) x*0-bx; -pterm1 = GRAD(num_dims,g1,0,'P','P'); +pterm1 = DIV(num_dims,g1,'',-1,'P','P','','','',dV); term1_x = SD_TERM({pterm1}); term1 = MD_TERM(num_dims,{term1_x,[],[],[],[],[]}); @@ -66,7 +75,7 @@ % term3 = term_fill({[],term3_y,[],[],[],[]}); g1 = @(y,p,t,dat) y*0-by; -pterm1 = GRAD(num_dims,g1,0,'P','P'); +pterm1 = DIV(num_dims,g1,'',-1,'P','P','','','',dV); term2_y = SD_TERM({pterm1}); term2 = MD_TERM(num_dims,{[],term2_y,[],[],[],[]}); @@ -78,7 +87,7 @@ % term4 = term_fill({[],[],term4_z,[],[],[]}); g1 = @(z,p,t,dat) z*0-bz; -pterm1 = GRAD(num_dims,g1,0,'P','P'); +pterm1 = DIV(num_dims,g1,'',-1,'P','P','','','',dV); term3_z = SD_TERM({pterm1}); term3 = MD_TERM(num_dims,{[],[],term3_z,[],[],[]}); @@ -90,7 +99,7 @@ % term5 = term_fill({[],[],[],term5_vx,[],[]}); g1 = @(x,p,t,dat) x*0-ax; -pterm1 = GRAD(num_dims,g1,0,'P','P'); +pterm1 = DIV(num_dims,g1,'',-1,'P','P','','','',dV); term4_vx = SD_TERM({pterm1}); term4 = MD_TERM(num_dims,{[],[],[],term4_vx,[],[]}); @@ -102,7 +111,7 @@ % term6 = term_fill({[],[],[],[],term6_vy,[]}); g1 = @(y,p,t,dat) y*0-ay; -pterm1 = GRAD(num_dims,g1,0,'P','P'); +pterm1 = DIV(num_dims,g1,'',-1,'P','P','','','',dV); term5_vy = SD_TERM({pterm1}); term5 = MD_TERM(num_dims,{[],[],[],[],term5_vy,[]}); @@ -114,7 +123,7 @@ % term7 = term_fill({[],[],[],[],[],term7_vz}); g1 = @(z,p,t,dat) z*0-az; -pterm1 = GRAD(num_dims,g1,0,'P','P'); +pterm1 = DIV(num_dims,g1,'',-1,'P','P','','','',dV); term6_vz = SD_TERM({pterm1}); term6 = MD_TERM(num_dims,{[],[],[],[],[],term6_vz}); @@ -233,7 +242,6 @@ soln_vy = @(vy,p,t) sin(vyarg*vy); soln_vz = @(vz,p,t) cos(vzarg*vz); soln_t = @(t) sin(targ*t); - soln1 = new_md_func(num_dims,{soln_x,soln_y,soln_z,soln_vx,soln_vy,soln_vz,soln_t}); solutions = {soln1}; diff --git a/pdes/diffusion1.m b/pdes/diffusion1.m index 7f82dc06..5dacf2a6 100644 --- a/pdes/diffusion1.m +++ b/pdes/diffusion1.m @@ -27,7 +27,7 @@ % asgard(@diffusion1,'CFL',0.01); % % implicit -% asgard(@diffusion1,'timestep_method','CN'); +% asgard(@diffusion1,'timestep_method','BE'); % % Notes % @@ -42,6 +42,7 @@ % Here we setup a 1D problem (x,y) nu = pi/2; %coefficient set to be very small to allow for stability % DLG - WTF is this? soln_x = @(x,p,t) cos(nu*x); +%soln_x = @(x,p,t) sin(nu*x); soln_t = @(t,p) exp(-2*nu^2*t); BCFunc = @(x,p,t) soln_x(x,p,t); @@ -62,6 +63,7 @@ }; dim_x = DIMENSION(0,1); +dim_x.moment_dV = @(x,p,t,dat) 0*x+1; dimensions = {dim_x}; num_dims = numel(dimensions); @@ -79,21 +81,40 @@ % term1 % -% eq1 : df/dt == d/dx g1(x) q(x,y) [grad,g1(x)=1, BCL=N, BCR=D] +% eq1 : df/dt == d/dx g1(x) q(x,y) [div ,g1(x)=1, BCL=N, BCR=D] % eq2 : q(x,y) == d/dx g2(x) f(x,y) [grad,g2(x)=1, BCL=D, BCR=D] % % coeff_mat = mat1 * mat2 +dV = @(x,p,t,dat) 0*x+1; + g1 = @(x,p,t,dat) x.*0+1; g2 = @(x,p,t,dat) x.*0+1; -pterm1 = GRAD(num_dims,g1,+1,'N','N'); -pterm2 = GRAD(num_dims,g2,-1,'D','D',BCL_fList,BCR_fList); +pterm1 = DIV(num_dims,g1,'',-1,'N','N','','','',dV); +pterm2 = GRAD(num_dims,g2,'',+1,'D','D',BCL_fList,BCR_fList,'',dV); term1_x = SD_TERM({pterm1,pterm2}); term1 = MD_TERM(num_dims,{term1_x}); -terms = {term1}; +%% Hack for interior penalty +pen = 0; +g3 = @(x,p,t,dat) 0.*x+pen; +g4 = @(x,p,t,dat) 0.*x-pen; + +pterm1 = DIV(num_dims,g3,'',-1,'D','D','','','',dV); +term2_x = SD_TERM({pterm1}); +term2 = MD_TERM(num_dims,{term2_x}); + +pterm1 = DIV(num_dims,g4,'', 0,'D','D','','','',dV); +term3_x = SD_TERM({pterm1}); +term3 = MD_TERM(num_dims,{term3_x}); + +%%% With penalty +terms = {term1,term2,term3}; + +%%% Without penalty +%terms = {term1}; %% Define some parameters and add to pde object. % These might be used within the various functions below. @@ -105,8 +126,9 @@ s1x = @(x,p,t) -nu^2*cos(nu*x); s1t = @(t,p) exp(-2*nu^2*t); -source1 = {s1x, s1t}; +source1 = new_md_func(num_dims,{s1x, s1t}); +%sources = {}; sources = {source1}; %% Define the analytic solution (optional). diff --git a/pdes/diffusion1_div.m b/pdes/diffusion1_div.m deleted file mode 100644 index 16ca6805..00000000 --- a/pdes/diffusion1_div.m +++ /dev/null @@ -1,148 +0,0 @@ -function pde = diffusion1_div(opts) -% Example PDE using the 1D Diffusion Equation. This example PDE is -% time dependent (although not all the terms are time dependent). This -% implies the need for an initial condition. -% PDE: -% -% df/dt = d^2 f/dx^2 -% -% Domain is [0,1] -% Inhomogeneous Dirichlet boundary condition -% Code is expected to be added to the 1d Advection Equation -% -% Diffusion terms are dealt with via LDG, i.e., splitting into two first -% order equations: -% -% d^2 f / dx^2 becomes -% -% dq/dx with free (homogeneous Neumann BC) -% -% and -% -% q=df/dx with Dirichlet BCs specified by analytic solution -% -% Run with -% -% explicit -% asgard(@diffusion1,'CFL',0.01); -% -% implicit -% asgard(@diffusion1,'timestep_method','BE'); -% -% Notes -% -% Louis: With small nu, stability is maintained for longer times -% asgard(@diffusion1,'lev',3,'deg',4,'timestep_method','BE', 'dt',0.05,'num_steps',20) -% DLG : it seems like the k and nu are mixed up / together here? i.e., the -% equation assumes nu = 1 since it is not present in g1 or g2, but nu is -% specified as != 1 below? - -%% Define the dimensions -% -% Here we setup a 1D problem (x,y) -nu = pi/2; %coefficient set to be very small to allow for stability % DLG - WTF is this? -soln_x = @(x,p,t) cos(nu*x); -%soln_x = @(x,p,t) sin(nu*x); -soln_t = @(t,p) exp(-2*nu^2*t); - -BCFunc = @(x,p,t) soln_x(x,p,t); -BCFunc_t = @(t,p) soln_t(t,p); - -% Domain is (a,b) - -% The function is defined for the plane -% x = a and x = b -BCL_fList = { ... - @(x,p,t) BCFunc(x,p,t), ... % replace x by a - @(t,p) BCFunc_t(t,p) - }; - -BCR_fList = { ... - @(x,p,t) BCFunc(x,p,t), ... % replace x by b - @(t,p) BCFunc_t(t,p) - }; - -dim_x = DIMENSION(0,1); -dimensions = {dim_x}; -num_dims = numel(dimensions); - -%% Initial conditions - -ic1 = new_md_func(num_dims,{soln_x,soln_t}); -initial_conditions = {ic1}; - -%% Define the terms of the PDE -% -% Here we have 1 term, with each term having nDims (x and y) operators. - -%% -% Setup the d^2_dx^2 term - -% term1 -% -% eq1 : df/dt == d/dx g1(x) q(x,y) [div ,g1(x)=1, BCL=N, BCR=D] -% eq2 : q(x,y) == d/dx g2(x) f(x,y) [grad,g2(x)=1, BCL=D, BCR=D] -% -% coeff_mat = mat1 * mat2 - -g1 = @(x,p,t,dat) x.*0+1; -g2 = @(x,p,t,dat) x.*0+1; - -pterm1 = DIV(num_dims,g1,'',-1,'N','N'); -pterm2 = GRAD(num_dims,g2,'',+1,'D','D',BCL_fList,BCR_fList); - -term1_x = SD_TERM({pterm1,pterm2}); -term1 = MD_TERM(num_dims,{term1_x}); - -pen = 0; -g3 = @(x,p,t,dat) 0.*x+pen; -g4 = @(x,p,t,dat) 0.*x-pen; - -pterm1 = DIV(num_dims,g3,'',-1,'N','N',BCL_fList,BCR_fList); -term2_x = SD_TERM({pterm1}); -term2 = MD_TERM(num_dims,{term2_x}); - -pterm1 = DIV(num_dims,g4,'', 0,'N','N',BCL_fList,BCR_fList); -term3_x = SD_TERM({pterm1}); -term3 = MD_TERM(num_dims,{term3_x}); - -terms = {term1,term2,term3}; - -%% Define some parameters and add to pde object. -% These might be used within the various functions below. - -params.parameter1 = 0; -params.parameter2 = 1; - -%% Define sources - -s1x = @(x,p,t) -nu^2*cos(nu*x); -s1t = @(t,p) exp(-2*nu^2*t); -source1 = {s1x, s1t}; - -%sources = {}; -sources = {source1}; - -%% Define the analytic solution (optional). -% This requires nDims+time function handles. - -soln1 = new_md_func(num_dims,{soln_x,soln_t}); -solutions = {soln1}; - - function dt=set_dt(pde,CFL) - - dims = pde.dimensions; - - % for Diffusion equation: dt = C * dx^2 - - lev = dims{1}.lev; - dx = 1/2^lev; - dt = CFL*dx^2; - - end - -%% Construct PDE - -pde = PDE(opts,dimensions,terms,[],sources,params,@set_dt,[],initial_conditions,solutions); - -end diff --git a/pdes/diffusion1_spherical.m b/pdes/diffusion1_spherical.m index c307430f..a1feb833 100644 --- a/pdes/diffusion1_spherical.m +++ b/pdes/diffusion1_spherical.m @@ -2,7 +2,7 @@ % Example of 1D diffusion in a non-cartesian coordinate system. This will % test the non-unit mass martix inversion within the LDG method. % -% p^2 * df/dt == -d/dp(p^2 * df/dp) +% df/dt == -1/p^2 d/dp(p^2 * df/dp) % % Run with % @@ -13,7 +13,7 @@ %% Define the dimensions dim_x = DIMENSION(0,1); -dim_x.jacobian = @(x,p,t,d) x.^2; +dim_x.moment_dV = @(x,p,t,d) x.^2; dimensions = {dim_x}; num_dims = numel(dimensions); @@ -26,12 +26,7 @@ initial_conditions = {soln1}; %% Define the LHS terms (the d/dt) - -gL = @(x,p,t,dat) x.^2; -ptermL = MASS(gL); -termL_p = SD_TERM({ptermL}); -termL = MD_TERM(num_dims,{termL_p}); -LHSterms = {termL}; +LHSterms = {}; %% Define the RHS terms (everything except d/dt) @@ -42,11 +37,12 @@ % % coeff_mat = mat1 * mat2 -g1 = @(x,p,t,dat) -x.^2; -g2 = @(x,p,t,dat) x.*0+1; +dV = @(x,p,t,dat) x.^2; + +g1 = @(x,p,t,dat) x.*0+1; -pterm1 = GRAD(num_dims,g1,+1,'D','N'); -pterm2 = GRAD(num_dims,g2,-1,'N','D'); +pterm1 = DIV(num_dims,g1,'',+1,'N','N','','','',dV); +pterm2 = GRAD(num_dims,g1,'',-1,'D','D',soln1,soln1,'',dV); term1_x = SD_TERM({pterm1,pterm2}); term1 = MD_TERM(num_dims,{term1_x}); @@ -61,7 +57,7 @@ %% Define sources -s1x = @(x,p,t) exp(-x.^2).*(-6+4.*x.^2).*x.^2.*x.^2; % note the extra x^2 here is the jacobian +s1x = @(x,p,t) -exp(-x.^2).*(-6+4.*x.^2); % note the extra x^2 here is the jacobian s1t = @(t,p) t.*0+1; source1 = {s1x, s1t}; diff --git a/pdes/diffusion2.m b/pdes/diffusion2.m index 11699e0a..ba3c512f 100644 --- a/pdes/diffusion2.m +++ b/pdes/diffusion2.m @@ -30,8 +30,10 @@ %% Define the dimensions -dim_y = DIMENSION(0,1); dim_x = DIMENSION(0,1); +dim_x.moment_dV = @(x,p,t,dat) 0*x+1; +dim_y = DIMENSION(0,1); +dim_y.moment_dV = @(x,p,t,dat) 0*x+1; dimensions = {dim_x,dim_y}; num_dims = numel(dimensions); @@ -57,6 +59,8 @@ % % Here we have 1 term, with each term having nDims (x and y) operators. +dV = @(x,p,t,dat) 0*x+1; + %% % Setup the d^2_dx^2 term @@ -70,11 +74,14 @@ g1 = @(x,p,t,dat) x.*0+1; g2 = @(x,p,t,dat) x.*0+1; -pterm1 = GRAD(num_dims,g1,+1,'N','N'); -pterm2 = GRAD(num_dims,g2,-1,'D','D',BCL,BCR); - +pterm1 = DIV(num_dims,g1,'',+1,'N','N','','','',dV); +pterm2 = GRAD(num_dims,g2,'',-1,'D','D',BCL,BCR,'',dV); term1_x = SD_TERM({pterm1,pterm2}); -term1 = MD_TERM(num_dims,{term1_x,[]}); + +pterm1 = MASS(g1); +term1_y = SD_TERM({pterm1,pterm1}); + +term1 = MD_TERM(num_dims,{term1_x,term1_y}); %% % Setup the d^2_dy^2 term @@ -89,11 +96,14 @@ g1 = @(y,p,t,dat) y.*0+1; g2 = @(y,p,t,dat) y.*0+1; -pterm1 = GRAD(num_dims,g1,+1,'N','N'); -pterm2 = GRAD(num_dims,g2,-1,'D','D',BCL,BCR); +pterm1 = MASS(g1); +term2_x = SD_TERM({pterm1,pterm1}); +pterm1 = DIV(num_dims,g1,'',+1,'N','N','','','',dV); +pterm2 = GRAD(num_dims,g2,'',-1,'D','D',BCL,BCR,'',dV); term2_y = SD_TERM({pterm1,pterm2}); -term2 = MD_TERM(num_dims,{[],term2_y}); + +term2 = MD_TERM(num_dims,{term2_x,term2_y}); terms = {term1, term2}; diff --git a/pdes/diffusion2_mixed.m b/pdes/diffusion2_mixed.m new file mode 100644 index 00000000..66428fda --- /dev/null +++ b/pdes/diffusion2_mixed.m @@ -0,0 +1,320 @@ +function pde = diffusion2_mixed(opts) +% Example PDE using the 2D diffusion with anisotropic diffusion tensor. +% This example PDE is +% time dependent (although not all the terms are time dependent). This +% implies the need for an initial condition. +% PDE: +% +% df/dt = div(B*B'\grad f) +% +% where +% +% D = [2 1;1 2]; +% +% D = B*B' where B = sqrt(2)/2*[-1 sqrt(3);1 sqrt(3)]; +% +% Domain is [0,1]x[0,1] +% Dirichlet boundary condition +% +% Diffusion terms are dealt with via LDG, i.e., splitting into two first +% order equations: +% +% div(B*B'\grad f) +% +% df/dt = div(B*q) with free boundary BC +% +% and +% +% q=B'\grad f with Dirichlet BCs specified by analytic solution. +% +% Note the choice of mixed variable will perserve a symmetric positive semi +% definite stiffness matrix. +% +% Run with +% +% implicit +% asgard(@diffusion2_mixed,'timestep_method','BE','dt',0.001,'num_steps',20) + +%% Define the dimensions + +dim_y = DIMENSION(0,1); +dim_x = DIMENSION(0,1); +dim_x.moment_dV = @(x,p,t,d) 0.*x+1; +dim_y.moment_dV = @(x,p,t,d) 0.*x+1; +dimensions = {dim_x,dim_y}; +num_dims = numel(dimensions); + +B = sqrt(2)/2*[-1 sqrt(3);1 sqrt(3)]; +%B = eye(2); + +%% Define the analytic solution (optional). + +soln_x = @(x,p,t) sin(pi*x); +soln_y = @(y,p,t) sin(pi*y); +soln_t = @(t,p) cos(t); +soln1 = new_md_func(num_dims,{soln_x,soln_y,soln_t}); + +solutions = {soln1}; + +%% Define the boundary conditions + +BCL = soln1; +BCR = soln1; + +%% Initial conditions + +initial_conditions = {soln1}; + +%% Define the terms of the PDE +% +% Here we have 1 term, with each term having nDims (x and y) operators. + +%Surface jacobian matches volume jacobian +dV = @(x,p,t,dat) 0*x+1; + +%Set local LF values for +LF_DIV = 0; +LF_GRD = 0; + +%% term1 + +g1 = @(x,p,t,dat) x.*0+B(1,1); +g2 = @(x,p,t,dat) x.*0+B(1,1); + +pterm1 = DIV(num_dims,g1,'',LF_DIV,'N','N','','','',dV); +pterm2 = GRAD(num_dims,g2,'',LF_GRD,'D','D',BCL,BCR,'',dV); +term_x = SD_TERM({pterm1,pterm2}); + +g1 = @(x,p,t,dat) x.*0+1; +g2 = @(x,p,t,dat) x.*0+1; + +pterm1 = MASS(g1,[],[],dV); +pterm2 = MASS(g2,[],[],dV); +term_y = SD_TERM({pterm1,pterm2}); + +term1 = MD_TERM(num_dims,{term_x,term_y}); + +%% term2 + +g1 = @(x,p,t,dat) x.*0+B(1,1); +g2 = @(x,p,t,dat) x.*0+1; + +pterm1 = DIV(num_dims,g1,'',LF_DIV,'N','N','','','',dV); +pterm2 = MASS(g2,[],[],dV); +term_x = SD_TERM({pterm1,pterm2}); + +g1 = @(x,p,t,dat) x.*0+1; +g2 = @(x,p,t,dat) x.*0+B(1,2); + +pterm1 = MASS(g1,[],[],dV); +pterm2 = GRAD(num_dims,g2,'',LF_GRD,'D','D',BCL,BCR,'',dV); +term_y = SD_TERM({pterm1,pterm2}); + +term2 = MD_TERM(num_dims,{term_x,term_y}); + +%% term3 + +g1 = @(x,p,t,dat) x.*0+1; +g2 = @(x,p,t,dat) x.*0+B(1,1); + +pterm1 = MASS(g1,[],[],dV); +pterm2 = GRAD(num_dims,g2,'',LF_DIV,'D','D',BCL,BCR,'',dV); +term_x = SD_TERM({pterm1,pterm2}); + +g1 = @(x,p,t,dat) x.*0+B(1,2); +g2 = @(x,p,t,dat) x.*0+1; + +pterm1 = DIV(num_dims,g1,'',LF_GRD,'N','N','','','',dV); +pterm2 = MASS(g2,[],[],dV); +term_y = SD_TERM({pterm1,pterm2}); + +term3 = MD_TERM(num_dims,{term_x,term_y}); + +%% term4 + +g1 = @(x,p,t,dat) x.*0+1; +g2 = @(x,p,t,dat) x.*0+1; + +pterm1 = MASS(g1,[],[],dV); +pterm2 = MASS(g2,[],[],dV); +term_x = SD_TERM({pterm1,pterm2}); + +g1 = @(x,p,t,dat) x.*0+B(1,2); +g2 = @(x,p,t,dat) x.*0+B(1,2); + +pterm1 = DIV(num_dims,g1,'',LF_DIV,'N','N','','','',dV); +pterm2 = GRAD(num_dims,g2,'',LF_GRD,'D','D',BCL,BCR,'',dV); +term_y = SD_TERM({pterm1,pterm2}); + +term4 = MD_TERM(num_dims,{term_x,term_y}); + +%% term5 + +g1 = @(x,p,t,dat) x.*0+B(2,1); +g2 = @(x,p,t,dat) x.*0+B(2,1); + +pterm1 = DIV(num_dims,g1,'',LF_DIV,'N','N','','','',dV); +pterm2 = GRAD(num_dims,g2,'',LF_GRD,'D','D',BCL,BCR,'',dV); +term_x = SD_TERM({pterm1,pterm2}); + +g1 = @(x,p,t,dat) x.*0+1; +g2 = @(x,p,t,dat) x.*0+1; + +pterm1 = MASS(g1,[],[],dV); +pterm2 = MASS(g2,[],[],dV); +term_y = SD_TERM({pterm1,pterm2}); + +term5 = MD_TERM(num_dims,{term_x,term_y}); + +%% term6 + +g1 = @(x,p,t,dat) x.*0+B(2,1); +g2 = @(x,p,t,dat) x.*0+1; + +pterm1 = DIV(num_dims,g1,'',LF_DIV,'N','N','','','',dV); +pterm2 = MASS(g2,[],[],dV); +term_x = SD_TERM({pterm1,pterm2}); + +g1 = @(x,p,t,dat) x.*0+1; +g2 = @(x,p,t,dat) x.*0+B(2,2); + +pterm1 = MASS(g1,[],[],dV); +pterm2 = GRAD(num_dims,g2,'',LF_GRD,'D','D',BCL,BCR,'',dV); +term_y = SD_TERM({pterm1,pterm2}); + +term6 = MD_TERM(num_dims,{term_x,term_y}); + +%% term7 + +g1 = @(x,p,t,dat) x.*0+1; +g2 = @(x,p,t,dat) x.*0+B(2,1); + +pterm1 = MASS(g1,[],[],dV); +pterm2 = GRAD(num_dims,g2,'',LF_GRD,'D','D',BCL,BCR,'',dV); +term_x = SD_TERM({pterm1,pterm2}); + +g1 = @(x,p,t,dat) x.*0+B(2,2); +g2 = @(x,p,t,dat) x.*0+1; + +pterm1 = DIV(num_dims,g1,'',LF_DIV,'N','N','','','',dV); +pterm2 = MASS(g2,[],[],dV); +term_y = SD_TERM({pterm1,pterm2}); + +term7 = MD_TERM(num_dims,{term_x,term_y}); + +%% term8 + +g1 = @(x,p,t,dat) x.*0+1; +g2 = @(x,p,t,dat) x.*0+1; + +pterm1 = MASS(g1,[],[],dV); +pterm2 = MASS(g2,[],[],dV); +term_x = SD_TERM({pterm1,pterm2}); + +g1 = @(x,p,t,dat) x.*0+B(2,2); +g2 = @(x,p,t,dat) x.*0+B(2,2); + +pterm1 = DIV(num_dims,g1,'',LF_DIV,'N','N','','','',dV); +pterm2 = GRAD(num_dims,g2,'',LF_GRD,'D','D',BCL,BCR,'',dV); +term_y = SD_TERM({pterm1,pterm2}); + +term8 = MD_TERM(num_dims,{term_x,term_y}); + +%% Penalty terms + +%% term9 + +g1 = @(x,p,t,dat) x.*0+1; +pterm1 = DIV(num_dims,g1,'',-1,'N','N','','','',dV); +term_x = SD_TERM({pterm1}); + +g1 = @(x,p,t,dat) x.*0+1; +pterm1 = MASS(g1,[],[],dV); +term_y = SD_TERM({pterm1}); + +term9 = MD_TERM(num_dims,{term_x,term_y}); + +%% term10 + +g1 = @(x,p,t,dat) x.*0-1; +pterm1 = DIV(num_dims,g1,'',0,'D','D','','','',dV); +term_x = SD_TERM({pterm1}); + +g1 = @(x,p,t,dat) x.*0+1; +pterm1 = MASS(g1,[],[],dV); +term_y = SD_TERM({pterm1}); + +term10 = MD_TERM(num_dims,{term_x,term_y}); + +%% term11 + +g1 = @(x,p,t,dat) x.*0+1; +pterm1 = MASS(g1,[],[],dV); +term_x = SD_TERM({pterm1}); + +g1 = @(x,p,t,dat) x.*0+1; +pterm1 = DIV(num_dims,g1,'',-1,'N','N','','','',dV); +term_y = SD_TERM({pterm1}); + +term11 = MD_TERM(num_dims,{term_x,term_y}); + +%% term12 + +g1 = @(x,p,t,dat) x.*0+1; +pterm1 = MASS(g1,[],[],dV); +term_x = SD_TERM({pterm1}); + +g1 = @(x,p,t,dat) x.*0-1; +pterm1 = DIV(num_dims,g1,'',0,'D','D','','','',dV); +term_y = SD_TERM({pterm1}); + +term12 = MD_TERM(num_dims,{term_x,term_y}); + +%%%Without penalty +terms = {term1, term2, term3, term4, term5, term6, term7, term8}; + +%%%With penalty +%terms = {term1, term2, term3, term4, term5, term6, term7, term8, ... +% term9, term10, term11, term12}; + +%% Define some parameters and add to pde object. +% These might be used within the various functions below. + +params.parameter1 = 0; +params.parameter2 = 1; + +%% Define sources + +sc_x = @(x,p,t,d) sin(pi*x); +sc_y = @(x,p,t,d) sin(pi*x); +sc_t = @(t,p) -sin(t); +s1 = new_md_func(num_dims,{sc_x,sc_y,sc_t}); + +sc_x = @(x,p,t,d) sin(pi*x); +sc_y = @(x,p,t,d) sin(pi*x); +sc_t = @(t,p) 4*pi^2*cos(t); +s2 = new_md_func(num_dims,{sc_x,sc_y,sc_t}); + +sc_x = @(x,p,t,d) cos(pi*x); +sc_y = @(x,p,t,d) cos(pi*x); +sc_t = @(t,p) -2*pi^2*cos(t); +s3 = new_md_func(num_dims,{sc_x,sc_y,sc_t}); + +sources = {s1,s2,s3}; + +%% Define a function to set dt + + function dt=set_dt(pde,CFL) + dims = pde.dimensions; + % for Diffusion equation: dt = C * dx^2 + lev = dims{1}.lev; + dx = 1/2^lev; + dt = CFL*dx^2; + end + +%% Construct PDE + +pde = PDE(opts,dimensions,terms,[],sources,params,@set_dt,[],initial_conditions,solutions); + +end + diff --git a/pdes/diffusion2_spherical.m b/pdes/diffusion2_spherical.m new file mode 100644 index 00000000..1e7d878f --- /dev/null +++ b/pdes/diffusion2_spherical.m @@ -0,0 +1,182 @@ +function pde = diffusion2_spherical(opts) + +% Test 2D LDG diffusion in spherical coordinates +% +% df/dt == div(grad f) in spherical cordinates +% +% (p,th) is a spherical coordinate (p,th,ph), so the div and grad look like +% +% div[A] = 1/p^2 * d/dp * p^2[A_p] + 1/(p*sin(th)) d/dth(sin(th) A_th +% +% where A = A_p \hat{p} + A_th \hat{th} +% +% grad[f] = df/dp \hat{p} + 1/r df/dth \hat{th} +% +% and the volument_element dV = p^2*sin(th) +% +% Run with +% +% asgard(@diffusion2_spherical,'timestep_method','BE','lev',3,'deg',4,'num_steps',50,'CFL',1.5) +% +% or +% +% asgard(@diffusion2_spherical,'timestep_method','matrix_exponential','lev',2,'deg',4,'grid_type','SG','num_steps',1,'dt',3) +% +% Analytic solution: f(r,th,t) = exp(-t)*(sin(r)/r^2-cos(r)/r)*cos(th) +% using approprite Dirichlet or Neumann BCs + +%% Define some parameters and add to pde object. + +params.parameter1 = 0; + +%% Define the dimensions +dV_p = @(x,p,t,d) x.^2; +%dim_p = DIMENSION(0,4.49340945790906); %Gives zero dirichlet BCs +dim_p = DIMENSION(0,pi); +dim_p.moment_dV = dV_p; +dim_th = DIMENSION(0,pi); +dim_th.moment_dV = @(x,p,t,d) sin(x); +dimensions = {dim_p,dim_th}; +num_dims = numel(dimensions); + +%% Define the analytic solution (optional). + +soln1 = new_md_func(num_dims,{@(x,p,t) soln_p(x,p,t),... + @(x,p,t) soln_th(x,p,t),... + @(t,p) exp(-t) }); + +% Just f(p,th,t) = 1 used in Neumann Case +func_one = new_md_func(num_dims,{@(x,p,t) 0*x+1,... + @(x,p,t) 0*x+1,... + @(t,p) 0*t+1}); + +% Dirichlet +solutions = {soln1}; + +% Neumann +%solutions = {soln1,func_one}; + +% Define derivatives of analytic solution for Neumann BCs +dsoln_dp = new_md_func(num_dims,{@(x,p,t) dsoln_p(x,p,t),... + @(x,p,t) soln_th(x,p,t),... + @(t,p) exp(-t)}); + +dsoln_dth = new_md_func(num_dims,{@(x,p,t) soln_p(x,p,t)./x,... + @(x,p,t) -sin(x),... + @(t,p) exp(-t)}); %df/dth*1/v = grad f\cdot n + +%% Define initial conditions + +initial_conditions = solutions; + +%% LHS terms (mass only) + +LHS_terms = {}; + +%% RHS terms + +% term1 is done using SLDG in p with mass in th +% +% Dirichlet +% eq1 : df/dt == div(q) [pterm1: div (g1(p)=1,+1, BCL=N, BCR=N)] +% eq2 : q == grad(f) [pterm2: grad(g2(p)=1,-1, BCL=D, BCR=D)] +% +% Neumann +% eq1 : df/dt == div(q) [pterm1: div (g1(p)=1,+1, BCL=D, BCR=D)] +% eq2 : q == grad(f) [pterm2: grad(g2(p)=1,-1, BCL=N, BCR=N)] +% + +% Define gfuncs and surface jacobian: r^2*sin(th) +g1 = @(x,p,t,dat) 0*x+1; +dV_p = @(x,p,t,d) x.^2; +dV_th = @(x,p,t,d) sin(x); + +% Dirichlet +pterm1 = DIV(num_dims,g1,'',-1,'N','N','','','',dV_p); +pterm2 = GRAD(num_dims,g1,'',+1,'D','D',soln1,soln1,'',dV_p); + +% Neumann +%pterm1 = DIV(num_dims,g1,'',+1,'D','D',dsoln_dp,dsoln_dp,'',dV_p); +%pterm2 = GRAD(num_dims,g1,'',-1,'N','N','','','',dV_p); + +term1_p = SD_TERM({pterm1,pterm2}); % order here is as in equation + +pterm1 = MASS(g1,[],[],dV_th); +term1_th = SD_TERM({pterm1,pterm1}); +term1 = MD_TERM(num_dims,{term1_p,term1_th}); + +% term2 is done using mass in p with SLDG in th. +% +% Dirichlet +% eq1 : df/dt == div(q) [pterm1: div (g1(p)=1,+1, BCL=N, BCR=N)] +% eq2 : q == grad(f) [pterm2: grad(g2(p)=1,-1, BCL=D, BCR=D)] +% +% Neumann +% eq1 : df/dt == div(q) [pterm1: div (g1(p)=1,+1, BCL=D, BCR=D)] +% eq2 : q == grad(f) [pterm2: grad(g2(p)=1,-1, BCL=N, BCR=N)] +% + +% Define gfuncs and surface jacobian: r*sin(th) +g1 = @(x,p,t,dat) 0*x+1; +dV_p = @(x,p,t,d) x; +dV_th = @(x,p,t,d) sin(x); + +pterm1 = MASS(g1,[],[],dV_p); +term2_p = SD_TERM({pterm1,pterm1}); + +% Dirichlet +pterm1 = DIV(num_dims,g1,'',-1,'N','N','','','',dV_th); +pterm2 = GRAD(num_dims,g1,'',+1,'D','D',soln1,soln1,'',dV_th); + +% Neumann +%pterm1 = DIV(num_dims,g1,'',+1,'D','D',dsoln_dth,dsoln_dth,'',dV_th); +%pterm2 = GRAD(num_dims,g1,'',-1,'N','N','','','',dV_th); + +term2_th = SD_TERM({pterm1,pterm2}); +term2 = MD_TERM(num_dims,{term2_p,term2_th}); +terms = {term1,term2}; + +%% Define sources + +sources = {}; + +%% Define function to set time step + function dt=set_dt(pde,CFL) + dims = pde.dimensions; + xRange = dims{1}.max-dims{1}.min; + lev = dims{1}.lev; + dx = xRange/2^lev; + dt = CFL * dx; + end + +%% Construct PDE + +pde = PDE(opts,dimensions,terms,LHS_terms,sources,params,@set_dt,[],initial_conditions,solutions); + +end + +% p part of the solution (taylor expansion so there's no division by 0) +function z = soln_p(x,p,t) + if abs(x) < 1e-7 + z = x/3 - x.^3/30 + x.^5/840; %Taylor expansion truncation near 0 + else + z = sin(x)./(x.^2) - cos(x)./x; + end +end + +% th part of the solution +function z = soln_th(x,p,t) + z = cos(x); +end + + +%df/dp +function z = dsoln_p(x,p,t) + if abs(x) < 1e-7 + z = 1/3 - x.^2/10 + x.^4/168 - x.^6/6480; + else + z = ((x.^2-2).*sin(x) + 2.*x.*cos(x))./(x.^3); + end +end + + diff --git a/pdes/fokkerplanck1_momentum_C.m b/pdes/fokkerplanck1_momentum_C.m index c17a2dee..e14f1959 100644 --- a/pdes/fokkerplanck1_momentum_C.m +++ b/pdes/fokkerplanck1_momentum_C.m @@ -2,30 +2,36 @@ % Test the momentum dynamics for the RE problem for E = R = 0 % -% df/dt == 1/x^2 * d/dx * x^2 ( psi(x)/x * df/dx + 2*psi(x)*f ) -% == 1/x^2 * d/dx*x^2*psi(x)/x*df/dx + 1/x^2 * d/dx*x^2*2*psi(x)*f +% df/dt == 1/p^2*d/dp*p^2 ( psi(p)/p*df/dp + 2*psi(p)*f ) +% == 1/p^2*d/dp*p^2 * (psi(p)/p*df/dp) + 1/p^2*d/dp*p^2 * (2*psi(p)*f) % \ / \ / % --------- term1 -------------- -------- term2 ---------- -% split into % -% term1 +% p is a spherical coordinate (p,th,ph), so the div and grad look like % -% eq1 : df/dt == g(x) q(x) [mass,g(x)=1/x^2, BC N/A for mass] -% eq2 : q(x) == d/dx g(x) p(x) [grad,g(x)=x^2*psi(x)/x, BCL=D, BCR=N] -% eq3 : p(x) == d/dx f(x) [grad,g(x)=1, BCL=N, BCR=D] +% div[] = 1/p^2 * d/dp * p^2[], grad[] = d/dp[] % -% coeff_mat = mat1 * mat2 * mat3 +% and the volument_element dV = p^2 % -% term2 +% +% split into two div(flux) terms (term1 and term2) % -% eq1 : df/dt == g(x) q(x) [mass,g(x)=1/x^2, BC N/A for mass] -% eq2 : q(x) == d/dx g(x) f(x) [grad,g(x)=x^2*2*psi(x), BCL=N, BCR=D] +% term1 is done using SLDG defining eta1(p)=sqrt(psi(p)/p) % -% coeff_mat = mat1 * mat2 +% eq1 : df/dt == div(eta(p) * q) [pterm1: div (g(p)=eta(p),+1, BCL=?, BCR=?)] +% eq2 : q == eta(p) * grad(f) [pterm2: grad(g(p)=eta(p),-1, BCL=D, BCR=N)] +% +% coeff_mat = pterm1.mat * pterm2.mat +% +% term2 is just a div +% +% eq1 : df/dt == div(2*psi(p) * f) [pterm1: div(g(p)=2*psi(p),+1, BCL=?, BCR=?] +% +% coeff_mat = pterm1.mat1 % % Run with % -% asgard(@fokkerplanck1_momentum_C,'timestep_method','CN','lev',3,'deg',4,'num_steps',50,'CFL',1.5,'case',1) +% asgard(@fokkerplanck1_momentum_C,'timestep_method','BE','lev',3,'deg',4,'num_steps',50,'dt',1.0,'case',1) % % case = 1 % maxwellian initial condition % case = 2 % step function initial condition @@ -74,77 +80,63 @@ ret = 4/sqrt(pi) * exp(-x.^2); end +%% Define some parameters and add to pde object. + +params.parameter1 = 0; + %% Define the dimensions -dim_x = DIMENSION(0,+10); -dim_x.jacobian = @(x,p,t,dat) x.^2; -dimensions = {dim_x}; +dV_p = @(x,p,t,d) x.^2; +dim_p = DIMENSION(0,+10); +dim_p.moment_dV = dV_p; +dimensions = {dim_p}; num_dims = numel(dimensions); %% Define the analytic solution (optional). -soln_z = @(z,p,t) soln(z); -soln1 = new_md_func(num_dims,{soln_z}); +soln_p = @(x,p,t) soln(x); +soln1 = new_md_func(num_dims,{soln_p}); solutions = {soln1}; %% Define initial conditions -ic_x = @(z,p,t) f0(z); -ic1 = new_md_func(num_dims,{ic_x}); -initial_conditions = {ic1}; - -%% Setup the terms of the PDE +ic_p = @(z,p,t) f0(z); +ic1 = new_md_func(num_dims,{ic_p}); +initial_conditions = {soln1}; -% LHS terms (mass matrix) +%% LHS terms (mass only) -gL = @(x,p,t,dat) x.^2; -ptermL = MASS(gL); -LHS_term_x = SD_TERM({ptermL}); -LHS_term = MD_TERM(num_dims,{LHS_term_x}); -LHS_terms = {LHS_term}; +LHS_terms = {}; -% RHS terms +%% RHS terms -% term1 +% term1 is done using SLDG defining eta(p)=sqrt(psi(p)/p) % -% p^2*df/dt == d/dp(p*psi*df/dp) -% -% (1) : gL*df/dt == d/dp(g1*w) [grad,g2=p*psi, BCL=D, BCR=N] -% (2) : w == d/dp(g2*f) [grad,g3=1, BCL=N, BCR=D] -% -% coeff_mat = mat1 * mat2 +% eq1 : df/dt == div(eta(p) * q) [pterm1: div (g1(p)=eta(p),+1, BCL=D, BCR=N)] +% eq2 : q == eta(p) * grad(f) [pterm2: grad(g2(p)=eta(p),-1, BCL=N, BCR=D)] -g1 = @(x,p,t,dat) x_psi(x); -g2 = @(x,p,t,dat) x.*0+1; +eta = @(p) sqrt(psi(p)./p); +g1 = @(x,p,t,dat) eta(x); +g2 = @(x,p,t,dat) eta(x); -pterm1 = GRAD(num_dims,g1,+1,'D','N'); -pterm2 = GRAD(num_dims,g2,-1,'N','D'); +pterm1 = DIV (num_dims,g1,'',+1,'D','N','','','',dV_p); +pterm2 = GRAD(num_dims,g2,'',-1,'N','D','','','',dV_p); -term1_x = SD_TERM({pterm1,pterm2}); % order here is as in equation -term1 = MD_TERM(num_dims,{term1_x}); +term1_p = SD_TERM({pterm1,pterm2}); % order here is as in equation +term1 = MD_TERM(num_dims,{term1_p}); -% term2 -% -% p^2*df/dt == d/dp(p^2*2*psi*f) -% -% (3) : gL*df/dt == d/dp(g3*f) [grad,g3=p^2*2*psi, BCL=N, BCR=D] +% term2 is just a div % -% coeff_mat = mat1 * mat2 +% eq1 : df/dt == div(2*psi(p) * f) [pterm1: div(g3(p)=2*psi(p),+1, BCL=N, BCR=D] -g3 = @(x,p,t,dat) 2.*x.*x_psi(x); +g3 = @(x,p,t,dat) 2 .* psi(x); -pterm3 = GRAD(num_dims,g3,-1,'N','D'); +pterm3 = DIV(num_dims,g3,'',-1,'N','D','','','',dV_p); -term2_x = SD_TERM({pterm3}); -term2 = MD_TERM(num_dims,{term2_x}); +term2_p = SD_TERM({pterm3}); +term2 = MD_TERM(num_dims,{term2_p}); -terms = {term1};%,term2}; - -%% Define some parameters and add to pde object. -% These might be used within the various functions below. - -params.parameter1 = 0; -params.parameter2 = 1; +terms = {term1,term2}; %% Define sources diff --git a/pdes/fokkerplanck1_momentum_C_LHS.m b/pdes/fokkerplanck1_momentum_C_LHS.m deleted file mode 100644 index 1446ff51..00000000 --- a/pdes/fokkerplanck1_momentum_C_LHS.m +++ /dev/null @@ -1,137 +0,0 @@ -function pde = fokkerplanck1_momentum_C_LHS(opts) -% Test the momentum dynamics for the RE problem for E = R = 0 -% -% x^2 * df/dt == d/dx * x^2 ( psi(x)/x * df/dx + 2*psi(x)*f ) -% == d/dx*x^2*psi(x)/x*df/dx + d/dx*x^2*2*psi(x)*f -% -% (note the x^2 moved to the left side) -% -% -% Run with -% -% asgard(@fokkerplanck1_momentum_C_LHS,'timestep_method','BE','lev',4,'deg',4,'num_steps',50,'CFL',1.5,'case',1) - - function ret = psi(x,t) - - phi = erf(x); - dphi_dx = 2./sqrt(pi) * exp(-x.^2); - - ret = 1./(2*x.^2) .* (phi - x.*dphi_dx); - end - - function ret = f0(x) - - test = opts.case_; - - ret = zeros(size(x)); - switch test - case 1 - a = 2; - ret = 4.0/(sqrt(pi)*a^3) * exp(-x.^2/a^2); - case 2 - for i=1:numel(x) - if x(i) <= 5 - ret(i) = 3/5^3; - else - ret(i) = 0; - end - end - - end - end - - function ret = x_psi(x) % manage the singularity at x=0 - ret = zeros(size(x)); - for i=1:numel(x) - if abs(x(i))<1e-5 - ret(i) = x(i).*0; - else - ret(i) = x(i).*psi(x(i)); - end - end - end - - function ret = soln(x) - ret = 4/sqrt(pi) * exp(-x.^2); - end - -%% Define the dimensions - -dim_x = DIMENSION(0,+10); -dimensions = {dim_x}; -num_dims = numel(dimensions); - -%% Define the initial conditions - -ic_x = @(z,p,t) f0(z); -ic1 = new_md_func(num_dims,{ic_x}); -initial_conditions = {ic1}; - -%% Define the terms of the PDE - -% x^2 * df/dt (LHS non-identity coeff requires special treatment) - -g1 = @(x,p,t,dat) x.^2; -pterm1 = MASS(g1); - -LHS_term_x = SD_TERM({pterm1}); -LHS_term = MD_TERM(num_dims,{LHS_term_x}); - -LHS_terms = {LHS_term}; - -%% -% d/dx*x^2*psi(x)/x*df/dx, split as two first order as -% -% df/dt == d/dx g1(x) q(x) [grad,g1(x)=x^2*psi(x)/x, BCL=D, BCR=N] -% q(x) == d/dx g2(x) f(x) [grad,g2(x)=1, BCL=N, BCR=D] - -g1 = @(x,p,t,dat) x_psi(x); -g2 = @(x,p,t,dat) x.*0+1; -pterm1 = GRAD(num_dims,g1,-1,'D','N'); -pterm2 = GRAD(num_dims,g2,+1,'N','D'); -term1_x = SD_TERM({pterm1,pterm2}); -term1 = MD_TERM(num_dims,{term1_x}); - -%% -% d/dx*x^2*2*psi(x)*f - -g1 = @(x,p,t,dat) x*2.*x_psi(x); -pterm1 = GRAD(num_dims,g1,-1,'N','D'); -term2_x = SD_TERM({pterm1}); -term2 = MD_TERM(num_dims,{term2_x}); - -terms = {term1,term2}; - -%% Define some parameters and add to pde object. -% These might be used within the various functions below. - -params.parameter1 = 0; -params.parameter2 = 1; - - -%% Define sources - -sources = {}; - -%% Define the analytic solution (optional). - -soln_x = @(x,p,t) soln(x); -soln1 = new_md_func(num_dims,{soln_x}); -solutions = {soln1}; - -%% Define function to set time step - function dt=set_dt(pde,CFL) - dims = pde.dimensions; - xRange = dims{1}.max-dims{1}.min; - lev = dims{1}.lev; - dx = xRange/2^lev; - dt = CFL * dx; - end - -%% Construct PDE - -pde = PDE(opts,dimensions,terms,LHS_terms,sources,params,@set_dt,[],initial_conditions,solutions); - -end - - diff --git a/pdes/fokkerplanck1_momentum_C_div.m b/pdes/fokkerplanck1_momentum_C_div.m deleted file mode 100644 index 852b9287..00000000 --- a/pdes/fokkerplanck1_momentum_C_div.m +++ /dev/null @@ -1,160 +0,0 @@ -function pde = fokkerplanck1_momentum_C_div(opts) - -% Test the momentum dynamics for the RE problem for E = R = 0 -% -% df/dt == 1/p^2*d/dp*p^2 ( psi(p)/p*df/dp + 2*psi(p)*f ) -% == 1/p^2*d/dp*p^2 * (psi(p)/p*df/dp) + 1/p^2*d/dp*p^2 * (2*psi(p)*f) -% \ / \ / -% --------- term1 -------------- -------- term2 ---------- -% -% p is a spherical coordinate (p,th,ph), so the div and grad look like -% -% div[] = 1/p^2 * d/dp * p^2[], grad[] = d/dp[] -% -% and the volument_element dV = p^2 -% -% -% split into two div(flux) terms (term1 and term2) -% -% term1 is done using SLDG defining eta1(p)=sqrt(psi(p)/p) -% -% eq1 : df/dt == div(eta(p) * q) [pterm1: div (g(p)=eta(p),+1, BCL=?, BCR=?)] -% eq2 : q == eta(p) * grad(f) [pterm2: grad(g(p)=eta(p),-1, BCL=D, BCR=N)] -% -% coeff_mat = pterm1.mat * pterm2.mat -% -% term2 is just a div -% -% eq1 : df/dt == div(2*psi(p) * f) [pterm1: div(g(p)=2*psi(p),+1, BCL=?, BCR=?] -% -% coeff_mat = pterm1.mat1 -% -% Run with -% -% asgard(@fokkerplanck1_momentum_C_div,'timestep_method','BE','lev',3,'deg',4,'num_steps',50,'CFL',1.5,'case',1) -% -% case = 1 % maxwellian initial condition -% case = 2 % step function initial condition - - function ret = psi(x,t) - - phi = erf(x); - dphi_dx = 2./sqrt(pi) * exp(-x.^2); - - ret = 1./(2*x.^2) .* (phi - x.*dphi_dx); - end - - function ret = f0(x) - - test = opts.case_; - - ret = zeros(size(x)); - switch test - case 1 - a = 2; - ret = 4.0/(sqrt(pi)*a^3) * exp(-x.^2/a^2); - case 2 - for i=1:numel(x) - if x(i) <= 5 - ret(i) = 3/5^3; - else - ret(i) = 0; - end - end - - end - end - - function ret = x_psi(x) % manage the singularity at x=0 - ret = zeros(size(x)); - for i=1:numel(x) - if abs(x(i))<1e-5 - ret(i) = x(i).*0; - else - ret(i) = x(i).*psi(x(i)); - end - end - end - - function ret = soln(x) - ret = 4/sqrt(pi) * exp(-x.^2); - end - -%% Define some parameters and add to pde object. - -params.parameter1 = 0; - -%% Define the dimensions - -dV_p = @(x,p,t,d) x.^2; -dim_p = DIMENSION(0,+10); -dim_p.moment_dV = dV_p; -dimensions = {dim_p}; -num_dims = numel(dimensions); - -%% Define the analytic solution (optional). - -soln_p = @(x,p,t) soln(x); -soln1 = new_md_func(num_dims,{soln_p}); -solutions = {soln1}; - -%% Define initial conditions - -ic_p = @(z,p,t) f0(z); -ic1 = new_md_func(num_dims,{ic_p}); -initial_conditions = {ic1}; - -%% LHS terms (mass only) - -LHS_terms = {}; - -%% RHS terms - -% term1 is done using SLDG defining eta(p)=sqrt(psi(p)/p) -% -% eq1 : df/dt == div(eta(p) * q) [pterm1: div (g1(p)=eta(p),+1, BCL=D, BCR=N)] -% eq2 : q == eta(p) * grad(f) [pterm2: grad(g2(p)=eta(p),-1, BCL=N, BCR=D)] - -eta = @(p) sqrt(psi(p)./p); -g1 = @(x,p,t,dat) eta(x); -g2 = @(x,p,t,dat) eta(x); - -pterm1 = DIV (num_dims,g1,'',+1,'D','N','','','',dV_p); -pterm2 = GRAD(num_dims,g2,'',-1,'N','D','','','',dV_p); - -term1_p = SD_TERM({pterm1,pterm2}); % order here is as in equation -term1 = MD_TERM(num_dims,{term1_p}); - -% term2 is just a div -% -% eq1 : df/dt == div(2*psi(p) * f) [pterm1: div(g3(p)=2*psi(p),+1, BCL=N, BCR=D] - -g3 = @(x,p,t,dat) 2 .* psi(x); - -pterm3 = DIV(num_dims,g3,'',-1,'N','D','','','',dV_p); - -term2_p = SD_TERM({pterm3}); -term2 = MD_TERM(num_dims,{term2_p}); - -terms = {term1,term2}; - -%% Define sources - -sources = {}; - -%% Define function to set time step - function dt=set_dt(pde,CFL) - dims = pde.dimensions; - xRange = dims{1}.max-dims{1}.min; - lev = dims{1}.lev; - dx = xRange/2^lev; - dt = CFL * dx; - end - -%% Construct PDE - -pde = PDE(opts,dimensions,terms,LHS_terms,sources,params,@set_dt,[],initial_conditions,solutions); - -end - - diff --git a/pdes/fokkerplanck1_momentum_E.m b/pdes/fokkerplanck1_momentum_E.m index ec641606..fae29547 100644 --- a/pdes/fokkerplanck1_momentum_E.m +++ b/pdes/fokkerplanck1_momentum_E.m @@ -10,35 +10,50 @@ % termE1 == -E*z*f(z) * 1/p^2 (d/dp p^2 f(p)) % termE2 == -E/p*f(p) * d/dz (1-z^2) f(z) % -% setting E=2 and z=0.5, and expanding the d/dz term, then setting d/dz=0, +% p is a spherical coordinate (p,th,ph), so the div and grad look like +% +% div[] = 1/p^2 * d/dp * p^2[], grad[] = d/dp[] +% +% and the volument_element dV = p^2 +% +% setting E=2 and z=0.5, and expanding the d/dz term via product rule, then setting d/dz=0, % we get for the momentum direction ... % -% termE1 = -1/p^2 d/dp p^2 f(p) + 2/p f(p) +% termE1 == -1/p^2 d/dp p^2 f(p) [pterm1: div(g(p)=-1,+1, BCL=?, BCR=?] +% termE2 == 2/p f(p) [pterm1: mass(g(p)=2/p] % % Run with % -% asgard(@fokkerplanck1_momentum_E,'timestep_method','matrix_exponential','dt',0.01,'num_steps',10,'case',2) +% asgard(@fokkerplanck1_momentum_E,'timestep_method','matrix_exponential','dt',0.1,'num_steps',10,'case',2,'lev',4,'deg',4,'calculate_mass',true) % % case = 1 % flat initial condition % case = 2 % maxwellian initial condition +% +% Notes: +% DLG - including the mass term gives rise to a system that does not +% conserve mass and I'm not sure why. Simply assuming d/dz==0 gives a +% systems without that mass term which does conserve mass so I'm using that +% for now (slightly different solution as noted below). params = fokkerplanck_parameters(opts); %% Setup the dimensions -dim_p = DIMENSION(0.0,+5); -dim_p.jacobian = @(x,p,t) x.^2; +dV_p = @(x,p,t,d) x.^2; +dim_p = DIMENSION(0,+10); +dim_p.moment_dV = dV_p; dimensions = {dim_p}; num_dims = numel(dimensions); %% Define the analytic solution (optional) -switch opts.case_ - case 1 - soln_p = @(x,p,t) x.*0 + 1; - case 2 - soln_p = @(x,p,t) exp(-(x-t).^2); -end + switch opts.case_ + case 1 + soln_p = @(x,p,t) x.*0 + 1; + case 2 +% soln_p = @(x,p,t) exp(-(x-4-t).^2); + soln_p = @(x,p,t) exp(-(x-4-t).^2) .*(x-t).^2 ./ x.^2; % solution to the mass conserving term2==0 system + end soln1 = new_md_func(num_dims,{soln_p}); solutions = {soln1}; @@ -57,29 +72,30 @@ %% Define the terms of the PDE -%% -div(flux_E) == termE1 + termE2 +%% -div(flux_E) == termE1 + +% termE1 == -1/p^2 (d/dp p^2 f(p)) [div, g1(p) = -1, BCL=D,BCR=N] -% termE1 == -1/p^2 (d/dp p^2 f(p)) -% == q(p) -% q(p) == g2(p) u(p) [mass, g2(p) = 1/p^2, BC N/A] -% u(p) == d/dp g3(p) f(p) [grad, g3(p) = p^2, BCL=N,BCR=D] +g1 = @(x,p,t,d) x.*0-1; +pterm1 = DIV (num_dims,g1,'',-1,'N','N',soln1,soln1,'',dV_p); -g2 = @(x,p,t,dat) -1./x.^2; -g3 = @(x,p,t,dat) x.^2; -pterm1 = MASS(g2); -pterm2 = GRAD(num_dims,g3,0,'D','D',soln1,soln1); -termE1_p = SD_TERM({pterm1,pterm2}); -termE1 = MD_TERM(num_dims,{termE1_p}); +termE1_p = SD_TERM({pterm1}); +termE1 = MD_TERM(num_dims,{termE1_p}); % termE2 == +2/p f % == g1(p) f(p) [mass, g1(p) = +2/p, BC N/A] -g1 = @(x,p,t,dat) +2./x; -pterm1 = MASS(g1); +g1 = @(x,p,t,d) +2./x; +pterm1 = MASS(g1,'','',dV_p); termE2_p = SD_TERM({pterm1}); -termE2= MD_TERM(num_dims,{termE2_p}); +termE2 = MD_TERM(num_dims,{termE2_p}); -terms = {termE1,termE2}; +switch opts.case_ + case 1 + terms = {termE1,termE2}; + case 2 + terms = {termE1}; +end %% Define sources diff --git a/pdes/fokkerplanck1_momentum_E_div.m b/pdes/fokkerplanck1_momentum_E_div.m deleted file mode 100644 index 642b767d..00000000 --- a/pdes/fokkerplanck1_momentum_E_div.m +++ /dev/null @@ -1,114 +0,0 @@ -function pde = fokkerplanck1_momentum_E_div(opts) -% Combining momentum and pitch angle dynamics for the E term -% -% d/dt f(p,z) == -div(flux_E) -% -% flux_E is the flux due to E accleration -% -% -div(flux_E) == termE1 + termE2 -% -% termE1 == -E*z*f(z) * 1/p^2 (d/dp p^2 f(p)) -% termE2 == -E/p*f(p) * d/dz (1-z^2) f(z) -% -% p is a spherical coordinate (p,th,ph), so the div and grad look like -% -% div[] = 1/p^2 * d/dp * p^2[], grad[] = d/dp[] -% -% and the volument_element dV = p^2 -% -% setting E=2 and z=0.5, and expanding the d/dz term via product rule, then setting d/dz=0, -% we get for the momentum direction ... -% -% termE1 == -1/p^2 d/dp p^2 f(p) [pterm1: div(g(p)=-1,+1, BCL=?, BCR=?] -% termE2 == 2/p f(p) [pterm1: mass(g(p)=2/p] -% -% Run with -% -% asgard(@fokkerplanck1_momentum_E_div,'timestep_method','matrix_exponential','dt',0.01,'num_steps',10,'case',2) -% -% case = 1 % flat initial condition -% case = 2 % maxwellian initial condition -% -% Notes: -% DLG - including the mass term gives rise to a system that does not -% conserve mass and I'm not sure why. Simply assuming d/dz==0 gives a -% systems without that mass term which does conserve mass so I'm using that -% for now (slightly different solution as noted below). - -params = fokkerplanck_parameters(opts); - -%% Setup the dimensions - -dV_p = @(x,p,t,d) x.^2; -dim_p = DIMENSION(0,+10); -dim_p.moment_dV = dV_p; -dimensions = {dim_p}; -num_dims = numel(dimensions); - -%% Define the analytic solution (optional) - - switch opts.case_ - case 1 - soln_p = @(x,p,t) x.*0 + 1; - case 2 -% soln_p = @(x,p,t) exp(-(x-4-t).^2); - soln_p = @(x,p,t) exp(-(x-4-t).^2) .*(x-t).^2 ./ x.^2; % solution to the mass conserving term2==0 system - end - -soln1 = new_md_func(num_dims,{soln_p}); -solutions = {soln1}; - -%% Define the initial conditions - -switch opts.case_ - case 1 - f0_p = @(x,p,t) x.*0+1; - ic_p = f0_p; - ic1 = new_md_func(num_dims,{ic_p}); - initial_conditions = {ic1}; - case 2 - initial_conditions = {soln1}; -end - -%% Define the terms of the PDE - -%% -div(flux_E) == termE1 - -% termE1 == -1/p^2 (d/dp p^2 f(p)) [div, g1(p) = -1, BCL=D,BCR=N] - -g1 = @(x,p,t,d) x.*0-1; -pterm1 = DIV (num_dims,g1,'',-1,'N','N',soln1,soln1,'',dV_p); - -termE1_p = SD_TERM({pterm1}); -termE1 = MD_TERM(num_dims,{termE1_p}); - -% termE2 == +2/p f -% == g1(p) f(p) [mass, g1(p) = +2/p, BC N/A] - -g1 = @(x,p,t,d) +2./x; -pterm1 = MASS(g1,'','',dV_p); -termE2_p = SD_TERM({pterm1}); -termE2 = MD_TERM(num_dims,{termE2_p}); - -terms = {termE1};%,termE2}; - -%% Define sources - -sources = {}; - -%% Define function to set time step - function dt=set_dt(pde,CFL) - dims = pde.dimensions; - xRange = dims{1}.max-dims{1}.min; - lev = dims{1}.lev; - dx = xRange/2^lev; - dt = CFL * dx; - end - -%% Construct PDE - -pde = PDE(opts,dimensions,terms,[],sources,params,@set_dt,[],initial_conditions,solutions); - -end - - diff --git a/pdes/fokkerplanck1_momentum_R_div.m b/pdes/fokkerplanck1_momentum_R.m similarity index 74% rename from pdes/fokkerplanck1_momentum_R_div.m rename to pdes/fokkerplanck1_momentum_R.m index 4fd16a80..a94760b4 100644 --- a/pdes/fokkerplanck1_momentum_R_div.m +++ b/pdes/fokkerplanck1_momentum_R.m @@ -1,17 +1,16 @@ -function pde = fokkerplanck1_momentum_R_div(opts) +function pde = fokkerplanck1_momentum_R(opts) % Combining momentum and pitch angle dynamics for the E term % % d/dt f(p,z) == -div(flux_R) % % flux_R is the flux due to radiative damping % -% -div(flux_R) == termR1 + termR2 +% -div(flux_R) == termR1 % % setting E=2 and z=0.5, and expanding the d/dz term via product rule, then setting d/dz=0, % we get for the momentum direction ... % % termR1 == -1/p^2 (d/dp p^2 3/4*f(p)) [pterm1: div (g(p)=-3/4,-1,BCL=N,BCR=N,dV=p^2] -% termR2 == +f(p)/(4p) [pterm2: mass(g(p)=1/4p,dV=p^2] % % p is a spherical coordinate (p,th,ph), so the div and grad look like % @@ -22,9 +21,14 @@ % % Run with % -% asgard(@fokkerplanck1_momentum_R_div,'timestep_method','matrix_exponential','dt',0.01,'num_steps',10,'case',1) +% asgard(@fokkerplanck1_momentum_R,'timestep_method','matrix_exponential','dt',0.1,'num_steps',10,'case',1,'lev',4,'deg',4) % % case = 1 % offset maxwellian +% +% Notes: +% DLG - at present this is a non-conservative PDE, so the mass will +% increase. I may fix this in future as I did with the +% fokkerplanck1_momentum_E_div test. Updated now. params = fokkerplanck_parameters(opts); @@ -41,9 +45,11 @@ function ans = soln(x,t) A = exp(-(-4+1./4*(-3.*t+4.*x)).^2); y = -3.*t+4.*x; - B = sign(y).*abs(y).^(5./3); - C = (8.*2.^(1./3).*x.^(5./3)); - ans = A .* B ./ C; +% B = sign(y).*abs(y).^(5./3); +% C = (8.*2.^(1./3).*x.^(5./3)); + D = 16.*x.^2; +% ans = A .* B ./ C; + ans = A .* y ./ D; end switch opts.case_ @@ -73,15 +79,7 @@ termR1_p = SD_TERM({pterm1}); termR1 = MD_TERM(num_dims,{termR1_p}); -% termR2 == +1/4p f -% == g1(p) f(p) [mass, g1(p) = +1/4p, BC N/A] - -g1 = @(x,p,t,d) +1./(4.*x); -pterm1 = MASS(g1,'','',dV_p); -termR2_p = SD_TERM({pterm1}); -termR2 = MD_TERM(num_dims,{termR2_p}); - -terms = {termR1,termR2}; +terms = {termR1}; %% Define sources diff --git a/pdes/fokkerplanck1_pitch_C.m b/pdes/fokkerplanck1_pitch_C.m index 15bc1e84..3a69d628 100644 --- a/pdes/fokkerplanck1_pitch_C.m +++ b/pdes/fokkerplanck1_pitch_C.m @@ -7,9 +7,11 @@ % % df/dt == d/dz( (1-z^2) df/dz ) becomes % -% eq1 : df/dt == d/dz g(z) q(z) [grad,g(z)=1-z^2,BCL=D,BCR=D] -% eq2 : q(z) == d/dz g(z) f(z) [grad,g(z)=1,BCL=N,BCR=N] +% eq1 : df/dt == div( q(z) ) [div ,g(z)=1,BCL=D,BCR=D] +% eq2 : q(z) == grad( f(z) ) [grad,g(z)=1,BCL=N,BCR=N] % +% Here div(F\hat(z)) = d/dz(sqrt(1-z^2)F) and +% grad(F) = sqrt(1-z^2)df/dz\hat(z) % % Run with % @@ -17,7 +19,7 @@ % asgard(@fokkerplanck1_pitch_C); % % implicit use in FP paper -% asgard(@fokkerplanck1_pitch_C,'timestep_method','CN','num_steps',20,'lev',3,'deg',3); +% asgard(@fokkerplanck1_pitch_C,'timestep_method','matrix_exponential','dt',1,'lev',3,'deg',3); function ret = soln(z,t) @@ -44,6 +46,7 @@ %% Define the dimensions dim_z = DIMENSION(-1,+1); +dim_z.moment_dV = @(x,p,t) 0*x+1; dimensions = {dim_z}; num_dims = numel(dimensions); @@ -68,10 +71,11 @@ % % d/dz( (1-z^2) df/dz ) -g1 = @(z,p,t,dat) 1-z.^2; -g2 = @(z,p,t,dat) z.*0+1; -pterm1 = GRAD(num_dims,g1,-1,'D','D'); -pterm2 = GRAD(num_dims,g2,+1,'N','N'); +dV_z = @(z,p,t,dat) sqrt(1-z.^2); +g1 = @(z,p,t,dat) 0*z+1; + +pterm1 = DIV(num_dims,g1,'',-1,'D','D','','','',dV_z); +pterm2 = GRAD(num_dims,g1,'',+1,'N','N','','','',dV_z); termC_z = SD_TERM({pterm1,pterm2}); termC = MD_TERM(num_dims,{termC_z}); @@ -105,3 +109,4 @@ end + diff --git a/pdes/fokkerplanck1_pitch_CE.m b/pdes/fokkerplanck1_pitch_CE.m index 923e7200..d0ce8c2a 100644 --- a/pdes/fokkerplanck1_pitch_CE.m +++ b/pdes/fokkerplanck1_pitch_CE.m @@ -45,6 +45,7 @@ %% Define the dimensions dim_z = DIMENSION(-1,+1); +dim_z.moment_dV = @(x,p,t,dat) 0*x+1; dimensions = {dim_z}; num_dims = numel(dimensions); @@ -66,19 +67,19 @@ %% % -E d/dz((1-z^2) f) +dV_z = @(z,p,t,dat) sqrt(1-z.^2); -g1 = @(z,p,t,dat) -E.*(1-z.^2); -pterm1 = GRAD(num_dims,g1,-1,'D','D'); +g1 = @(z,p,t,dat) -E.*sqrt(1-z.^2); +pterm1 = DIV(num_dims,g1,'',-1,'D','D','','','',dV_z); termE_z = SD_TERM({pterm1}); termE = MD_TERM(num_dims,{termE_z}); %% % +C * d/dz( (1-z^2) df/dz ) -g1 = @(z,p,t,dat) 1-z.^2; -g2 = @(z,p,t,dat) z.*0+1; -pterm1 = GRAD(num_dims,g1,-1,'D','D'); -pterm2 = GRAD(num_dims,g2,+1,'N','N'); +g1 = @(z,p,t,dat) 0*z+1; +pterm1 = DIV(num_dims,g1,'',-1,'D','D','','','',dV_z); +pterm2 = GRAD(num_dims,g1,'',+1,'N','N','','','',dV_z); termC_z = SD_TERM({pterm1,pterm2}); termC = MD_TERM(num_dims,{termC_z}); diff --git a/pdes/fokkerplanck1_pitch_CER.m b/pdes/fokkerplanck1_pitch_CER.m index 7575e6d6..11ef45d4 100644 --- a/pdes/fokkerplanck1_pitch_CER.m +++ b/pdes/fokkerplanck1_pitch_CER.m @@ -5,9 +5,19 @@ % % df/dt == -E d/dz((1-z^2) f) + C d/dz((1-z^2) df/dz) - R d/dz(z(1-z^2) f) % +% df/dt == -div( (F_E + F_C + F_R)\hat{z} ) +% +% where +% +% F_E = E*sqrt(1-z^2)f +% +% F_C = C*grad(f) +% +% F_R = R*z*sqrt(1-z^2)f +% % Run with % -% asgard(@fokkerplanck1_pitch_CER,'timestep_method','CN','lev',3,'CFL',0.5,'num_steps',50,'case',1) +% asgard(@fokkerplanck1_pitch_CER,'timestep_method','matrix_exponential','lev',3,'deg',4,'dt',1,'num_steps',50,'case',1,'normalize_by_mass',true) sig = 0.1; E = 2.0; @@ -37,6 +47,7 @@ %% Define the dimensions dim_z = DIMENSION(-1,+1); +dim_z.moment_dV = @(x,p,t,dat) 0*x+1; dimensions = {dim_z}; num_dims = numel(dimensions); @@ -47,30 +58,30 @@ initial_conditions = {ic1}; %% Define the terms of the PDE +dV_z = @(z,p,t,dat) sqrt(1-z.^2); %% % -E d/dz((1-z^2) f) -g1 = @(z,p,t,dat) -E.*(1-z.^2); -pterm1 = GRAD(num_dims,g1,-1,'D','D'); +g1 = @(z,p,t,dat) -E.*sqrt(1-z.^2); +pterm1 = DIV(num_dims,g1,'',-1,'D','D','','','',dV_z); termE_z = SD_TERM({pterm1}); termE = MD_TERM(num_dims,{termE_z}); %% % +C * d/dz( (1-z^2) df/dz ) -g1 = @(z,p,t,dat) 1-z.^2; -g2 = @(z,p,t,dat) z.*0+1; -pterm1 = GRAD(num_dims,g1,-1,'D','D'); -pterm2 = GRAD(num_dims,g2,+1,'N','N'); +g1 = @(z,p,t,dat) 0*z+1; +pterm1 = DIV(num_dims,g1,'',-1,'D','D','','','',dV_z); +pterm2 = GRAD(num_dims,g1,'',+1,'N','N','','','',dV_z); termC_z = SD_TERM({pterm1,pterm2}); termC = MD_TERM(num_dims,{termC_z}); %% % - R d/dz(z(1-z^2) f) -g1 = @(z,p,t,dat) -R * z.*(1-z.^2); -pterm1 = GRAD(num_dims,g1,-1,'D','D'); +g1 = @(z,p,t,dat) -R * z.*sqrt(1-z.^2); +pterm1 = DIV(num_dims,g1,'',-1,'D','D','','','',dV_z); termR_z = SD_TERM({pterm1}); termR = MD_TERM(num_dims,{termR_z}); diff --git a/pdes/fokkerplanck1_pitch_E.m b/pdes/fokkerplanck1_pitch_E.m index 69f349ce..20cc1a5c 100644 --- a/pdes/fokkerplanck1_pitch_E.m +++ b/pdes/fokkerplanck1_pitch_E.m @@ -2,8 +2,13 @@ % 1D test case using continuity equation, i.e., % df/dt == -d/dz ( (1-z^2)f ) % +% df/dt = -div( sqrt(1-z^2)f\hat{z} ) +% % Problem is left to right convection, so we can upwind and only require -% one boundary condition, which is neumann on the left. +% one boundary condition, which is Dirichlet on the left. +% +% When the domain is [-1,1] then the BC don't really matter (as they will +% be annihilated) % % Run with % @@ -40,6 +45,7 @@ %% Define the dimensions dim_z = DIMENSION(-1,+1); +dim_z.moment_dV = @(x,p,t,dat) 0*x+1; dimensions = {dim_z}; num_dims = numel(dimensions); @@ -62,8 +68,10 @@ %% % -d/dz ( (1-z^2)*f ) -g1 = @(z,p,t,dat) -1.*(1-z.^2); -pterm1 = GRAD(num_dims,g1,-1,'N','N'); +g1 = @(z,p,t,dat) -sqrt(1-z.^2); +dV_z = @(z,p,t,dat) sqrt(1-z.^2); + +pterm1 = DIV(num_dims,g1,'',-1,'N','N','','','',dV_z); term1_x = SD_TERM({pterm1}); term1 = MD_TERM(num_dims,{term1_x}); diff --git a/pdes/fokkerplanck1_pitch_R.m b/pdes/fokkerplanck1_pitch_R.m index ba6658ae..78260f54 100644 --- a/pdes/fokkerplanck1_pitch_R.m +++ b/pdes/fokkerplanck1_pitch_R.m @@ -2,6 +2,8 @@ % Problem 4.3 from the RE paper - radiation damping term % df/dt == -d/dz ( z(1-z^2)f ) % +% df/dt = -div( z*sqrt(1-z^2)f\hat{z} ) +% % Run with % % explicit @@ -44,6 +46,7 @@ end dim_z = DIMENSION(-1,+1); +dim_z.moment_dV = @(x,p,t,dat) 0*x+1; dimensions = {dim_z}; num_dims = numel(dimensions); @@ -66,8 +69,9 @@ %% % -d/dz ( z(1-z^2)f ) -g1 = @(z,p,t,dat) -z.*(1-z.^2); -pterm1 = GRAD(num_dims,g1,-1,'D','D'); +g1 = @(z,p,t,dat) -z.*sqrt(1-z.^2); +dV = @(z,p,t,dat) sqrt(1-z.^2); +pterm1 = DIV(num_dims,g1,'',-1,'D','D','','','',dV); term1_z = SD_TERM({pterm1}); term1 = MD_TERM(num_dims,{term1_z}); diff --git a/pdes/fokkerplanck2_C.m b/pdes/fokkerplanck2_C.m index bb0151ca..336e1957 100644 --- a/pdes/fokkerplanck2_C.m +++ b/pdes/fokkerplanck2_C.m @@ -3,11 +3,29 @@ % % Problems 6.1, 6.2, and 6.3 from the RE paper. % -% d/dt f(p,z,t) == termC1 + termC2 + termC3 +% d/dt f(p,z,t) == div( A^2*F_C1 + F_C2 ) % -% termC1 == 1/p^2*d/dp*p^2*Ca*df/dp -% termC2 == 1/p^2*d/dp*p^2*Cf*f -% termC3 == Cb(p)/p^4 * d/dz( (1-z^2) * df/dz ) +% where +% +% \F_C1 = grad(f) and \F_C2 = C_F(p)f\hat{p} +% +% Here +% +% div(F_p\hat{p} + F_z\hat{z}) = 1/p^2*d/dp(p^2F_p) +% + 1/p*d/dz(sqrt(1-z^2)F_z) +% and +% +% grad(f) = df/dp*hat{p} + 1/p*sqrt(1-z^2)*df/dz*hat{z}. +% +% The diffusion tensor A^2 is given by +% +% A\hat{p} = sqrt(C_A(p))\hat{p} and A\hat{z} = 1/p*sqrt(C_B(p))\hat{z}. +% +% MIXED formulation: +% +% d/dt f(p,z,t) == -div( A*q + Gamma_C2 ) +% +% q = A*grad(f) = q_p\hat{p} + q_z\hat{z} % % Run with % @@ -26,15 +44,16 @@ %% Setup the dimensions dim_p = DIMENSION(0,+10); -dim_p.jacobian = @(x,p,t) x.^2; +dim_p.moment_dV = @(x,p,t) x.^2; dim_z = DIMENSION(-1,+1); +dim_z.moment_dV = @(x,p,t) 0*x+1; dimensions = {dim_p,dim_z}; num_dims = numel(dimensions); %% Define the analytic solution (optional) -soln_p = @(x,p,t) p.soln_p(x,t); -soln_z = @(x,p,t) p.soln_z(x,t); +soln_p = @(x,p,t) p.soln_p(x,p,t); +soln_z = @(x,p,t) p.soln_z(x,p,t); soln1 = new_md_func(num_dims,{soln_p,soln_z}); solutions = {soln1}; @@ -59,58 +78,92 @@ %% Define the terms of the PDE %% -% termC1 == 1/p^2*d/dp*p^2*Ca*df/dp +% termC1 = LDG for q_p variable. +% +% LDG in q_p variable gives LDG in p, MASS in z % % becomes % -% termC1 == g1(p) q(p) [mass, g1(p) = 1/p^2, BC N/A] -% q(p) == d/dp g2(p) r(p) [grad, g2(p) = p^2*Ca, BCL=D,BCR=N] -% r(p) == d/dp g3(p) f(p) [grad, g3(p) = 1, BCL=N,BCR=D] +% LDG in p +% div( A*q_p*\hat{p} ) [div , g1(p) = sqrt(C_A), BCL=D,BRC=N] +% q(p) == A*grad(f)*\hat{p} [grad, g2(p) = sqrt(C_A), BCL=N,BCR=D] +% +% MASS in z (first eqn) [mass, g1(z) = 1, BC=NA] +% (secnd eqn) [mass, g1(z) = 1, BC=NA] -g1 = @(x,p,t,dat) 1./x.^2; -g2 = @(x,p,t,dat) x.^2.*p.Ca(x); -g3 = @(x,p,t,dat) x.*0+1; +% Surface jacobian is for p constant is p^2 +dV_p = @(x,p,t,dat) x.^2; +dV_z = @(x,p,t,dat) 0*x+1; -pterm1 = MASS(g1); -pterm2 = GRAD(num_dims,g2,+1,'D','D'); -pterm3 = GRAD(num_dims,g3,-1,'N','N'); -term1_p = SD_TERM({pterm1,pterm2,pterm3}); -termC1 = MD_TERM(num_dims,{term1_p,[]}); +% LDG in p +g1 = @(x,p,t,dat) sqrt(p.Ca(x)); +pterm1 = DIV(num_dims,g1,'',+1,'D','N','','','',dV_p); +pterm2 = GRAD(num_dims,g1,'',-1,'N','D','','','',dV_p); +term1_p = SD_TERM({pterm1,pterm2}); + +% MASS in z +g1 = @(x,p,t,dat) 0*x+1; +pterm1 = MASS(g1,'','',dV_z); +term1_z = SD_TERM({pterm1,pterm1}); + +termC1 = MD_TERM(num_dims,{term1_p,term1_z}); %% -% termC2 == 1/p^2*d/dp*p^2*Cf*f +% termC2 == -div(Gamma_C2) % -% becomes +% Gamma_C2 = -C_F(p)f\hat{p} <-- Flow is right to left % -% termC2 == g1(p) q(p) [mass, g1(p)=1/p^2, BC N/A] -% q(p) == d/dp g2(p) f(p) [grad, g2(p)=p^2*Cf, BCL=N,BCR=D] +% This term is DIV in p and MASS in z +% +% DIV in p +% == div( C_F(p)f\hat{p}) [div, g1(p)=C_f(p), BCL=N, BCR=D] +% +% MASS in z [mass, g1(z) = 1, BC=NA] + +% Surface jacobian for p constant is p^2 +dV_p = @(x,p,t,dat) x.^2; +dV_z = @(x,p,t,dat) 0*x+1; -g1 = @(x,p,t,dat) 1./x.^2; -g2 = @(x,p,t,dat) x.^2.*p.Cf(x); +% DIV in p +g1 = @(x,p,t,dat) p.Cf(x); +pterm1 = DIV(num_dims,g1,'',-1,'N','D','','','',dV_p); +term2_p = SD_TERM({pterm1}); -pterm1 = MASS(g1); -pterm2 = GRAD(num_dims,g2,+1,'N','N'); -term2_p = SD_TERM({pterm1,pterm2}); -termC2 = MD_TERM(num_dims,{term2_p,[]}); +% MASS in z +g1 = @(x,p,t,dat) 0*x+1; +pterm1 = MASS(g1,'','',dV_z); +term2_z = SD_TERM({pterm1}); + +termC2 = MD_TERM(num_dims,{term2_p,term2_z}); %% -% termC3 == Cb(p)/p^4 * d/dz( (1-z^2) * df/dz ) +% termC3 = LDG for q_z variable. +% +% LDG in q_z variable gives MASS in p, LDG in z % % becomes +% MASS in p (first eqn) [mass, g1(p) = sqrt(C_b(p)), BC=NA] +% (secnd eqn) [mass, g1(p) = sqrt(C_b(p)), BC=NA] +% +% LDG in z +% div( A*q_z*\hat{z} ) [div , g1(p) = 1, BCL=D,BRC=N] +% q(p) == A*grad(f)*\hat{z} [grad, g2(p) = 1, BCL=N,BCR=D] % -% termC3 == q(p) r(z) -% q(p) == g1(p) [mass, g1(p) = Cb(p)/p^4, BC N/A] -% r(z) == d/dz g2(z) s(z) [grad, g2(z) = 1-z^2, BCL=D,BCR=D] -% s(z) == d/dz g3(z) f(z) [grad, g3(z) = 1, BCL=N,BCR=N] -g1 = @(x,p,t,dat) min(p.Cb(x)./x.^4,1e2); % DLG - NOTE the limiter here -pterm1 = MASS(g1); -term3_p = SD_TERM({pterm1}); +% Surface jacobian for z constnat is p*sqrt(1-z^2) +dV_p = @(x,p,t,dat) x; +dV_z = @(x,p,t,dat) sqrt(1-x.^2); + +% MASS in p + +g1 = @(x,p,t,dat) sqrt(p.Cb(x)); +pterm1 = MASS(g1,'','',dV_p); +term3_p = SD_TERM({pterm1,pterm1}); -g2 = @(x,p,t,dat) (1-x.^2); -g3 = @(x,p,t,dat) x.*0+1; -pterm1 = GRAD(num_dims,g2,+1,'D','D'); -pterm2 = GRAD(num_dims,g3,-1,'N','N'); +% LDG in z +g1 = @(x,p,t,dat) x.*0+1; +pterm1 = DIV(num_dims,g1,'',+1,'D','D','','','',dV_z); +pterm2 = GRAD(num_dims,g1,'',-1,'N','N','','','',dV_z); term3_z = SD_TERM({pterm1,pterm2}); termC3 = MD_TERM(num_dims,{term3_p,term3_z}); diff --git a/pdes/fokkerplanck2_C_LHS.m b/pdes/fokkerplanck2_C_LHS.m deleted file mode 100644 index eb4295fa..00000000 --- a/pdes/fokkerplanck2_C_LHS.m +++ /dev/null @@ -1,138 +0,0 @@ -function pde = fokkerplanck2_C_LHS(opts) -% Combining momentum and pitch angle dynamics -% -% Problems 6.1, 6.2, and 6.3 from the RE paper. -% -% p^2 * d/dt f(p,z,t) == termC1 + termC2 + termC3 -% -% termC1 == d/dp*p^2*Ca*df/dp -% termC2 == d/dp*p^2*Cf*f -% termC2 == Cb(p)/p^2 * d/dz( (1-z^2) * df/dz ) -% -% Run with -% -% explicit -% asgard(@fokkerplanck2_C_LHS,'CFL',0.01,'case',1) -% -% implicit -% asgard(@fokkerplanck2_C_LHS,'timestep_method','CN','num_steps',20,'CFL',1.0,'deg',3,'lev',4,'case',1) -% -% NOTES -% DLG - case 3 doesn't seem to be working, although it does work for the -% nonLHS version of this PDE? - -params = fokkerplanck_parameters(opts); - -%% Define the dimensions - -dim_p = DIMENSION(0.01,+10); -dim_z = DIMENSION(-1,+1); -dimensions = {dim_p,dim_z}; -num_dims = numel(dimensions); - -%% Define the analytic solution (optional) - -soln_p = @(x,p,t) p.soln_p(x,t); -soln_z = @(z,p,t) p.soln_z(z,t); -soln1 = new_md_func(num_dims,{soln_p,soln_z}); -solutions = {soln1}; - -%% Define the initial conditions - -ic_p = @(x,p,t) p.f0_p(x); -ic_z = @(x,p,t) p.f0_z(x); -ic1 = new_md_func(num_dims,{ic_p,ic_z}); -initial_conditions = {ic1}; - -%% Define the terms of the PDE - -%% -% LHS_term == p^2 d/dt f(p,z,t) - -g1 = @(x,p,t,dat) x.^2; -pterm1 = MASS(g1); - -LHS_term_p = SD_TERM({pterm1}); -LHS_term = MD_TERM(num_dims,{LHS_term_p,[]}); - -LHS_terms = {LHS_term}; - -%% -% termC1 == d/dp*p^2*Ca*df/dp -% -% becomes -% -% termC1 == d/dp g2(p) r(p) [grad, g2(p) = p^2*Ca, BCL=D,BCR=N] -% r(p) == d/dp g3(p) f(p) [grad, g3(p) = 1, BCL=N,BCR=D] - -g2 = @(x,p,t,dat) x.^2.*p.Ca(x); -g3 = @(x,p,t,dat) x.*0+1; - -pterm2 = GRAD(num_dims,g2,+1,'D','N'); -pterm3 = GRAD(num_dims,g3,-1,'N','D'); -term1_p = SD_TERM({pterm2,pterm3}); -termC1 = MD_TERM(num_dims,{term1_p,[]}); - -%% -% termC2 == d/dp*p^2*Cf*f -% -% becomes -% -% termC2 == d/dp g2(p) f(p) [grad, g2(p)=p^2*Cf, BCL=N,BCR=D] - -g2 = @(x,p,t,dat) x.^2.*p.Cf(x); - -pterm2 = GRAD(num_dims,g2,+1,'N','D'); -term2_p = SD_TERM({pterm2}); -termC2 = MD_TERM(num_dims,{term2_p,[]}); - -%% -% termC3 == Cb(p)/p^2 * d/dz( (1-z^2) * df/dz ) -% -% becomes -% -% termC3 == q(p) r(z) -% q(p) == g1(p) [mass, g1(p) = Cb(p)/p^2, BC N/A] -% r(z) == d/dz g2(z) s(z) [grad, g2(z) = 1-z^2, BCL=D,BCR=D] -% s(z) == d/dz g3(z) f(z) [grad, g3(z) = 1, BCL=N,BCR=N] - -g1 = @(x,p,t,dat) p.Cb(x)./x.^2; -pterm1 = MASS(g1); -term3_p = SD_TERM({pterm1}); - -g2 = @(x,p,t,dat) (1-x.^2); -g3 = @(x,p,t,dat) x.*0+1; -pterm1 = GRAD(num_dims,g2,+1,'D','D'); -pterm2 = GRAD(num_dims,g3,-1,'N','N'); -term3_z = SD_TERM({pterm1,pterm2}); - -termC3 = MD_TERM(num_dims,{term3_p,term3_z}); - -terms = {termC1,termC2,termC3}; - -%% Defin some parameters and add to pde object. -% These might be used within the various functions below. - -params.parameter1 = 0; -params.parameter2 = 1; - -%% Define sources - -sources = {}; - -%% Define function to set time step - function dt=set_dt(pde,CFL) - dims = pde.dimensions; - xRange = dims{1}.max-dims{1}.min; - lev = dims{1}.lev; - dx = xRange/2^lev; - dt = CFL * dx; - end - -%% Construct PDE - -pde = PDE(opts,dimensions,terms,LHS_terms,sources,params,@set_dt,[],initial_conditions,solutions); - -end - - diff --git a/pdes/fokkerplanck2_E.m b/pdes/fokkerplanck2_E.m index 70f2ed61..fd6f189b 100644 --- a/pdes/fokkerplanck2_E.m +++ b/pdes/fokkerplanck2_E.m @@ -1,14 +1,15 @@ function pde = fokkerplanck2_E(opts) % Combining momentum and pitch angle dynamics for the E term % -% d/dt f(p,z) == -div(flux_E) +% d/dt f(p,z) == div( F_p(f)\hat{p} + F_z(f)\hat{z} ) % -% flux_E is the flux due to E accleration +% where % -% -div(flux_E) == termE1 + termE2 +% F_p(f) = -Ezf and F_z(f) = -Esqrt(1-z^2)f % -% termE1 == -E*z*f(z) * 1/p^2 (d/dp p^2 f(p)) -% termE2 == -E/p*f(p) * d/dz (1-z^2) f(z) +% Here +% +% div( A_p\hat{p} + A_z\hat{z} ) = 1/p^2*d/dp( p^2*A_p ) + 1/p*d/dz( sqrt(1-z^2)A_z ) % % Run with % @@ -29,8 +30,8 @@ dim_p = DIMENSION(0,+10); dim_z = DIMENSION(-1,+1); -dim_p.jacobian = @(x,p,t) x.^2; -dim_z.jacobian = @(x,p,t) x.*0+1; +dim_p.moment_dV = @(x,p,t) x.^2; +dim_z.moment_dV = @(x,p,t) x.*0+1; dimensions = {dim_p,dim_z}; num_dims = numel(dimensions); @@ -71,58 +72,103 @@ end initial_conditions = {ic1}; +%% Boundary Conditions + +switch opts.case_ + case 1 + BCL = soln1; + BCR = soln1; + case 2 + BCL = ''; + BCR = ''; + case 3 + BCL = soln1; + BCR = soln1; +end %% Define the terms of the PDE -%% -div(flux_E) == termE1 + termE2 +%% -% termE1 == -E*z*f(z) * 1/p^2 (d/dp p^2 f(p)) -% == r(z) * q(p) -% r(z) == g1(z) f(z) [mass, g1(z) = -E*z, BC N/A] -% q(p) == g2(p) u(p) [mass, g2(p) = 1/p^2, BC N/A] -% u(p) == d/dp g3(p) f(p) [grad, g3(p) = p^2, BCL=N,BCR=D] +% termE1+E2 == div( F_p(f)\hat{p} ) +% +% DIV in p and MASS in z +% +% Since z changes sign on [-1,1] we have to split the term into two terms +% and upwind based on the sign of z. + +% Surface jacobian for p constant is p^2 +dV_p = @(x,p,t,dat) x.^2; +dV_z = @(x,p,t,dat) 0*x+1; -cap = 1e2; +% Term for z>0, then |z| = z and we use standard upwinding. -g1 = @(z,p,t,dat) -p.E .* z; -g2 = @(x,p,t,dat) min(1./x.^2,cap); -g3 = @(x,p,t,dat) x.^2; -pterm1 = MASS(g1); +g1 = @(x,p,t,dat) 0*x-p.E; +pterm1 = DIV(num_dims,g1,'',-1,'D','N',BCR,'','',dV_p); +termE1_p = SD_TERM({pterm1}); + +g1 = @(x,p,t,dat) x.*(x > 0); +pterm1 = MASS(g1,'','',dV_z); termE1_z = SD_TERM({pterm1}); -pterm1 = MASS(g2); -pterm2 = GRAD(num_dims,g3,0,'N','N'); % central flux due to change of z sign within domain -termE1_p = SD_TERM({pterm1,pterm2}); + termE1 = MD_TERM(num_dims,{termE1_p,termE1_z}); -figure(50) -p = 0:.001:10; -plot(p,g1(p,params,[],[])); -hold on -plot(p,g2(p,params,[],[])); -plot(p,g3(p,params,[],[])); -hold off - -% termE2 == -E/p*f(p) * d/dz (1-z^2) f(z) -% == q(p) * r(z) -% q(p) == g1(p) f(p) [mass, g1(p) = -E*p, BC N/A] -% r(z) == d/dz g2(z) f(z) [grad, g2(z) = 1-z^2, BCL=N,BCR=N] - -g1 = @(x,p,t,dat) -p.E * min(1 ./ x,cap); -g2 = @(z,p,t,dat) 1-z.^2; -pterm1 = MASS(g1); +% Term for z<0. +% If z < 0, then |z| = -z. +% Assume f(p,z) = f_p(p)f_z(z) and v(p,z) = v_p(p)v_z(z). +% Let <.,.>_p be the edge integral in p and (.,.)_z be the volume integral +% in z. +% Standard upwinding jump flux becomes +% <|Ez|[f],[v]>_{z,p} = <|E|[f_p],[v_p]>_p(|z|f_z,v_z)_z +% = -<|E|[f_p],[v_p]>_p( z f_z,v_z)_z +% So we downwind in p when z is negative. + +g1 = @(x,p,t,dat) 0*x-p.E; +pterm1 = DIV(num_dims,g1,'',+1,'N','D','',BCL,'',dV_p); termE2_p = SD_TERM({pterm1}); -pterm1 = GRAD(num_dims,g2,0,'N','N'); % central flux due to change of z sign within domain + +g1 = @(x,p,t,dat) x.*(x < 0); +pterm1 = MASS(g1,'','',dV_z); termE2_z = SD_TERM({pterm1}); -termE2= MD_TERM(num_dims,{termE2_p,termE2_z}); -figure(51) -p = 0:.001:10; -plot(p,g1(p,params,[],[])); -hold on -plot(p,g2(p,params,[],[])); -hold off +termE2 = MD_TERM(num_dims,{termE2_p,termE2_z}); + + +%%%%%% +g1 = @(x,p,t,dat) 0*x-p.E; +pterm1 = DIV(num_dims,g1,'',-1,'N','N','','','',dV_p); +termE4_p = SD_TERM({pterm1}); + +g1 = @(x,p,t,dat) x; +pterm1 = MASS(g1,'','',dV_z); +termE4_z = SD_TERM({pterm1}); +termE4 = MD_TERM(num_dims,{termE4_p,termE4_z}); + +%% + +% termE3 == div( F_z(f)\hat{z} ) +% +% MASS in p and DIV in z +% +% + +% Surface jacobian for z constant is p*sqrt(1-z^2) +dV_p = @(x,p,t,dat) x; +dV_z = @(x,p,t,dat) sqrt(1-x.^2); + +g1 = @(x,p,t,dat) 0*x+1; +pterm1 = MASS(g1,'','',dV_p); +termE3_p = SD_TERM({pterm1}); + +g1 = @(x,p,t,dat) -p.E*sqrt(1-x.^2); +pterm1 = DIV(num_dims,g1,'',-1,'D','D','','','',dV_z); +termE3_z = SD_TERM({pterm1}); +termE3 = MD_TERM(num_dims,{termE3_p,termE3_z}); + +%% -terms = {termE1,termE2}; +terms = {termE1,termE2,termE3}; +%terms = {termE4,termE3}; %% Define sources diff --git a/pdes/fokkerplanck2_E_LHS.m b/pdes/fokkerplanck2_E_LHS.m deleted file mode 100644 index 00f2c19e..00000000 --- a/pdes/fokkerplanck2_E_LHS.m +++ /dev/null @@ -1,197 +0,0 @@ -function pde = fokkerplanck2_E_LHS(opts) -% Combining momentum and pitch angle dynamics for the E term -% -% d/dt f(p,z) == -div(flux_E) -% -% flux_E is the flux due to E accleration -% -% -div(flux_E) == termE1 + termE2 -% -% termE1 == -E*z*f(z) * 1/p^2 (d/dp p^2 f(p)) -% termE2 == -E/p*f(p) * d/dz (1-z^2) f(z) -% -% Run with -% -% asgard(@fokkerplanck2_E_LHS,'timestep_method','BE','dt',0.01,'num_steps',10,'case',3,'lev',4,'deg',4) -% -% case = 1 % flat initial condition, solution stays the same -% case = 2 % made up initial conditions, no known solution -% case = 3 % manufactured solution with sources - -params = fokkerplanck_parameters(opts); - -switch opts.case_ - case 3 - params.E = 0.25; -end - -%% Setup the dimensions - -dim_p = DIMENSION(0,+10); -dim_z = DIMENSION(-1,+1); -dim_p.jacobian = @(x,p,t) x.^2; -dim_z.jacobian = @(x,p,t) x.*0+1; -dimensions = {dim_p,dim_z}; -num_dims = numel(dimensions); - -%% Define the analytic solution (optional) - -switch opts.case_ - case 1 - soln_p = @(x,p,t) x.*0+1; - soln_z = @(x,p,t) x.*0+1; - soln1 = new_md_func(num_dims,{soln_p,soln_z}); - solutions = {soln1}; - case 2 - solutions = {}; - case 3 - soln_p = @(x,p,t) exp(-x.^2); - soln_z = @(z,p,t) cos(z.*pi)+1; - soln_t = @(t,p) exp(-t); - soln1 = new_md_func(num_dims,{soln_p,soln_z,soln_t}); - solutions = {soln1}; -end - - -%% Define the initial conditions - -switch opts.case_ - case 1 - ic_p = @(x,p,t) x.*0+1; - ic_z = @(z,p,t) z.*0+1; - ic1 = new_md_func(num_dims,{ic_p,ic_z}); - case 2 - % ic_p = @(x,p,t) exp(-x.^2); - % ic_z = @(z,p,t) cos(z*pi)+1; - ic_p = @(x,p,t) p.f0_p(x); - ic_z = @(x,p,t) p.f0_z(x); - ic1 = new_md_func(num_dims,{ic_p,ic_z}); - case 3 - ic1 = soln1; -end -initial_conditions = {ic1}; - - -%% Define the terms of the PDE - -% p^2 * df/dt (LHS non-identity coeff requires special treatment) - -g1 = @(x,p,t,dat) x.^2; -pterm1 = MASS(g1); -LHS_term_p = SD_TERM({pterm1}); -LHS_term = MD_TERM(num_dims,{LHS_term_p,[]}); -LHS_terms = {LHS_term}; - -%% -div(flux_E) == termE1 + termE2 - -% termE1 == -E*z*f(z) * (d/dp p^2 f(p)) -% == r(z) * q(p) -% r(z) == g1(z) f(z) [mass, g1(z) = -E*z, BC N/A] -% q(p) == g2(p) u(p) [mass, g2(p) = 1, BC N/A] -% u(p) == d/dp g3(p) f(p) [grad, g3(p) = p^2, BCL=N,BCR=D] - -g1 = @(z,p,t,dat) -p.E .* z; -g3 = @(x,p,t,dat) x.^2; -pterm1 = MASS(g1); -termE1_z = SD_TERM({pterm1}); -pterm2 = GRAD(num_dims,g3,0,'N','N'); % central flux due to change of z sign within domain -termE1_p = SD_TERM({pterm2}); -termE1 = MD_TERM(num_dims,{termE1_p,termE1_z}); - -% figure(50) -% p = 0:.001:10; -% plot(p,g1(p,params,[],[])); -% hold on -% plot(p,g2(p,params,[],[])); -% plot(p,g3(p,params,[],[])); -% hold off - -% termE2 == -E*p*f(p) * d/dz (1-z^2) f(z) -% == q(p) * r(z) -% q(p) == g1(p) f(p) [mass, g1(p) = -E*p, BC N/A] -% r(z) == d/dz g2(z) f(z) [grad, g2(z) = 1-z^2, BCL=N,BCR=N] - -g1 = @(x,p,t,dat) -p.E .* x; -g2 = @(z,p,t,dat) 1-z.^2; -pterm1 = MASS(g1); -termE2_p = SD_TERM({pterm1}); -pterm1 = GRAD(num_dims,g2,0,'N','N'); % central flux due to change of z sign within domain -termE2_z = SD_TERM({pterm1}); -termE2= MD_TERM(num_dims,{termE2_p,termE2_z}); - -figure(51) -p = 0:.001:10; -plot(p,g1(p,params,[],[])); -hold on -plot(p,g2(p,params,[],[])); -hold off - -terms = {termE1,termE2}; - -%% Define sources - -switch opts.case_ - case 1 - sources = {}; - case 2 - sources = {}; - case 3 - ep2t = @(x,t) exp(-x.^2-t); - - fac=1; - - s1_p = @(x,p,t) -ep2t(x,t)*fac .* x.^2; - s1_z = @(z,p,t) 1+cos(pi*z); - s1 = new_md_func(num_dims,{s1_p,s1_z}); - - s21_p = @(x,p,t) 2*ep2t(x,t)./x.*p.E*fac .* x.^2; - s21_z = @(z,p,t) z; - s21 = new_md_func(num_dims,{s21_p,s21_z}); - - s22_p = @(x,p,t) -2*ep2t(x,t) .* x .* p.E*fac .* x.^2; - s22_z = @(z,p,t) z; - s22 = new_md_func(num_dims,{s22_p,s22_z}); - - s23_p = @(x,p,t) +2*ep2t(x,t) ./ x .* p.E*fac .* x.^2; - s23_z = @(z,p,t) z .* cos(pi*z); - s23 = new_md_func(num_dims,{s23_p,s23_z}); - - s24_p = @(x,p,t) -2*ep2t(x,t) .* x .* p.E*fac .* x.^2; - s24_z = @(z,p,t) z .* cos(pi*z); - s24 = new_md_func(num_dims,{s24_p,s24_z}); - - s31_p = @(x,p,t) -2*ep2t(x,t) ./ x*fac .* p.E .* x.^2; - s31_z = @(z,p,t) z; - s31 = new_md_func(num_dims,{s31_p,s31_z}); - - s32_p = @(x,p,t) -2*ep2t(x,t) ./ x*fac .* p.E .* x.^2; - s32_z = @(z,p,t) z .* cos(pi*z); - s32 = new_md_func(num_dims,{s32_p,s32_z}); - - s33_p = @(x,p,t) -ep2t(x,t) ./ x*fac .* p.E .* x.^2; - s33_z = @(z,p,t) pi * sin(pi * z); - s33 = new_md_func(num_dims,{s33_p,s33_z}); - - s34_p = @(x,p,t) ep2t(x,t) ./ x*fac .* p.E .* x.^2; - s34_z = @(z,p,t) pi * z.^2 .* sin(pi * z); - s34 = new_md_func(num_dims,{s34_p,s34_z}); - - sources = {s1,s21,s22,s23,s24,s31,s32,s33,s34}; -end - -%% Define function to set time step - function dt=set_dt(pde,CFL) - dims = pde.dimensions; - xRange = dims{1}.max-dims{1}.min; - lev = dims{1}.lev; - dx = xRange/2^lev; - dt = CFL * dx; - end - -%% Construct PDE - -pde = PDE(opts,dimensions,terms,LHS_terms,sources,params,@set_dt,[],initial_conditions,solutions); - -end - - diff --git a/pdes/fokkerplanck2_complete.m b/pdes/fokkerplanck2_complete.m index 8d3a9467..e47e24be 100644 --- a/pdes/fokkerplanck2_complete.m +++ b/pdes/fokkerplanck2_complete.m @@ -11,21 +11,35 @@ % flux_E is the flux due to E accleration % flux_R is the flux due to radiation damping % -% -div(flux_C) == termC1 + termC2 + termC3 +% flux_C == A^2*F_C1 + F_C2 % -% termC1 == 1/p^2*d/dp*p^2*Ca*df/dp -% termC2 == 1/p^2*d/dp*p^2*Cf*f -% termC3 == Cb(p)/p^4 * d/dz( (1-z^2) * df/dz ) +% where +% +% A\hat{p} = sqrt(C_A(p))\hat{p} and A\hat{z} = 1/p*sqrt(C_B(p))\hat{z} +% +% and +% +% \F_C1 = grad(f) and \F_C2 = C_F(p)f\hat{p} +% +% +% flux_E == F_Ep(f)\hat{p} + F_Ez(f)\hat{z} +% +% where % -% -div(flux_E) == termE1 + termE2 +% F_Ep(f) = -Ezf and F_Ez(f) = -Esqrt(1-z^2)f % -% termE1 == -E*z*f(z) * 1/p^2 (d/dp p^2 f(p)) -% termE2 == -E/p*f(p) * d/dz (1-z^2) f(z) % -% -div(flux_R) == termR1 + termR2 +% flux_R == F_Rp \hat{p} + F_Rz \hat{z} +% +% where +% +% F_Rp = gamma(p)p/tau*(1-z^2)f(z) +% F_Rz = -1/(tau*gamma(p))z*sqrt(1-z^2) f(z) +% +% Here +% +% div( A_p\hat{p} + A_z\hat{z} ) = 1/p^2*d/dp( p^2*A_p ) + 1/p*d/dz( sqrt(1-z^2)f ) % -% termR1 == 1/p^2 d/dp p^2 gamma(p) p / tau f(p) * (1-z^2) * f(z) -% termR2 == -1/(tau*gam(p)) f(p) * d/dz z(1-z^2) f(z) % % Run with % @@ -41,183 +55,270 @@ % NOTES % % For Lin's case the command that should reproduce her results -% asgard(@fokkerplanck2_complete,'timestep_method','BE','lev',6,'deg',5,'dt',0.01,'num_steps',3000,'time_independent_A',true,'case',1) +% asgard(@fokkerplanck2_complete_div,'timestep_method','BE','lev',6,'deg',5,'dt',0.01,'num_steps',3000,'time_independent_A',true,'case',1) % % David's adjustment can be run as follows ... -% asgard(@fokkerplanck2_complete,'timestep_method','BE','lev',3,'deg',6,'dt',1,'num_steps',50,'grid_type','FG','time_independent_A',true,'case',1) +% asgard(@fokkerplanck2_complete_div,'timestep_method','BE','lev',3,'deg',6,'dt',1,'num_steps',50,'grid_type','FG','time_independent_A',true,'case',1) % or, run with the high order time integrator ... -% asgard(f@okkerplanck2_complete,'timestep_method','ode15s','lev',3,'deg',5,'dt',50,'num_steps',1,'grid_type','SG','case',1) +% asgard(f@okkerplanck2_complete_div,'timestep_method','ode15s','lev',3,'deg',5,'dt',50,'num_steps',1,'grid_type','SG','case',1) params = fokkerplanck_parameters(opts); %% Setup the dimensions -dim_p = DIMENSION(0,+10); +p_max = 10; +if isfield(opts.cmd_args,'p_max') + p_max = opts.cmd_args.p_max; +end + +dim_p = DIMENSION(0,p_max); dim_z = DIMENSION(-1,+1); -dim_p.jacobian = @(x,p,t) x.^2; -dim_z.jacobian = @(x,p,t) x.*0+1; +dim_p.moment_dV = @(x,p,t,dat) x.^2; +dim_z.moment_dV = @(x,p,t,dat) x.*0+1; dimensions = {dim_p,dim_z}; num_dims = numel(dimensions); -%% Define the analytic solution (optional) - -solutions = {}; - %% Define the initial conditions ic_p = @(x,p,t) p.f0_p(x); ic_z = @(x,p,t) p.f0_z(x); +%ic_p = @(x,p,t) 0*x+1; ic_z = @(x,p,t) 0*x+1; ic1 = new_md_func(num_dims,{ic_p,ic_z}); initial_conditions = {ic1}; +%% Define the analytic solution (optional) + +solutions = {ic1}; + %% Define the terms of the PDE %% -div(flux_C) == termC1 + termC2 + termC3 -%% -% termC1 == 1/p^2*d/dp*p^2*Ca*df/dp +%% C terms + +%% +% termC1 = LDG for q_p variable. % -% becomes +% LDG in q_p variable gives LDG in p, MASS in z % -% termC1 == g1(p) q(p) [mass, g1(p) = 1/p^2, BC N/A] -% q(p) == d/dp g2(p) r(p) [grad, g2(p) = p^2*Ca, BCL=D,BCR=N] -% r(p) == d/dp g3(p) f(p) [grad, g3(p) = 1, BCL=N,BCR=D] +% becomes +% +% LDG in p +% div( A*q_p*\hat{p} ) [div , g1(p) = sqrt(C_A), BCL=D,BRC=N] +% q(p) == A*grad(f)*\hat{p} [grad, g2(p) = sqrt(C_A), BCL=N,BCR=D] +% +% MASS in z (first eqn) [mass, g1(z) = 1, BC=NA] +% (secnd eqn) [mass, g1(z) = 1, BC=NA] -g1 = @(x,p,t,dat) 1./x.^2; -g2 = @(x,p,t,dat) x.^2.*p.Ca(x); -g3 = @(x,p,t,dat) x.*0+1; +% Surface jacobian is for p constant is p^2 +dV_p = @(x,p,t,dat) x.^2; +dV_z = @(x,p,t,dat) 0*x+1; -pterm1 = MASS(g1); -pterm2 = GRAD(num_dims,g2,+1,'D','D'); -pterm3 = GRAD(num_dims,g3,-1,'N','N'); +% LDG in p +g1 = @(x,p,t,dat) sqrt(p.Ca(x)); +pterm1 = DIV(num_dims,g1,'',+1,'D','N','','','',dV_p); +pterm2 = GRAD(num_dims,g1,'',-1,'N','D','','','',dV_p); +term1_p = SD_TERM({pterm1,pterm2}); -term1_p = SD_TERM({pterm1,pterm2,pterm3}); -termC1 = MD_TERM(num_dims,{term1_p,[]}); +% MASS in z +g1 = @(x,p,t,dat) 0*x+1; +pterm1 = MASS(g1,'','',dV_z); +term1_z = SD_TERM({pterm1,pterm1}); + +termC1 = MD_TERM(num_dims,{term1_p,term1_z}); %% -% termC2 == 1/p^2*d/dp*p^2*Cf*f +% termC2 == -div(Gamma_C2) % -% becomes +% Gamma_C2 = -C_F(p)f\hat{p} <-- Flow is right to left % -% termC2 == g1(p) q(p) [mass, g1(p)=1/p^2, BC N/A] -% q(p) == d/dp g2(p) f(p) [grad, g2(p)=p^2*Cf, BCL=N,BCR=D] +% This term is DIV in p and MASS in z +% +% DIV in p +% == div( C_F(p)f\hat{p}) [div, g1(p)=C_f(p), BCL=N, BCR=D] +% +% MASS in z [mass, g1(z) = 1, BC=NA] + +% Surface jacobian for p constant is p^2 +dV_p = @(x,p,t,dat) x.^2; +dV_z = @(x,p,t,dat) 0*x+1; -g1 = @(x,p,t,dat) 1./x.^2; -g2 = @(x,p,t,dat) x.^2.*p.Cf(x); +% DIV in p +g1 = @(x,p,t,dat) p.Cf(x); +pterm1 = DIV(num_dims,g1,'',-1,'N','D','','','',dV_p); +term2_p = SD_TERM({pterm1}); -pterm1 = MASS(g1); -pterm2 = GRAD(num_dims,g2,-1,'N','N'); +% MASS in z +g1 = @(x,p,t,dat) 0*x+1; +pterm1 = MASS(g1,'','',dV_z); +term2_z = SD_TERM({pterm1}); -term2_p = SD_TERM({pterm1,pterm2}); -termC2 = MD_TERM(num_dims,{term2_p,[]}); +termC2 = MD_TERM(num_dims,{term2_p,term2_z}); %% -% termC3 == Cb(p)/p^4 * d/dz( (1-z^2) * df/dz ) +% termC3 = LDG for q_z variable. +% +% LDG in q_z variable gives MASS in p, LDG in z % % becomes +% MASS in p (first eqn) [mass, g1(p) = sqrt(C_b(p)), BC=NA] +% (secnd eqn) [mass, g1(p) = sqrt(C_b(p)), BC=NA] +% +% LDG in z +% div( A*q_z*\hat{z} ) [div , g1(p) = 1, BCL=D,BRC=N] +% q(p) == A*grad(f)*\hat{z} [grad, g2(p) = 1, BCL=N,BCR=D] % -% termC3 == q(p) r(z) -% q(p) == g1(p) [mass, g1(p) = Cb(p)/p^4, BC N/A] -% r(z) == d/dz g2(z) s(z) [grad, g2(z) = 1-z^2, BCL=D,BCR=D] -% s(z) == d/dz g3(z) f(z) [grad, g3(z) = 1, BCL=N,BCR=N] -g1 = @(x,p,t,dat) min(p.Cb(x)./x.^4,100); -pterm1 = MASS(g1); -term3_p = SD_TERM({pterm1}); +% Surface jacobian for z constnat is p*sqrt(1-z^2) +dV_p = @(x,p,t,dat) x; +dV_z = @(x,p,t,dat) sqrt(1-x.^2); -g2 = @(x,p,t,dat) (1-x.^2); -g3 = @(x,p,t,dat) x.*0+1; -pterm1 = GRAD(num_dims,g2,+1,'D','D'); -pterm2 = GRAD(num_dims,g3,-1,'N','N'); +% MASS in p +g1 = @(x,p,t,dat) sqrt(p.Cb(x)); +pterm1 = MASS(g1,'','',dV_p); +term3_p = SD_TERM({pterm1,pterm1}); + +% LDG in z +g1 = @(x,p,t,dat) x.*0+1; +pterm1 = DIV(num_dims,g1,'',+1,'D','D','','','',dV_z); +pterm2 = GRAD(num_dims,g1,'',-1,'N','N','','','',dV_z); term3_z = SD_TERM({pterm1,pterm2}); termC3 = MD_TERM(num_dims,{term3_p,term3_z}); -%% -div(flux_E) == termE1 + termE2 +%% E terms + +%% div(flux_E) == termE1 + termE2 -% termE1 == -E*z*f(z) * 1/p^2 (d/dp p^2 f(p)) -% == r(z) * q(p) -% r(z) == g1(z) f(z) [mass, g1(z) = -E*z, BC N/A] -% q(p) == g2(p) u(p) [mass, g2(p) = 1/p^2, BC N/A] -% u(p) == d/dp g3(p) f(p) [grad, g3(p) = p^2, BCL=N,BCR=D] +%% + +% termE1+E2 == div( F_p(f)\hat{p} ) +% +% DIV in p and MASS in z +% +% Since z changes sign on [-1,1] we have to split the term into two terms +% and upwind based on the sign of z. -g1 = @(z,p,t,dat) -p.E .* z; -g2 = @(x,p,t,dat) min(1./x.^2,1e3); -g3 = @(x,p,t,dat) x.^2; -pterm1 = MASS(g1); +% Surface jacobian for p constant is p^2 +dV_p = @(x,p,t,dat) x.^2; +dV_z = @(x,p,t,dat) 0*x+1; + +% Term for z>0, then |z| = z and we use standard upwinding. + +g1 = @(x,p,t,dat) 0*x-p.E; +pterm1 = DIV(num_dims,g1,'',-1,'D','N','','','',dV_p); +termE1_p = SD_TERM({pterm1}); + +g1 = @(x,p,t,dat) x.*(x > 0); +pterm1 = MASS(g1,'','',dV_z); termE1_z = SD_TERM({pterm1}); -pterm1 = MASS(g2); -pterm2 = GRAD(num_dims,g3,0,'N','N');% Lin's Setting (DLG-why is this central flux?) -termE1_p = SD_TERM({pterm1,pterm2}); + termE1 = MD_TERM(num_dims,{termE1_p,termE1_z}); -% p = 0:.001:10; -% plot(p,g1(p,params,[],[])); -% hold on -% plot(p,g2(p,params,[],[])); -% plot(p,g3(p,params,[],[])); -% hold off - -% termE2 == -E/p*f(p) * d/dz (1-z^2) f(z) -% == q(p) * r(z) -% q(p) == g1(p) f(p) [mass, g1(p) = -E*p, BC N/A] -% r(z) == d/dz g2(z) f(z) [grad, g2(z) = 1-z^2, BCL=N,BCR=N] - -g1 = @(x,p,t,dat) -p.E ./ x; -g2 = @(x,p,t,dat) 1-x.^2; -pterm1 = MASS(g1); +% Term for z<0. +% If z < 0, then |z| = -z. +% Assume f(p,z) = f_p(p)f_z(z) and v(p,z) = v_p(p)v_z(z). +% Let <.,.>_p be the edge integral in p and (.,.)_z be the volume integral +% in z. +% Standard upwinding jump flux becomes +% <|Ez|[f],[v]>_{z,p} = <|E|[f_p],[v_p]>_p(|z|f_z,v_z)_z +% = -<|E|[f_p],[v_p]>_p( z f_z,v_z)_z +% So we downwind in p when z is negative. + +g1 = @(x,p,t,dat) 0*x-p.E; +pterm1 = DIV(num_dims,g1,'',+1,'N','D','','','',dV_p); termE2_p = SD_TERM({pterm1}); -pterm1 = GRAD(num_dims,g2,0,'N','N');% Lin's Setting + +g1 = @(x,p,t,dat) x.*(x < 0); +pterm1 = MASS(g1,'','',dV_z); termE2_z = SD_TERM({pterm1}); -termE2= MD_TERM(num_dims,{termE2_p,termE2_z}); -%% -div(flux_R) == termR1 + termR2 +termE2 = MD_TERM(num_dims,{termE2_p,termE2_z}); -% termR1 == 1/p^2 d/dp p^2 gamma(p) p / tau f(p) * (1-z^2) * f(z) -% == q(p) * r(z) -% q(p) == g1(p) u(p) [mass, g1(p) = 1/p^2, BC N/A] -% u(p) == d/dp g2(p) f(p) [grad, g2(p) = p^3 * gamma(p) / tau, BCL=N,BCR=D] -% r(z) == g3(z) f(z) [mass, g3(z) = 1-z^2, BC N/A] +%% -g1 = @(x,p,t,dat) 1./x.^2; -g2 = @(x,p,t,dat) x.^3 .* p.gamma(x) ./ p.tau; -g3 = @(x,p,t,dat) 1-x.^2; +% termE3 == div( F_z(f)\hat{z} ) +% +% MASS in p and DIV in z +% +% + +% Surface jacobian for z constant is p*sqrt(1-z^2) +dV_p = @(x,p,t,dat) x; +dV_z = @(x,p,t,dat) sqrt(1-x.^2); + +g1 = @(x,p,t,dat) 0*x+1; +pterm1 = MASS(g1,'','',dV_p); +termE3_p = SD_TERM({pterm1}); + +g1 = @(x,p,t,dat) -p.E*sqrt(1-x.^2); +pterm1 = DIV(num_dims,g1,'',-1,'N','N','','','',dV_z); +termE3_z = SD_TERM({pterm1}); +termE3 = MD_TERM(num_dims,{termE3_p,termE3_z}); + +%% R terms + +%% div(flux_R) == termR1 + termR2 -pterm1 = MASS(g1);% This is not needed - by Lin -pterm2 = GRAD(num_dims,g2,1,'N','N');% Lin's Setting +% termR1 == div( F_Rp \hat{p} ) +% +% DIV in p and MASS in z + +% Surface jacobian for p constant is p^2 +dV_p = @(x,p,t,dat) x.^2; +dV_z = @(x,p,t,dat) 0*x+1; -termR1_p = SD_TERM({pterm1,pterm2}); +g1 = @(x,p,t,dat) x .* p.gamma(x) ./ p.tau; +pterm1 = DIV(num_dims,g1,'',-1,'N','D','','','',dV_p); +termR1_p = SD_TERM({pterm1}); -pterm1 = MASS(g3); +g1 = @(x,p,t,dat) 1-x.^2; %Always positive +pterm1 = MASS(g1,'','',dV_z); termR1_z = SD_TERM({pterm1}); termR1 = MD_TERM(num_dims,{termR1_p,termR1_z}); -% termR2 == -1/(tau*gam(p)) f(p) * d/dz z(1-z^2) f(z) -% == q(p) * r(z) -% q(p) == g1(p) f(p) [mass, g1(p) = -1/(tau*gamma(p)), BC N/A] -% r(z) == d/dz g2(z) f(z) [grad, g2(z) = z(1-z^2), BCL=N,BCR=N] +% termR2 == div( F_Rz \hat{z} ) +% +% MASS in p and DIV in z -g1 = @(x,p,t,dat) -1./(p.tau.*p.gamma(x)); -g2 = @(x,p,t,dat) x.*(1-x.^2); +% Surface jacobian for z constant is p*sqrt(1-z^2) +dV_p = @(x,p,t,dat) x; +dV_z = @(x,p,t,dat) sqrt(1-x.^2); -pterm1 = MASS(g1); +g1 = @(x,p,t,dat) x./(p.tau.*p.gamma(x)); +pterm1 = MASS(g1,'','',dV_p); termR2_p = SD_TERM({pterm1}); -pterm1 = GRAD(num_dims,g2,0,'N','N');% Lin's Setting - +g1 = @(x,p,t,dat) -x.*sqrt(1-x.^2); +pterm1 = DIV(num_dims,g1,'',-1,'N','N','','','',dV_z); termR2_z = SD_TERM({pterm1}); termR2 = MD_TERM(num_dims,{termR2_p, termR2_z}); -% terms = {termC1, termC2, termC3, termE1, termE2};%, termR1, termR2}; -terms = {termE1, termE2};%, termR1, termR2}; +%terms = {termC1, termC2, termC3, termE1, termE2, termE3, termR1, termR2}; +%terms = {termC1, termC2, termC3, termR1, termR2}; +terms = {termC1, termC2, termC3, termE1, termE2, termE3}; +%terms = {termC1, termC2, termC3}; %% Define sources sources = {}; + function res = my_alpha(x,p,t) +% disp(num2str(p.alpha_z(x))); + res = p.alpha_z(x); + end + +switch opts.case_ + case 5 + source1_p = @(x,p,t,d) p.f0_p(x); + source1_z = @(x,p,t,d) my_alpha(x,p,t); + source1 = new_md_func(num_dims,{source1_p,source1_z}); + sources = {source1}; +end + %% Define function to set time step function dt=set_dt(pde,CFL) dims = pde.dimensions; diff --git a/pdes/fokkerplanck2_complete_DBC.m b/pdes/fokkerplanck2_complete_DBC.m new file mode 100644 index 00000000..acc05551 --- /dev/null +++ b/pdes/fokkerplanck2_complete_DBC.m @@ -0,0 +1,322 @@ +function pde = fokkerplanck2_complete_DBC(opts) +% Combining momentum and pitch angle dynamics +% +% Full PDE from the 2D runaway electron paper +% +% d/dt f(p,z) == -div(flux_C + flux_E + flux_R) +% +% where +% +% flux_C is flux due to electron-ion collisions +% flux_E is the flux due to E accleration +% flux_R is the flux due to radiation damping +% +% flux_C == A^2*F_C1 + F_C2 +% +% where +% +% A\hat{p} = sqrt(C_A(p))\hat{p} and A\hat{z} = 1/p*sqrt(C_B(p))\hat{z} +% +% and +% +% \F_C1 = grad(f) and \F_C2 = C_F(p)f\hat{p} +% +% +% flux_E == F_Ep(f)\hat{p} + F_Ez(f)\hat{z} +% +% where +% +% F_Ep(f) = -Ezf and F_Ez(f) = -Esqrt(1-z^2)f +% +% +% flux_R == F_Rp \hat{p} + F_Rz \hat{z} +% +% where +% +% F_Rp = gamma(p)p/tau*(1-z^2)f(z) +% F_Rz = -1/(tau*gamma(p))z*sqrt(1-z^2) f(z) +% +% Here +% +% div( A_p\hat{p} + A_z\hat{z} ) = 1/p^2*d/dp( p^2*A_p ) + 1/p*d/dz( sqrt(1-z^2)f ) +% +% +% Run with +% +% explicit +% asgard(@fokkerplanck2_complete_DBC,'CFL',0.01,'case',1) +% +% implicit +% asgard(@fokkerplanck2_complete_DBC,'timestep_method','CN','num_steps',20,'CFL',1.0,'deg',3,'lev',4,'case',1) +% +% with adaptivity +% asgard(@fokkerplanck2_complete_DBC,'timestep_method','CN','num_steps',20,'CFL',1.0,'deg',3,'lev',4, 'adapt', true,'case',1) +% +% NOTES +% +% For Lin's case the command that should reproduce her results +% asgard(@fokkerplanck2_complete_DBC,'timestep_method','BE','lev',6,'deg',5,'dt',0.01,'num_steps',3000,'time_independent_A',true,'case',1) +% +% David's adjustment can be run as follows ... +% asgard(@fokkerplanck2_complete_DBC,'timestep_method','BE','lev',3,'deg',6,'dt',1,'num_steps',50,'grid_type','FG','time_independent_A',true,'case',1) +% or, run with the high order time integrator ... +% asgard(f@okkerplanck2_complete_DBC,'timestep_method','ode15s','lev',3,'deg',5,'dt',50,'num_steps',1,'grid_type','SG','case',1) + +params = fokkerplanck_parameters(opts); + +%% Setup the dimensions + +dim_p = DIMENSION(0,opts.cmd_args.p_max); +dim_z = DIMENSION(-1,+1); +dim_p.moment_dV = @(x,p,t,dat) x.^2; +dim_z.moment_dV = @(x,p,t,dat) x.*0+1; +dimensions = {dim_p,dim_z}; +num_dims = numel(dimensions); + +%% Define the analytic solution (optional) + +solutions = {}; + +%% Define the initial conditions +ic_p = @(x,p,t) p.f0_p(x); +ic_z = @(x,p,t) p.f0_z(x); +%ic_p = @(x,p,t) 0*x+1; ic_z = @(x,p,t) 0*x+1; +ic1 = new_md_func(num_dims,{ic_p,ic_z}); +initial_conditions = {ic1}; + +BC1 = new_md_func(num_dims,{@(x,p,t) 0*x+1,@(x,p,t) 0*x+1,@(t,p) 0*t+1}); + +%% Define the terms of the PDE + +%% -div(flux_C) == termC1 + termC2 + termC3 + +%% C terms + +%% +% termC1 = LDG for q_p variable. +% +% LDG in q_p variable gives LDG in p, MASS in z +% +% becomes +% +% LDG in p +% div( A*q_p*\hat{p} ) [div , g1(p) = sqrt(C_A), BCL=D,BRC=N] +% q(p) == A*grad(f)*\hat{p} [grad, g2(p) = sqrt(C_A), BCL=N,BCR=D] +% +% MASS in z (first eqn) [mass, g1(z) = 1, BC=NA] +% (secnd eqn) [mass, g1(z) = 1, BC=NA] + +% Surface jacobian is for p constant is p^2 +DBC_tol = 1e-5; +lim0val = 1; %%% This needs to be set to lim_{p\to 0} C_A(p)*p^2 + %%% which should be a constant. +dV_p1 = @(x,p,t,dat) x.^2; +dV_p2 = @(x,p,t,dat) x.^2.*(x > DBC_tol) + 1*(x <= DBC_tol); +dV_z = @(x,p,t,dat) 0*x+1; + +% LDG in p +g1 = @(x,p,t,dat) 0*x+1; +g2 = @(x,p,t,dat) p.Ca(x).*(x > DBC_tol) + lim0val*(x <= DBC_tol); +pterm1 = DIV(num_dims,g1,'',+1,'N','N','','','',dV_p1); +pterm2 = GRAD(num_dims,g2,'',-1,'D','D',BC1,'','',dV_p2); +term1_p = SD_TERM({pterm1,pterm2}); + +% MASS in z +g1 = @(x,p,t,dat) 0*x+1; +pterm1 = MASS(g1,'','',dV_z); +term1_z = SD_TERM({pterm1,pterm1}); + +termC1 = MD_TERM(num_dims,{term1_p,term1_z}); + +%% +% termC2 == -div(Gamma_C2) +% +% Gamma_C2 = -C_F(p)f\hat{p} <-- Flow is right to left +% +% This term is DIV in p and MASS in z +% +% DIV in p +% == div( C_F(p)f\hat{p}) [div, g1(p)=C_f(p), BCL=N, BCR=D] +% +% MASS in z [mass, g1(z) = 1, BC=NA] + +% Surface jacobian for p constant is p^2 +dV_p = @(x,p,t,dat) x.^2; +dV_z = @(x,p,t,dat) 0*x+1; + +% DIV in p +g1 = @(x,p,t,dat) p.Cf(x); +pterm1 = DIV(num_dims,g1,'',-1,'N','D','','','',dV_p); +term2_p = SD_TERM({pterm1}); + +% MASS in z +g1 = @(x,p,t,dat) 0*x+1; +pterm1 = MASS(g1,'','',dV_z); +term2_z = SD_TERM({pterm1}); + +termC2 = MD_TERM(num_dims,{term2_p,term2_z}); + +%% +% termC3 = LDG for q_z variable. +% +% LDG in q_z variable gives MASS in p, LDG in z +% +% becomes +% MASS in p (first eqn) [mass, g1(p) = sqrt(C_b(p)), BC=NA] +% (secnd eqn) [mass, g1(p) = sqrt(C_b(p)), BC=NA] +% +% LDG in z +% div( A*q_z*\hat{z} ) [div , g1(p) = 1, BCL=D,BRC=N] +% q(p) == A*grad(f)*\hat{z} [grad, g2(p) = 1, BCL=N,BCR=D] +% + +% Surface jacobian for z constnat is p*sqrt(1-z^2) +dV_p = @(x,p,t,dat) x; +dV_z = @(x,p,t,dat) sqrt(1-x.^2); + +% MASS in p + +g1 = @(x,p,t,dat) min(sqrt(p.Cb(x))./x,1e7); %Limiting so we don't get 0/0. +pterm1 = MASS(g1,'','',dV_p); +term3_p = SD_TERM({pterm1,pterm1}); + +% LDG in z +g1 = @(x,p,t,dat) x.*0+1; +pterm1 = DIV(num_dims,g1,'',+1,'D','D','','','',dV_z); +pterm2 = GRAD(num_dims,g1,'',-1,'N','N','','','',dV_z); +term3_z = SD_TERM({pterm1,pterm2}); + +termC3 = MD_TERM(num_dims,{term3_p,term3_z}); + +%% E terms + +%% div(flux_E) == termE1 + termE2 + +%% + +% termE1+E2 == div( F_p(f)\hat{p} ) +% +% DIV in p and MASS in z +% +% Since z changes sign on [-1,1] we have to split the term into two terms +% and upwind based on the sign of z. + +% Surface jacobian for p constant is p^2 +dV_p = @(x,p,t,dat) x.^2; +dV_z = @(x,p,t,dat) 0*x+1; + +% Term for z>0, then |z| = z and we use standard upwinding. + +g1 = @(x,p,t,dat) 0*x-p.E; +pterm1 = DIV(num_dims,g1,'',-1,'D','N','','','',dV_p); +termE1_p = SD_TERM({pterm1}); + +g1 = @(x,p,t,dat) x.*(x > 0); +pterm1 = MASS(g1,'','',dV_z); +termE1_z = SD_TERM({pterm1}); + +termE1 = MD_TERM(num_dims,{termE1_p,termE1_z}); + +% Term for z<0. +% If z < 0, then |z| = -z. +% Assume f(p,z) = f_p(p)f_z(z) and v(p,z) = v_p(p)v_z(z). +% Let <.,.>_p be the edge integral in p and (.,.)_z be the volume integral +% in z. +% Standard upwinding jump flux becomes +% <|Ez|[f],[v]>_{z,p} = <|E|[f_p],[v_p]>_p(|z|f_z,v_z)_z +% = -<|E|[f_p],[v_p]>_p( z f_z,v_z)_z +% So we downwind in p when z is negative. + +g1 = @(x,p,t,dat) 0*x-p.E; +pterm1 = DIV(num_dims,g1,'',+1,'N','D','','','',dV_p); +termE2_p = SD_TERM({pterm1}); + +g1 = @(x,p,t,dat) x.*(x < 0); +pterm1 = MASS(g1,'','',dV_z); +termE2_z = SD_TERM({pterm1}); + +termE2 = MD_TERM(num_dims,{termE2_p,termE2_z}); + +%% + +% termE3 == div( F_z(f)\hat{z} ) +% +% MASS in p and DIV in z +% +% + +% Surface jacobian for z constant is p*sqrt(1-z^2) +dV_p = @(x,p,t,dat) x; +dV_z = @(x,p,t,dat) sqrt(1-x.^2); + +g1 = @(x,p,t,dat) 0*x+1; +pterm1 = MASS(g1,'','',dV_p); +termE3_p = SD_TERM({pterm1}); + +g1 = @(x,p,t,dat) -p.E*sqrt(1-x.^2); +pterm1 = DIV(num_dims,g1,'',-1,'N','N','','','',dV_z); +termE3_z = SD_TERM({pterm1}); +termE3 = MD_TERM(num_dims,{termE3_p,termE3_z}); + +%% R terms + +%% div(flux_R) == termR1 + termR2 + +% termR1 == div( F_Rp \hat{p} ) +% +% DIV in p and MASS in z + +% Surface jacobian for p constant is p^2 +dV_p = @(x,p,t,dat) x.^2; +dV_z = @(x,p,t,dat) 0*x+1; + +g1 = @(x,p,t,dat) x .* p.gamma(x) ./ p.tau; +pterm1 = DIV(num_dims,g1,'',-1,'N','D','','','',dV_p); +termR1_p = SD_TERM({pterm1}); + +g1 = @(x,p,t,dat) 1-x.^2; %Always positive +pterm1 = MASS(g1,'','',dV_z); +termR1_z = SD_TERM({pterm1}); + +termR1 = MD_TERM(num_dims,{termR1_p,termR1_z}); + +% termR2 == div( F_Rz \hat{z} ) +% +% MASS in p and DIV in z + +% Surface jacobian for z constant is p*sqrt(1-z^2) +dV_p = @(x,p,t,dat) x; +dV_z = @(x,p,t,dat) sqrt(1-x.^2); + +g1 = @(x,p,t,dat) x./(p.tau.*p.gamma(x)); +pterm1 = MASS(g1,'','',dV_p); +termR2_p = SD_TERM({pterm1}); + +g1 = @(x,p,t,dat) -x.*sqrt(1-x.^2); +pterm1 = DIV(num_dims,g1,'',-1,'N','N','','','',dV_z); +termR2_z = SD_TERM({pterm1}); + +termR2 = MD_TERM(num_dims,{termR2_p, termR2_z}); + +terms = {termC1, termC2, termC3, termE1, termE2, termE3, termR1, termR2}; + +%% Define sources + +sources = {}; + +%% Define function to set time step + function dt=set_dt(pde,CFL) + dims = pde.dimensions; + xRange = dims{1}.max-dims{1}.min; + lev = dims{1}.lev; + dx = xRange/2^lev; + dt = CFL * dx; + end + +%% Construct PDE + +pde = PDE(opts,dimensions,terms,[],sources,params,@set_dt,[],initial_conditions,solutions); + +end + + diff --git a/pdes/fokkerplanck_parameters.m b/pdes/fokkerplanck_parameters.m index f17a5d53..f30f8df5 100644 --- a/pdes/fokkerplanck_parameters.m +++ b/pdes/fokkerplanck_parameters.m @@ -26,6 +26,12 @@ Z = 5; E = 0.4; tau = 10^5; + case 5 % for the runaway production rate electric field scan + delta = 0.044; + Z = 1; + E = opts.cmd_args.E; + tau = 1.2e5; + alpha_z = @(z) z.*0; end phi = @phi_; @@ -77,6 +83,8 @@ end case 4 ret = x.*0 + 1; + case 5 + ret = x.*0 + 1; end end @@ -111,6 +119,9 @@ Q = Q+sum(w.*Fun(xi).*xi.^2); end ret = exp(-2/delta^2*sqrt(1+delta^2*x.^2))/(2*Q); + case 5 + a = 1; + ret = 2/(sqrt(pi)*a^3) * exp(-x.^2/a^2); end end diff --git a/pdes/fokkerplanck_test.m b/pdes/fokkerplanck_test.m index 561c04ac..7e2a1a8b 100644 --- a/pdes/fokkerplanck_test.m +++ b/pdes/fokkerplanck_test.m @@ -15,7 +15,7 @@ function fp1_C_pitch_test(testCase) [err,fval,fval_realspace,nodes,err_realspace] = asgard_run_pde(opts,pde); % assert on correctness rel_err = err / norm(fval); -verifyLessThan(testCase,rel_err,1e-5); +verifyLessThan(testCase,rel_err,3e-4); end function fp1_E_pitch_test(testCase) @@ -46,7 +46,7 @@ function fp1_E_pitch_test(testCase) [err,fval,fval_realspace,nodes,err_realspace] = asgard_run_pde(opts,pde); % assert on correctness rel_err = err / norm(fval); -verifyLessThan(testCase,rel_err,1e-4); +verifyLessThan(testCase,rel_err,3e-5); end function fp1_R_pitch_test(testCase) @@ -112,7 +112,7 @@ function fp1_CE_pitch_test(testCase) [err,fval,fval_realspace,nodes,err_realspace] = asgard_run_pde(opts,pde); % assert on correctness rel_err = err / norm(fval); -verifyLessThan(testCase,rel_err,1e-5); +verifyLessThan(testCase,rel_err,4e-5); % setup PDE - case 2 args = {'lev',4,'deg',6,'dt',50e-1,'quiet',true,'num_steps',10,'timestep_method','matrix_exponential','case',2}; @@ -162,7 +162,7 @@ function fp1_CER_pitch_test(testCase) [err,fval,fval_realspace,nodes,err_realspace,output] = asgard_run_pde(opts,pde); % assert on correctness rel_err = output.rel_err{end}; -verifyLessThan(testCase,rel_err,1e-5); +verifyLessThan(testCase,rel_err,3e-5); end @@ -194,14 +194,14 @@ function fp1_C_momentum_test(testCase) end -function fp1_C_momentum_LHS_test(testCase) +function fp1_C_momentum_test_2(testCase) addpath(genpath(pwd)); -disp('Testing the momentum dimension for C terms within fokkerplanck1_LHS'); +disp('Testing the momentum dimension for C terms within fokkerplanck1'); % setup PDE - case 1 (Maxwellian initial condition) args = {'lev',4,'deg',4,'dt',2,'quiet',true,'num_steps',50,'timestep_method','BE','case',1,'normalize_by_mass',false}; opts = OPTS(args); -pde = fokkerplanck1_momentum_C_LHS(opts); +pde = fokkerplanck1_momentum_C(opts); % modify PDE - not needed here % run PDE [err,fval,fval_realspace,nodes,err_realspace,output] = asgard_run_pde(opts,pde); @@ -212,7 +212,7 @@ function fp1_C_momentum_LHS_test(testCase) % setup PDE - case 2 (step function initial condition) args = {'lev',4,'deg',4,'dt',2,'quiet',true,'num_steps',50,'timestep_method','BE','case',2,'normalize_by_mass',false}; opts = OPTS(args); -pde = fokkerplanck1_momentum_C_LHS(opts); +pde = fokkerplanck1_momentum_C(opts); % modify PDE - not needed here % run PDE [err,fval,fval_realspace,nodes,err_realspace,output] = asgard_run_pde(opts,pde); @@ -227,7 +227,7 @@ function fp2_C_test(testCase) disp('Testing the momentum and pitch dimensions for term C within fokkerplanck2_C'); % setup PDE - case 1 (Step function initial condition) -args = {'lev',4,'deg',5,'dt',500,'quiet',true,'num_steps',1,'timestep_method','matrix_exponential','case',1,'normalize_by_mass',false}; +args = {'lev',4,'deg',5,'dt',500,'quiet',true,'num_steps',1,'timestep_method','matrix_exponential','case',1,'normalize_by_mass',true}; opts = OPTS(args); pde = fokkerplanck2_C(opts); % modify PDE - not needed here @@ -263,7 +263,7 @@ function fp1_E_momentum_test(testCase) [err,fval,fval_realspace,nodes,err_realspace,output] = asgard_run_pde(opts,pde); % assert on correctness rel_err = output.rel_err{end}; -verifyLessThan(testCase,rel_err,1e-4); +verifyLessThan(testCase,rel_err,1e-10); % setup PDE - case 2 (Maxwellian initial condition) args = {'lev',4,'deg',5,'dt',0.1,'quiet',true,'num_steps',1,'timestep_method','matrix_exponential','case',2,'normalize_by_mass',false}; @@ -274,7 +274,7 @@ function fp1_E_momentum_test(testCase) [err,fval,fval_realspace,nodes,err_realspace,output] = asgard_run_pde(opts,pde); % assert on correctness rel_err = output.rel_err{end}; -verifyLessThan(testCase,rel_err,1e-4); +verifyLessThan(testCase,rel_err,1e-5); end @@ -294,7 +294,7 @@ function fp2_E_test(testCase) verifyLessThan(testCase,rel_err,1e-12); % setup PDE - case 3 (manufactured solution) -args = {'lev',4,'deg',4,'dt',0.01,'quiet',false,'num_steps',1,'timestep_method','BE','case',3,'normalize_by_mass',false}; +args = {'lev',4,'deg',4,'dt',0.01,'quiet',true,'num_steps',1,'timestep_method','BE','case',3,'normalize_by_mass',false}; opts = OPTS(args); pde = fokkerplanck2_E(opts); % modify PDE - not needed here @@ -304,32 +304,4 @@ function fp2_E_test(testCase) rel_err = output.rel_err{end}; verifyLessThan(testCase,rel_err,1e-5); -end - -function fp2_E_LHS_test(testCase) -addpath(genpath(pwd)); -disp('Testing term E in 2D within fokkerplanck2_E'); - -% setup PDE - case 1 (flat function initial condition - solution does not change) -args = {'lev',4,'deg',4,'dt',0.01,'quiet',true,'num_steps',1,'timestep_method','matrix_exponential','case',1,'normalize_by_mass',false}; -opts = OPTS(args); -pde = fokkerplanck2_E_LHS(opts); -% modify PDE - not needed here -% run PDE -[err,fval,fval_realspace,nodes,err_realspace,output] = asgard_run_pde(opts,pde); -% assert on correctness -rel_err = output.rel_err{end}; -verifyLessThan(testCase,rel_err,1e-12); - -% setup PDE - case 3 (manufactured solution) -args = {'lev',4,'deg',4,'dt',0.01,'quiet',false,'num_steps',1,'timestep_method','BE','case',3,'normalize_by_mass',false}; -opts = OPTS(args); -pde = fokkerplanck2_E_LHS(opts); -% modify PDE - not needed here -% run PDE -[err,fval,fval_realspace,nodes,err_realspace,output] = asgard_run_pde(opts,pde); -% assert on correctness -rel_err = output.rel_err{end}; -verifyLessThan(testCase,rel_err,1e-5); - end \ No newline at end of file diff --git a/pdes/lb_collision.m b/pdes/lb_collision.m new file mode 100644 index 00000000..71617c59 --- /dev/null +++ b/pdes/lb_collision.m @@ -0,0 +1,114 @@ +function pde = lb_collision(opts) +% Lenard-Bernstein Equation in 1D +% +% PDE: +% +% df/dt = div( (v-u)f + th\grad f) +% +% Domain is [0,1]x[0,1] +% Dirichlet boundary condition in advection +% Neumann boundary condition in diffusion +% +% Diffusion terms are dealt with via LDG +% +% Run with +% +% explicit +% asgard(@lb_collision,'CFL',0.01); +% +% implicit +% asgard(@lb_collision,'timestep_method','BE','dt',0.001,'num_steps',20) + +%% Define the dimensions + +params.n = 2; +params.u = 0; +params.th = 1; + +dim_x = DIMENSION(-5,5); +dim_x.moment_dV = @(x,p,t,dat) 0*x+1; +dimensions = {dim_x}; +num_dims = numel(dimensions); + +%% Define the analytic solution (optional). + +soln_x = @(x,p,t) p.n/sqrt(2*pi*p.th)*exp(-(x-p.u).^2/(2*p.th)); +soln_t = @(t,p) 0*t+1; +soln1 = new_md_func(num_dims,{soln_x,soln_t}); + +solutions = {soln1}; + +%% Define the boundary conditions + +BCL = new_md_func(num_dims,{@(x,p,t,dat) 0*x,@(t,p) 0*t+1}); +BCR = new_md_func(num_dims,{@(x,p,t,dat) 0*x,@(t,p) 0*t+1}); + +%% Initial conditions + +ic_x = @(x,p,t,d) (x > -3) - (x > -1); +ic_t = @(t,p) 0*t+1; +ic = new_md_func(num_dims,{ic_x,ic_t}); +initial_conditions = {ic}; + +%% Define the terms of the PDE +% +% Here we have 1 term, with each term having nDims (x and y) operators. + +dV = @(x,p,t,dat) 0*x+1; + +%% +% Setup the advection div( (v-u)f ) + +g1 = @(x,p,t,dat) x-p.u; + +pterm1 = DIV(num_dims,g1,'',-1,'D','D',BCL,BCR,'',dV); +term1_x = SD_TERM({pterm1}); + +term1 = MD_TERM(num_dims,{term1_x}); + +%% +% Setup the diffusion term div(theta\grad f) term + +% div(theta\grad f) is the system +% +% div(sqrt(theta)q) +% +% q = sqrt(theta)\grad f + +g1 = @(x,p,t,dat) x.*0+sqrt(p.th); +g2 = @(x,p,t,dat) x.*0+sqrt(p.th); + +pterm1 = DIV(num_dims,g1,'',+1,'D','D',BCL,BCR,'',dV); +pterm2 = GRAD(num_dims,g2,'',-1,'N','N','','','',dV); +term1_x = SD_TERM({pterm1,pterm2}); + +term2 = MD_TERM(num_dims,{term1_x}); + +terms = {term1, term2}; + +%% Define some parameters and add to pde object. +% These might be used within the various functions below. + +params.parameter1 = 0; +params.parameter2 = 1; + +%% Define sources + +sources = {}; + +%% Define a function to set dt + + function dt=set_dt(pde,CFL) + dims = pde.dimensions; + % for Diffusion equation: dt = C * dx^2 + lev = dims{1}.lev; + dx = 1/2^lev; + dt = CFL*dx^2; + end + +%% Construct PDE + +pde = PDE(opts,dimensions,terms,[],sources,params,@set_dt,[],initial_conditions,solutions); + +end + diff --git a/pdes/mirror1_collision.m b/pdes/mirror1_collision.m new file mode 100644 index 00000000..b9997cc8 --- /dev/null +++ b/pdes/mirror1_collision.m @@ -0,0 +1,107 @@ +function pde = mirror1_collision(opts) + +%Testing the collision operator for the 1D form of the mirror equations +% +% df/dt = 1/v^2 (flux_v) +% +% flux_v == v^3[(m_a/(m_a + m_b))nu_s f) + 0.5*nu_par*v*d/dv(f)] +% +% df/dt = 1/v^2 (d/dv(v^3[(m_a/(m_a + m_b))nu_s f) + 0.5*nu_par*v*d/dv(f)])*v^2 +% +% Run with +% +% asgard(@mirror1_collision,'timestep_method','BE','dt',1e-5,'num_steps',50,'lev',5,'deg',2,'normalize_by_mass',false, 'calculate_mass', false) + +params = mirror_parameters(); + +%% Define the dimensions + +dim_v = DIMENSION(0,1e6); +dim_v.jacobian = @(v,p,t) 4*pi.*v.^2; +dimensions = {dim_v}; +num_dims = numel(dimensions); + +%% Define the analytic solution (optional) + +% function ret = solution(v,p,t) +% ret = p.soln_v(v,p,t); +% if isfield(p,'norm_fac') +% ret = p.norm_fac .* ret; +% end +% end +soln_v = @solution_v; + function ret = solution_v(v,p,t) + ret = p.maxwell(v,0,p.v_th(p.b.T_eV,p.a.m)); + if isfield(p,'norm_fac') + ret = p.norm_fac .* ret; + end + end + +soln1 = new_md_func(num_dims,{soln_v}); +solutions = {soln1}; + +%% Define the initial conditions + +ic_v = @(v,p,t) p.init_cond_v(v); +ic1 = new_md_func(num_dims,{ic_v}); +initial_conditions = {ic1}; + +%% Define the boundary conditions + +%% Define the boundary conditions + +BCL = new_md_func(num_dims,{... + @(v,p,t) v.*0, ... + params.boundary_cond_t}); + + +BCR = new_md_func(num_dims,{... + params.boundary_cond_v, ... + params.boundary_cond_t}); + +% term V1 == 1/v^2 d/dv(v^3(m_a/(m_a + m_b))nu_s f)) +% term V1 == g(v) q(v) [mass, g(v) = 1/v^2, BC N/A] +% q(v) == d/dv(g2(v)f(v)) [grad, g2(v) = v^3(m_a/(m_a + m_b))nu_s, BCL= N, BCR=N] + +g1 = @(v,p,t,dat) 1./v.^2;%v.*0 + 1; +g2 = @(v,p,t,dat) v.^3*p.a.m.*p.nu_s(v,p.a,p.b)./(p.a.m + p.b.m); + +pterm1 = MASS(g1); +pterm2 = GRAD(num_dims,g2,0,'N','D', BCL, BCR); +termV_s = SD_TERM({pterm1,pterm2}); +termV1 = MD_TERM(num_dims,{termV_s}); + +%% +% term V2 == 1/v^2 d/dv(v^4*0.5*nu_par*d/dv(f)) +% term V2 == g(v) q(v) [mass, g(v) = 1/v^2, BC N/A] +% q(v) == d/dv(g2(v)r(v)) [grad, g2(v) = v^4*0.5*nu_par, BCL= D, BCR=D] +% r(v) = d/dv(g3(v)f) [grad, g3(v) = 1, BCL=N, BCR=N] + +g1 = @(v,p,t,dat) 1./v.^2; %v.*0 + 1; +g2 = @(v,p,t,dat) v.^4.*0.5.*p.nu_par(v,p.a,p.b); +g3 = @(v,p,t,dat) v.*0 + 1; + +pterm1 = MASS(g1); +pterm2 = GRAD(num_dims,g2,-1,'D','N'); +pterm3 = GRAD(num_dims,g3,+1,'N','D', BCL, BCR); +termV_par = SD_TERM({pterm1,pterm2,pterm3}); +termV2 = MD_TERM(num_dims,{termV_par}); + +terms = {termV1,termV2}; + +%% Define sources + +sources = {}; + +%% Define function to set time step + function dt=set_dt(pde,CFL) + Lmax = pde.dimensions{1}.max; + LevX = pde.dimensions{1}.lev; + dt = Lmax/2^LevX*CFL; + end + +%% Construct PDE + +pde = PDE(opts,dimensions,terms,[],sources,params,@set_dt,[],initial_conditions,solutions); + +end \ No newline at end of file diff --git a/pdes/mirror1_collision_div.m b/pdes/mirror1_collision_div.m new file mode 100644 index 00000000..afb92a93 --- /dev/null +++ b/pdes/mirror1_collision_div.m @@ -0,0 +1,157 @@ +function pde = mirror1_collision_div(opts) + +%Testing the collision operator for the 1D form of the mirror equations +% +% df/dt == 1/v^2 (d/dv(v^2[v (m_a/(m_a + m_b))nu_s f) + 0.5*nu_par*v^2*d/dv(f)]) +% == 1/v^2 (d/dv (v^2[0.5*nu_par*v^2*d/dv(f)]) %%term1 +% + 1/v^2 (d/dv(v^2[v (m_a/(m_a + m_b))nu_s f)]) %%term2 + % +% v is a spherical coordinate (v,th,phi), so the div and grad look like +% +% div[] = 1/v^2 * d/dv * v^2[], grad[] = d/dv[] +% +% and the volument_element dV = v^2 +% +% +% split into two div(flux) terms (term1 and term2) +% +% term1 is done using SLDG defining A(v)= sqrt(0.5*nu_par*v^2) +% +% eq1 : df/dt == div(A(v) * q) [pterm1: div (g(v)=A(v),+1, BCL=?, BCR=?)] +% eq2 : q == A(v) * grad(f) [pterm2: grad(g(v)=A(v),-1, BCL=D, BCR=N)] +% +% term2 is a div using B(v) = v (m_a/(m_a + m_b))nu_s +% +% eq1 : df/dt == div(B(v) * f) [pterm1: div(g(p)=B(v),+1, BCL=?, BCR=?] +% +% +% Run with +% +% asgard(@mirror1_collision_div,'timestep_method','BE','dt',1e-5,'num_steps',50,'lev',5,'deg',2,'normalize_by_mass',false, 'calculate_mass', false) + +params = mirror_parameters(opts); + +%% Define the dimensions + +dim_v = DIMENSION(0,1e6); +dV_v = @(x,p,t,d) x.^2; +dim_v.moment_dV = dV_v; +dimensions = {dim_v}; +num_dims = numel(dimensions); + +%% Define the analytic solution (optional) + +% function ret = solution(v,p,t) +% ret = p.soln_v(v,p,t); +% if isfield(p,'norm_fac') +% ret = p.norm_fac .* ret; +% end +% end +soln_v = @solution_v; + function ret = solution_v(v,p,t) + ret = p.maxwell(v,0,p.v_th(p.b.T_eV,p.a.m),p.a)./p.a.n; + if isfield(p,'norm_fac') + ret = p.norm_fac .* ret; + end + end + +soln1 = new_md_func(num_dims,{soln_v}); +solutions = {soln1}; + +%% Define the initial conditions + +ic_v = @(v,p,t) p.init_cond_v(v)./p.a.n; +ic1 = new_md_func(num_dims,{ic_v}); +initial_conditions = {ic1}; + +%% LHS terms (mass only) + +LHS_terms = {}; + +%% Define the boundary conditions + +%% Define the boundary conditions + +BCL = new_md_func(num_dims,{... + @(v,p,t) v.*0, ... + params.boundary_cond_t}); + + +BCR = new_md_func(num_dims,{... + params.boundary_cond_v, ... + params.boundary_cond_t}); + + +%% +% term1 is done using SLDG defining A(v)= sqrt(0.5*nu_par*v^2) +% +% eq1 : df/dt == div(A(v) * q) [pterm1: div (g(v)=A(v),+1, BCL=?, BCR=?)] +% eq2 : q == A(v) * grad(f) [pterm2: grad(g(v)=A(v),-1, BCL=D, BCR=N)] + +A = @(v,p) sqrt(0.5.*v.^2.*p.nu_par(v,p.a,p.b)); +g1 = @(v,p,t,dat) A(v,p); +g2 = @(v,p,t,dat) A(v,p); + +pterm1 = DIV (num_dims,g1,'',+1,'D','N','','','',dV_v); +pterm2 = GRAD(num_dims,g2,'',-1,'N','D','','','',dV_v); +term1_v = SD_TERM({pterm1,pterm2}); +term1 = MD_TERM(num_dims,{term1_v}); + +% term2 is a div using B(v) = v (m_a/(m_a + m_b))nu_s +% +% eq1 : df/dt == div(B(v) * f) [pterm1: div(g(p)=B(v),+1, BCL=?, BCR=?] + +B = @(v,p) v*p.a.m.*p.nu_s(v,p.a,p.b)./(p.a.m + p.b.m); +g3 = @(v,p,t,dat) B(v,p); + +pterm3 = DIV(num_dims,g3,'',-1,'N','D','','','',dV_v); + +term2_v = SD_TERM({pterm3}); +term2 = MD_TERM(num_dims,{term2_v}); + +%repeating but adding second background species + +% term3 is done using SLDG defining A(v)= sqrt(0.5*nu_par*v^2) +% +% eq1 : df/dt == div(A(v) * q) [pterm1: div (g(v)=A(v),+1, BCL=?, BCR=?)] +% eq2 : q == A(v) * grad(f) [pterm2: grad(g(v)=A(v),-1, BCL=D, BCR=N)] + +A = @(v,p) sqrt(0.5.*v.^2.*p.nu_par(v,p.a,p.b2)); +g1 = @(v,p,t,dat) A(v,p); +g2 = @(v,p,t,dat) A(v,p); + +pterm1 = DIV (num_dims,g1,'',+1,'D','N','','','',dV_v); +pterm2 = GRAD(num_dims,g2,'',-1,'N','D','','','',dV_v); +term3_v = SD_TERM({pterm1,pterm2}); +term3 = MD_TERM(num_dims,{term3_v}); + +% term4 is a div using B(v) = v (m_a/(m_a + m_b2))nu_s +% +% eq1 : df/dt == div(B(v) * f) [pterm1: div(g(p)=B(v),+1, BCL=?, BCR=?] + +B = @(v,p) v*p.a.m.*p.nu_s(v,p.a,p.b2)./(p.a.m + p.b2.m); +g3 = @(v,p,t,dat) B(v,p); + +pterm3 = DIV(num_dims,g3,'',-1,'N','D','','','',dV_v); + +term4_v = SD_TERM({pterm3}); +term4 = MD_TERM(num_dims,{term4_v}); + +terms = {term1,term2,term3,term4}; + +%% Define sources + +sources = {}; + +%% Define function to set time step + function dt=set_dt(pde,CFL) + Lmax = pde.dimensions{1}.max; + LevX = pde.dimensions{1}.lev; + dt = Lmax/2^LevX*CFL; + end + +%% Construct PDE + +pde = PDE(opts,dimensions,terms,LHS_terms,sources,params,@set_dt,[],initial_conditions,solutions); + +end \ No newline at end of file diff --git a/pdes/mirror1_pitch.m b/pdes/mirror1_pitch.m index 8c9c4cea..405907b4 100644 --- a/pdes/mirror1_pitch.m +++ b/pdes/mirror1_pitch.m @@ -6,10 +6,10 @@ % distribution that has a Maxwellian form. % PDE: % -% df/dt == nu_D/(2*sin(z)) d/dz ( sin(z) df/dz ) +% df/dt == -cos(z)*f + nu_D/(2*sin(z)) d/dz ( sin(z) df/dz ) % % nu_D is the deflection frequency -% Domain is [-pi,pi] +% Domain is [0,pi] % Homogeneous Neumann boundary condition % Code will be added to equation involving velocity dimension % @@ -19,7 +19,7 @@ % Run with % % implicit -% asgard(@mirror1_pitch,'timestep_method','matrix_exponential','dt',5e-7,'num_steps',20,'lev',3,'deg',3); +% asgard(@mirror1_pitch,'timestep_method','BE','dt',5e-7,'num_steps',20,'lev',3,'deg',3, 'calculate_mass', true, 'normalize_by_mass', true); % function ret = psi(x) @@ -31,29 +31,29 @@ end %Background Parameters -k_b = 1.380*10^-23; %Boltzmann constant in Joules/Kelvin +boltz = 1.380*10^-23; %Boltzmann constant in Joules/Kelvin n_b = 10^19; %background density in SI units (particles/m.^3) -T_b = 116050; %background temperature in Kelvin -z_b = 1; %atomic number of background specie +temp_b = 116050; %background temperature in Kelvin +% z_b = 1; %atomic number of background specie m_b = 9.109*10^-31; %background mass in kg -v_b = sqrt(2*k_b*T_b/m_b); %background velocity in m/s -eps_o = 8.85*10^-12; %permittivity of free space in Farad/m - -%Target Specie Parameters -z_a = 1; -e = 1.602*10^-19; %charge in Coulombs -ln_Delt = 10; %Coulomb logarithm -m_a = 1.6726*10^-27; %target mass in kg -L_ab = (e^2/(m_a*eps_o))^2; %Coefficient accounting for Coluomb force +v_b = sqrt(2*boltz*temp_b/m_b); %background velocity in m/s +% eps_o = 8.85*10^-12; %permittivity of free space in Farad/m +% +% %Target Specie Parameters +% z_a = 1; +% e = 1.602*10^-19; %charge in Coulombs +% ln_Delt = 10; %Coulomb logarithm +% m_a = 1.6726*10^-27; %target mass in kg +% coeff_ab = (e^2/(m_a*eps_o))^2; %Coefficient accounting for Coluomb force nu_D = 10^4; %deflection frequency in s^-1 %Initial parameters for target specie -n_o = 0.5*n_b; %initial number density for specie at specific velocity -v_o = 0.5*v_b; %initial known velocity + n_o = 0.5*n_b; %initial number density for specie at specific velocity + v_o = 0.5*v_b; %initial known velocity %% Define the dimensions -dim_z = DIMENSION(0,pi/2); +dim_z = DIMENSION(0,pi); dim_z.jacobian = @(z,p,t) sin(z); dimensions = {dim_z}; num_dims = numel(dimensions); @@ -83,15 +83,30 @@ % Here we have 1 term1, having only nDims=1 (x) operators. %% -% termC == nu_D/(2*sin(z))*d/dz sin(z)*df/dz + +% LHS_term == df/dt sin(z) +g1 = @(z,p,t,dat) dim_z.jacobian(z,p,t); +pterm1 = MASS(g1); +LHS_term_z = SD_TERM({pterm1}); +LHS_term = MD_TERM(num_dims,{LHS_term_z}); +LHS_terms = {LHS_term}; + +%term V2 == -cos(z)*f +%term V2 == g1(v)*f [mass, g1(v) = -cos(z), BC = N/A] +g1 = @(z,p,t,dat) -cos(z); +pterm1 = MASS(g1); +termM_z = SD_TERM({pterm1}); +termM= MD_TERM(num_dims,{termM_z}); + +% termC == nu_D/(2sin(z))*d/dz sin(z)*df/dz % % becomes % -% termC == g1(z) q(z) [mass, g1(p) = nu_D/(2*sin(z)), BC N/A] +% termC == g1(z) q(z) [mass, g1(p) = nu_D/2, BC N/A] % q(p) == d/dz g2(z) r(z) [grad, g2(p) = sin(z), BCL=N,BCR=D] % r(p) == d/dp g3(z) f(z) [grad, g3(p) = 1, BCL=D,BCR=N] -g1 = @(z,p,t,dat) nu_D./(2*sin(z)); +g1 = @(z,p,t,dat) nu_D./(2.*sin(z)); g2 = @(z,p,t,dat) sin(z); g3 = @(z,p,t,dat) z.*0 + 1; pterm1 = MASS(g1); @@ -100,7 +115,7 @@ termC_z = SD_TERM({pterm1,pterm2,pterm3}); termC = MD_TERM(num_dims,{termC_z}); -terms = {termC}; +terms = {termM,termC}; %% Define some parameters and add to pde object. % These might be used within the various functions below. diff --git a/pdes/mirror1_pitch_div.m b/pdes/mirror1_pitch_div.m new file mode 100644 index 00000000..90a61d18 --- /dev/null +++ b/pdes/mirror1_pitch_div.m @@ -0,0 +1,133 @@ +function pde = mirror1_pitch_div(opts) +% PDE using the 1D Diffusion Equation for a case involving pitcha angle to axis \ +% of the magnetic field line in a mirror configuration. This PDE is +% time dependent (although not all the terms are time dependent). The test +% particle is a hydrogen ion colliding with a background electron +% distribution that has a Maxwellian form. +% PDE: +% +% df/dt == -cos(z)*f + 1/sin(z) d/dz ( sin(z) nu_D/2 df/dz ) +% +% nu_D is the deflection frequency +% Domain is [0,pi] +% Homogeneous Neumann boundary condition +% Code will be added to equation involving velocity dimension +% +% Diffusion term is dealt with via LDG, i.e., splitting into two first +% order equations +% +% Run with +% +% implicit +% asgard(@mirror1_pitch_div,'timestep_method','BE','dt',5e-7,'num_steps',20,'lev',3,'deg',3, 'calculate_mass', true, 'normalize_by_mass', true); +% + + function ret = psi(x) + + phi = erf(x); + dphi_dx = 2./sqrt(pi) * exp(-x.^2); + + ret = 1./(2*x.^2) .* (phi - x.*dphi_dx); + end + +%Background Parameters +boltz = 1.380*10^-23; %Boltzmann constant in Joules/Kelvin +n_b = 10^19; %background density in SI units (particles/m.^3) +temp_b = 116050; %background temperature in Kelvin +% z_b = 1; %atomic number of background specie +m_b = 9.109*10^-31; %background mass in kg +v_b = sqrt(2*boltz*temp_b/m_b); %background velocity in m/s +% eps_o = 8.85*10^-12; %permittivity of free space in Farad/m +% +% %Target Specie Parameters +% z_a = 1; +% e = 1.602*10^-19; %charge in Coulombs +% ln_Delt = 10; %Coulomb logarithm +% m_a = 1.6726*10^-27; %target mass in kg +% coeff_ab = (e^2/(m_a*eps_o))^2; %Coefficient accounting for Coluomb force +nu_D = 10^4; %deflection frequency in s^-1 + +%Initial parameters for target specie + n_o = 0.5*n_b; %initial number density for specie at specific velocity + v_o = 0.5*v_b; %initial known velocity + +%% Define the dimensions + +dim_th = DIMENSION(0,pi); +dV_th = @(x,p,t,d) sin(x); +dim_th.moment_dV = dV_th; + +dimensions = {dim_th}; +num_dims = numel(dimensions); + +%% Define the analytic solution (optional) + +soln_z = @(z,p,t) n_o.*cos(z); +soln_t = @(t,p) exp(-nu_D*t); +soln1 = new_md_func(num_dims,{soln_z,soln_t}); +solutions = {soln1}; + +%% Define the initial conditions + +ic1 = soln1; +initial_conditions = {ic1}; + +%% Define the boundary conditions + +bcl_x = @(x,p,t) x.*0; +bcl_t = soln_t; +BCL = new_md_func(num_dims,{bcl_x,bcl_t}); + +BCR = soln1; + +%% Define the terms of the PDE +% +% Here we have 1 term1, having only nDims=1 (x) operators. + +%% + +%term V2 == -cos(z)*f +%term V2 == g1(v)*f [mass, g1(v) = -cos(z), BC = N/A] +g1 = @(z,p,t,dat) -cos(z); +pterm1 = MASS(g1,'','',dV_th); +termM_z = SD_TERM({pterm1}); +termM = MD_TERM(num_dims,{termM_z}); + +% termC is done using SLDG defining C(v) = sqrt(nu_D(v)/2) +% +% eq1 : df/dt == div( q) [pterm1: div (g(v)=C(v),+1, BCL=D, BCR=D] +% eq2 : q == grad(f) [pterm2: grad(g(v)=C(v),-1, BCL=N, BCR=N] + + +D = @(v,p) v.*0 + sqrt(nu_D/2); +g5 = @(v,p,t,dat) D(v,p); +pterm1 = DIV (num_dims,g5,'',+1,'D','D','','','',dV_th); +pterm2 = GRAD(num_dims,g5,'',-1,'N','N','','','',dV_th); +termC_z = SD_TERM({pterm1,pterm2}); +termC = MD_TERM(num_dims,{termC_z}); + +terms = {termM,termC}; + +%% Define some parameters and add to pde object. +% These might be used within the various functions below. + +params.parameter1 = 0; +params.parameter2 = 1; + +%% Define sources + +sources = {}; + + function dt=set_dt(pde,CFL) + dims = pde.dimensions; + % for Diffusion equation: dt = C * dx^2 + lev = dims{1}.lev; + dx = 1/2^lev; + dt = CFL*dx^2; + end + +%% Construct PDE + +pde = PDE(opts,dimensions,terms,[],sources,params,@set_dt,[],initial_conditions,solutions); + +end \ No newline at end of file diff --git a/pdes/mirror1_space_div.m b/pdes/mirror1_space_div.m new file mode 100644 index 00000000..86a2e6be --- /dev/null +++ b/pdes/mirror1_space_div.m @@ -0,0 +1,112 @@ +function pde = mirror1_space_div(opts) +% 1D mirror case along magnetic axis direction, i.e., +% +% df/dt f B(s) == -cos(pi/4)*df/ds B(s) - cos(pi/4)*dB/ds/B(s) f B(s) +% +% Run with +% +% explicit +% asgard(@mirror1_space_div, 'calculate_mass', false, 'normalize_by_mass', false) + +% implicit +% asgard(@mirror1_space_div,'timestep_method','BE', 'calculate_mass', true, 'normalize_by_mass', true) + +params = mirror_parameters(opts); + +params.B_func = @(s) exp(s); %magnetic field as a function of spatial coordinate +params.dB_ds = @(s) params.B_func(s); %derivative of magnetic field + +params.vel_test = 1; %test value for velocity in coefficient +params.pitch_test = pi/4; %test value for pitch angle in coefficient +decay_coeff = @(v,z) v.*cos(z); + +%% Define the dimensions + +dim_s = DIMENSION(-3,3); +dV_s = @(x,p,t,d) params.B_func(x); +dim_s.moment_dV = dV_s; +dimensions = {dim_s}; +num_dims = numel(dimensions); + +%% Define the analytic solution + +sol_s = @(s,p,t) exp(s); +sol_t = @(t,p) exp(-2*decay_coeff(params.vel_test,params.pitch_test).*t); +soln1 = new_md_func(num_dims,{sol_s,sol_t}); +solutions = {soln1}; + +%% Define the initial conditions + +ic1 = new_md_func(num_dims,{sol_s}); +initial_conditions = {ic1}; + +%% Define the boundary conditions + +BCL = soln1; +BCR = soln1; + +%% Define the terms of the PDE +% + +% We have an advection and mass term + +%% Advection term +% -B(s)*d(vtest*cos(ztest)f)/ds +g1 = @(s,p,t,dat) s.*0 - decay_coeff(p.vel_test,p.pitch_test)*(p.pitch_test > pi/2); +pterm1 = DIV(num_dims,g1,'',-1,'D','D','','','', dV_s); +%pterm1 = GRAD(num_dims,g1,-1,'N','N'); +term1a_s = SD_TERM({pterm1}); +term1a = MD_TERM(num_dims,{term1a_s}); + +g1 = @(s,p,t,dat) s.*0 - decay_coeff(p.vel_test,p.pitch_test)*(p.pitch_test < pi/2); +pterm1 = DIV(num_dims,g1,'',+1,'D','D','','','', dV_s); +%pterm1 = GRAD(num_dims,g1,-1,'N','N'); +term1b_s = SD_TERM({pterm1}); +term1b = MD_TERM(num_dims,{term1b_s}); + +%% +% Add terms to the pde object + +%% Mass term +% B(s)*(vcosz/B)dB/ds f +g2 = @(s,p,t,dat) s.*0 - decay_coeff(p.vel_test,p.pitch_test).*(p.dB_ds(s)./p.B_func(s)).*(p.pitch_test < pi/2).*(p.B_func(s) > 0); +pterm1 = MASS(g2,'','',dV_s); +termB1a = SD_TERM({pterm1}); + +term2a = MD_TERM(num_dims,{termB1a}); + +g2 = @(s,p,t,dat) s.*0 - decay_coeff(p.vel_test,p.pitch_test).*(p.dB_ds(s)./p.B_func(s)).*(p.pitch_test > pi/2).*(p.B_func(s) < 0); +pterm1 = MASS(g2,'','',dV_s); +termB1b = SD_TERM({pterm1}); + +term2b = MD_TERM(num_dims,{termB1b}); + +terms = {term1a,term1b,term2a,term2b}; + +%% Define some parameters and add to pde object. +% These might be used within the various functions below. + +params.parameter1 = 0; +params.parameter2 = 1; + +%% Define sources + +sources = {}; + +%% Define function to set time step + + function dt=set_dt(pde,CFL) + dim = pde.dimensions{1}; + lev = dim.lev; + xMax = dim.max; + xMin = dim.min; + xRange = xMax-xMin; + dx = xRange/(2^lev); + dt = CFL*dx; + end + +%% Construct PDE + +pde = PDE(opts,dimensions,terms,[],sources,params,@set_dt,[],initial_conditions,solutions); + +end diff --git a/pdes/mirror1_velocity.m b/pdes/mirror1_velocity.m index 6a104f87..c11eb8d4 100644 --- a/pdes/mirror1_velocity.m +++ b/pdes/mirror1_velocity.m @@ -1,21 +1,25 @@ function pde = mirror1_velocity(opts) -% One-dimensional magnetic mirror from the FP paper - evolution of the ion velocity dependence +% Strong form of one-dimensional magnetic mirror from the FP paper - evolution of the ion velocity dependence % of f in the presence of Coulomb collisions with background electrons % -% df/dt == 1/v^2 (d/dv(flux_v)) +% df/dt == -(1 - v^2/2*sin^2(pi/4))*cos(pi/4)*df/dv - v*cos(pi/4)*f + 1/v^2 (d/dv(flux_v)) % % flux_v == v^3[(m_a/(m_a + m_b))nu_s f) + 0.5*nu_par*v*d/dv(f)] % +% df/dt == -( 1-v^2/4)*sqrt(2)/2*df/dv*v^2 -v*sqrt(2)/2*f + 1/v^2 (d/dv(v^3[(m_a/(m_a + +% m_b))nu_s f) + 0.5*nu_par*v*d/dv(f)])*v^2 +% +% % Run with % -% asgard(@mirror1_velocity,'timestep_method','matrix_exponential','case',3,'dt',1e-8,'num_steps',50,'lev',3,'deg',4,'normalize_by_mass',true) +% asgard(@mirror1_velocity,'timestep_method','BE','dt',1e-7,'num_steps',50,'lev',5,'deg',2,'normalize_by_mass',false, 'calculate_mass', false) params = mirror_parameters(); %% Define the dimensions -dim_v = DIMENSION(0,0.5e7); -dim_v.jacobian = @(v,p,t) 2.*pi.*v.^2; +dim_v = DIMENSION(0,1e6); +dim_v.jacobian = @(v,p,t) 2*pi.*v.^2; dimensions = {dim_v}; num_dims = numel(dimensions); @@ -33,14 +37,22 @@ %% Define the initial conditions -ic_v = @(v,p,t) p.init_cond_v(v); +ic_v = @(v,p,t) p.a.n.*p.init_cond_v(v); ic1 = new_md_func(num_dims,{ic_v}); initial_conditions = {ic1}; %% Define the boundary conditions -BCL = ic1; -BCR = ic1; +%% Define the boundary conditions + +BCL = new_md_func(num_dims,{... + @(v,p,t) v.*0, ... + params.boundary_cond_t}); + + +BCR = new_md_func(num_dims,{... + params.boundary_cond_v, ... + params.boundary_cond_t}); %% Define the terms of the PDE @@ -54,21 +66,40 @@ %% -% term V1 == 1/v^2 d/dv(v^3(m_a/(m_a + m_b))nu_s f)) -% term V1 == g(v) q(v) [mass, g(v) = 1/v^2, BC N/A] + +% term V1 == -(1 - v^2/4)*sqrt(2)/2*df/dv +% term V1 == g(v) q(v) +% g(v) = g1(v) [mass, g1(z) = (1 - v^2/4)*sqrt(2)/2, BC = N/A] +% q(v) = d/dv (g2(v) f) [grad, g2(v) = 1, BCL=N, BCR=D ] +g1 = @(v,p,t,dat) -(1-v.^2./4.)*sqrt(2)/2; +g2 = @(v,p,t,dat) v.*0 + 1; +pterm1 = MASS(g1); +pterm2 = GRAD(num_dims,g2,0,'N','D', BCL, BCR); +termV_v = SD_TERM({pterm1,pterm2}); +termV1 = MD_TERM(num_dims,{termV_v}); + +%term V2 == -v*sqrt(2)/2*f +%term V2 == g1(v)*f [ma.ss, g1(v) = -v, BC = N/A] +g1 = @(v,p,t,dat) -v.^3*sqrt(2)./2; +pterm1 = MASS(g1); +termV_v = SD_TERM({pterm1}); +termV2 = MD_TERM(num_dims,{termV_v}); + +% term V3 == 1/v^2 d/dv(v^3(m_a/(m_a + m_b))nu_s f))*v^2 +% term V3 == g(v) q(v) [mass, g(v) = 1/v^2, BC N/A] % q(v) == d/dv(g2(v)f(v)) [grad, g2(v) = v^3(m_a/(m_a + m_b))nu_s, BCL= N, BCR=N] g1 = @(v,p,t,dat) 1./v.^2; g2 = @(v,p,t,dat) v.^3*p.a.m.*p.nu_s(v,p.a,p.b)./(p.a.m + p.b.m); pterm1 = MASS(g1); -pterm2 = GRAD(num_dims,g2,-1,'N','D', BCL, BCR); +pterm2 = GRAD(num_dims,g2,0,'N','D', BCL, BCR); termV_s = SD_TERM({pterm1,pterm2}); -termV1 = MD_TERM(num_dims,{termV_s}); +termV3 = MD_TERM(num_dims,{termV_s}); %% -% term V2 == 1/v^2 d/dv(v^4*0.5*nu_par*d/dv(f)) -% term V2 == g(v) q(v) [mass, g(v) = 1/v^2, BC N/A] +% term V4 == 1/v^2 d/dv(v^4*0.5*nu_par*d/dv(f)) +% term V4 == g(v) q(v) [mass, g(v) = 1/v^2, BC N/A] % q(v) == d/dv(g2(v)r(v)) [grad, g2(v) = v^4*0.5*nu_par, BCL= D, BCR=D] % r(v) = d/dv(g3(v)f) [grad, g3(v) = 1, BCL=N, BCR=N] @@ -78,11 +109,11 @@ pterm1 = MASS(g1); pterm2 = GRAD(num_dims,g2,+1,'D','N'); -pterm3 = GRAD(num_dims,g3, -1,'N','D', BCL, BCR); +pterm3 = GRAD(num_dims,g3,-1,'N','D', BCL, BCR); termV_par = SD_TERM({pterm1,pterm2,pterm3}); -termV2 = MD_TERM(num_dims,{termV_par}); +termV4 = MD_TERM(num_dims,{termV_par}); -terms = {termV1,termV2}; +terms = {termV1,termV3,termV4}; %% Define sources diff --git a/pdes/mirror2_advection_Efield_div.m b/pdes/mirror2_advection_Efield_div.m new file mode 100644 index 00000000..e72da763 --- /dev/null +++ b/pdes/mirror2_advection_Efield_div.m @@ -0,0 +1,179 @@ +function pde = mirror2_advection_Efield_div(opts) + +params = mirror_parameters(opts); + +% +% switch opts.case_ +% case 1 +% params_si.a.T_eV = 0.05*params_si.b.T_eV; %Target temperature in Kelvin\ +% offset = 10^6; %case with offset and change in Temperature +% case 2 +% params_si.a.T_eV = 0.05*params_si.b.T_eV; +% offset = 0; %case with no offset but change in Temperature +% case 3 +% n_cgs = 5e13; %equilibrium density in cm.^-3 +% m_e_cgs = 9.109*10^-28; %electron mass in g +% m_D_cgs = 3.3443*10^-24; %Deuterium mass in g +% m_He_cgs = 6.7*10^-24; %helium 4 mass in g +% m_B_cgs = 1.82*10^-23; %Boron 11 mass in g +% temp_cgs = 1.6022e-10; %temperature in erg +% params_cgs.a.n = n_cgs; +% params_cgs.b.n = n_cgs; +% params_cgs.b2.n = n_cgs; +% % params_cgs.a.vth = sqrt(2*temp_cgs/m_e_cgs); +% % params_cgs.b.vth = sqrt(2*temp_cgs/m_e_cgs); +% params_cgs.a.m = m_e_cgs; %beam is electrons +% params_cgs.b.m = m_e_cgs; %background is electrons +% params_cgs.b2.m = m_B_cgs; +% params_cgs.a.Z = -1; +% params_cgs.b.Z = -1; +% params_cgs.b2.Z = 5; +% params_cgs.e = 4.803*10^-10; %charge in Fr +% params_cgs.E = 2.6e-5; %E field in statvolt/cm +% params_si.a.n = 10^6*params_cgs.a.n;%converting to m^-3 +% params_si.b.n = 10^6*params_cgs.b.n; +% params_si.b2.n = 10^6*params_cgs.b2.n; +% % params_si.a.vth = 0.01*params_cgs.a.vth; %converting to m/s +% % params_si.b.vth = 0.01*params_cgs.b.vth; +% params_si.a.m = 0.001*params_cgs.a.m; %converting to kg +% params_si.b.m = 0.001*params_cgs.b.m; +% params_si.b2.m = 0.001*params_cgs.b2.m; +% params_si.a.Z = params_cgs.a.Z; +% params_si.b.Z = params_cgs.b.Z; +% params_si.b2.Z = params_cgs.b2.Z; +% %params_si.E = 2.9979*10^4*params_cgs.E; %converting to V/m +% params_si.a.E_eV = 7.665; +% params_si.a.T_eV = 1000;%2/3*params_si.a.E_eV; +% params_si.b.T_eV = params_si.a.T_eV; +% params_si.b2.T_eV = params_si.a.T_eV; +% params_si.a.vth = params_si.v_th(params_si.a.T_eV,params_si.a.m); +% params_si.b.vth = params_si.v_th(params_si.b.T_eV,params_si.b.m); +% params_si.b2.v.th = params_si.v_th(params_si.b2.T_eV,params_si.b2.m); +% params_si.ln_delt = 15; +% E_dreicer_si = params_si.a.n.*params_si.e^3*params_si.ln_delt/(4*pi*params_si.eps0^2*params_si.a.m ... +% *params_si.a.vth^2); +% params_si.E = 10^-3*E_dreicer_si; +% %vel_norm = @(v,vth) v./vth; %normalized velocity to thermal velocity +% params_si.maxwell = @(v,offset,vth) params_si.a.n/(pi.^(3/2)*vth^3).*exp(-((v-offset)/vth).^2); +% params_si.init_cond_v = @(v,p,t) params_si.maxwell(v,0,params_si.a.vth); +% params_si.soln_v = @(v,p,t) solution_v(v,p,t); +% %params_cgs.nu_ab0 = @(a,b) b.n * params_cgs.e^4 * a.Z^2 * b.Z^2 * params_cgs.ln_delt / (pi^3/2.*a.m^2*b.vth^3); %scaling coefficient +% %params.eps0 = 1/(4*pi); +% end + + function ret = solution_v(v,p,t) + ret = params.a.n/(pi^3/2.*params.v_th(params.b.T_eV,params.a.m).^3).*... + exp(-(v./params.v_th(params.b.T_eV,params.a.m)).^2); + if isfield(p,'norm_fac') + ret = p.norm_fac .* ret; + end + end + +dim_v = DIMENSION(0,15*params.a.vth); +dV_v = @(x,p,t,d) x.^2; +dim_v.moment_dV = dV_v; + +dim_th = DIMENSION(0,pi); +dV_th = @(x,p,t,d) sin(x); +dim_th.moment_dV = dV_th; + +dimensions = {dim_v, dim_th}; +num_dims = numel(dimensions); + +%% Define the analytic solution (optional) + +soln1 = new_md_func(num_dims,{ ... + params.soln_v, ... + params.soln_z, ... + }); +solutions = {soln1}; + +%% Define the initial conditions + +ic1 = new_md_func(num_dims,{params.init_cond_v,params.init_cond_z,params.init_cond_t}); +initial_conditions = {ic1}; + +%% Define the boundary conditions + +BCL = new_md_func(num_dims,{... + params.init_cond_v, ... + params.boundary_cond_z, ... + params.boundary_cond_t}); + +BCR = new_md_func(num_dims,{... + @(v,p,t) v.*0, ... + params.boundary_cond_z, ... + params.boundary_cond_t}); + +%% Define the terms of the PDE + +% termE1a is done combining mass and div defining F(th) = (ZeE/m cos(th)) and +% G(v) = 1 +% +% eq1 : df/dt == div(F(th) f) [pterm1: div(g(v)=G(v),-1, BCL=D,BCR=N)] + + dV_v = @(x,p,t,d) x.^2; + dV_th = @(x,p,t,d) sin(x); + +F = @(x,p) cos(x); +g1 = @(x,p,t,dat) F(x,p).*(x>pi/2); +pterm1 = MASS(g1,'','',dV_th); +termE1_th = SD_TERM({pterm1}); + +G = @(v,p) v.*0 - p.a.Z.*p.e.*p.E./p.a.m; +g2 = @(v,p,t,dat) G(v,p); +pterm1 = DIV(num_dims,g2,'',+1,'D','N',BCL,'','',dV_v); +termE1_v = SD_TERM({pterm1}); +termE1a = MD_TERM(num_dims,{termE1_v,termE1_th}); + +%termE1b is the same form as term1 but accounting for the flow in the +%opposite direction + +F = @(x,p) cos(x); +g1 = @(x,p,t,dat) F(x,p).*(x 0 and therefore we use upwinding +%eq1: df/dt == div(mag(s) f) [pterm1: div(g(th)=C(th),-1, BCL=N,BCR=N)] + +dV_th = @(x,p,t,d) sin(x); +dV_s = @(x,p,t,d) params.B_func(x)/params.a.m; + +g1 = @(x,p,t,d) mag(x).*(mag(x) > 0); +pterm1 = MASS(g1,'','',dV_s); +termZa_s = SD_TERM({pterm1}); + +C = @(z) sin(z); +g2 = @(z,p,t,dat) C(z); +pterm2 = DIV(num_dims,g2,'',-1,'N','D','',BCR,'',dV_th); +termZa_z = SD_TERM({pterm2}); + +termZa = MD_TERM(num_dims,{termZa_z,termZa_s}); + +%termZb is a done combining mass ad div defining C(th) = sin(th) and using +%the function mag(s) = dB/ds/(2*B). This applies to the domain where +% mag(s) < 0 and therefore we use downwinding +%eq1: df/dt == div(mag(s) f) [pterm1: div(g(th)=C(th),+1, BCL=N,BCR=N)] + +dV_th = @(x,p,t,d) sin(x); +dV_s = @(x,p,t,d) params.B_func(x)/params.a.m; + +g1 = @(x,p,t,d) mag(x).*(mag(x) < 0); +pterm1 = MASS(g1,'','',dV_s); +termZb_s = SD_TERM({pterm1}); + +C = @(z) sin(z); +g2 = @(z,p,t,dat) C(z); +pterm2 = DIV(num_dims,g2,'',+1,'D','N',BCL,'','',dV_th); +termZb_z = SD_TERM({pterm2}); + +termZb = MD_TERM(num_dims,{termZb_z,termZb_s}); + +%termSa is done combining mass and div G(th) = +%cos(th) and H(s) = -1. Here we restrict to z < pi/2 and use upwinding +%eq1 : df/dt == div(G(th) f) [pterm1: div(g(s)=H(s),-1, BCL=D,BCR=N)] + +dV_th = @(x,p,t,d) sin(x); +dV_s = @(x,p,t,d) params.B_func(x)./params.a.m; + +G = @(z) cos(z).*(z < pi/2); +g2 = @(z,p,t,dat) G(z); +pterm1 = MASS(g2,'','',dV_th); +termSa_z = SD_TERM({pterm1}); + +H = @(s) s.*0 - 1; +g3 = @(s,p,t,dat) H(s); +pterm2 = DIV(num_dims,g3,'',-1,'D','N','',BCR,'',dV_s); +termSa_s = SD_TERM({pterm2}); + +termSa = MD_TERM(num_dims,{termSa_z,termSa_s}); + +%termSb is done combining mass and div G(th) = +%cos(th) and H(s) = -1. Here we restrict to z > pi/2 and use downwinding +%eq1 : df/dt == div(G(th) f) [pterm1: div(g(s)=H(s),-1, BCL=D,BCR=N)] + +dV_th = @(x,p,t,d) sin(x); +dV_s = @(x,p,t,d) params.B_func(x)/params.a.m; + +G = @(z) cos(z).*(z > pi/2); +g2 = @(z,p,t,dat) G(z); +pterm1 = MASS(g2,'','',dV_th); +termSb_z = SD_TERM({pterm1}); + +H = @(s) s.*0 - 1; +g3 = @(s,p,t,dat) H(s); +pterm2 = DIV(num_dims,g3,'',+1,'N','D',BCL,'','',dV_s); +termSb_s = SD_TERM({pterm2}); + +termSb = MD_TERM(num_dims,{termSb_z,termSb_s}); + +%% Mass term +% termM == cos(z)dB/ds/(2*B) f +% termM == r(z)*w(s) +% r(z) == g1(z) [mass, g1(z) = -cos(z), BC N/A] +% w(s) == g2(s) f [mass, g2(s) = mag(s), BC N/A] + +% dV_th = @(x,p,t,d) sin(x); +% dV_s = @(x,p,t,d) params.B_func(x); +% +% G = @(z) cos(z); +% g2 = @(z,p,t,dat) G(z); +% pterm2 = MASS(g2,'','',dV_th); +% termB1_z = SD_TERM({pterm2}); +% +% g3 = @(s,p,t,dat) mag(s); +% pterm3 = MASS(g3,'','',dV_s); +% termB1_s = SD_TERM({pterm3}); +% +% termM = MD_TERM(num_dims,{termB1_z,termB1_s}); + +terms = {termZa,termZb,termSa,termSb}; + + + +%% Define the analytic solution (optional) + + +soln1_z = @(z,p,t,d) cos(z); +soln1_s = @(s,p,t,d) s; +solution = new_md_func(num_dims,{soln1_z,soln1_s}); +solutions = {solution}; + + +%% Define sources +%source1_v = @(x,p,t,d) p.f0_v(x); +source1_z = @(x,p,t,d) (sin(x)).^2 - (cos(x)).^2; +source1 = new_md_func(num_dims,{source1_z,[]}); +sources = {source1}; + +%% Define function to set time step + function dt=set_dt(pde,CFL) + Lmax = pde.dimensions{1}.max; + LevX = pde.dimensions{1}.lev; + dt = Lmax/2^LevX*CFL; + end + + + +%% Construct PDE + +pde = PDE(opts,dimensions,terms,[],sources,params,@set_dt,[],initial_conditions,solutions); +end \ No newline at end of file diff --git a/pdes/mirror2_velocity.m b/pdes/mirror2_velocity.m new file mode 100644 index 00000000..95d36180 --- /dev/null +++ b/pdes/mirror2_velocity.m @@ -0,0 +1,178 @@ +function pde = mirror2_velocity(opts) +% Two-dimensional magnetic mirror from the FP paper - evolution of the ion velocity dependence +% of f in the presence of Coulomb collisions with background electrons +% Also applied to the 2D test for CQL4D equations + +% df/dt == -eE/m cos(th) df/dv + eE/m sin(th) df/dth + sum_{b} ( nu_D/(2*sin(th)) d/dth ( sin(th) 1/v d (v f) /dth ) + +% 1/v^2 (d/dv(v^2[(m_a/(m_a + m_b))v nu_s f) + 0.5*nu_par*v^2*d/dv(f)]) +% +% v,th are spherical coordinates (v,th,phi), so the div and grad look like +% +% div[] = 1/v^2 * d/dv * v^2[] + 1/sin(th) d/dth (sin(th)[]), grad[] = +% d/dv[],1/v * d/dth[] +% +% Run with +% +% asgard(@mirror2_velocity,'timestep_method','BE','case',3,'dt',1e-6) + +params = mirror_parameters(); + +switch opts.case_ + case 1 + params.a.T_eV = 0.05*params.b.T_eV; %Target temperature in Kelvin\ + offset = 10^6; %case with offset and change in Temperature + case 2 + params.a.T_eV = 0.05*params.b.T_eV; + offset = 0; %case with no offset but change in Temperature + case 3 + n_o = 8e14; %equilibrium density in cm.^-3 + m_e = 9.109*10^-28; %electron mass in g + temp = 1.6022e-10; %temperature in erg + params.a.n = n_o; + params.b.n = n_o; + params.a.vth = sqrt(2*temp/m_e); + params.b.vth = sqrt(2*temp/m_e); + params.a.m = m_e; %beam is electrons + params.b.m = m_e; %background is electrons + params.E = 3.33e-7; %E field in statvolt/cm + params.init_cond_v = @(v,p,t) params.maxwell(v,0,a.vth); +end + +maxwell = @(v,x,y) a.n/(pi^3/2.*y^3).*exp(-((v-x)/y).^2); + +%% Define the dimensions + +dim_v = DIMENSION(0,1e6); +dim_z = DIMENSION(0,pi); + +dim_v.jacobian = @(v,p,t) 2.*pi.*v.^2; +dim_z.jacobian = @(z,p,t) sin(z); + +dimensions = {dim_v, dim_z}; +num_dims = numel(dimensions); + +%% Define the analytic solution (optional) + +soln1 = new_md_func(num_dims,{ ... + params.soln_v, ... + params.soln_z, ... + }); +solutions = {soln1}; + +%% Define the initial conditions + +ic1 = new_md_func(num_dims,{params.init_cond_v,params.init_cond_z,params.init_cond_t}); +initial_conditions = {ic1}; + +%% Define the boundary conditions + +BCL = new_md_func(num_dims,{... + @(v,p,t) v.*0, ... + params.boundary_cond_z, ... + params.boundary_cond_t}); + +BCR = new_md_func(num_dims,{... + params.boundary_cond_v, ... + params.boundary_cond_z, ... + params.boundary_cond_t}); + + +%% Define the terms of the PDE + +% -eE*Z_a/m_a cos(z) d/dv(f) + +g1 = @(v,p,t,dat) -p.e.*p.E.*p.a.Z./p.a.m; +g2 = @(v,p,t,dat) v.*0 + 1; + +pterm1 = MASS(g1); +pterm2 = GRAD(num_dims,g2,-1,'N','D',BCL,BCR); +termE_v = SD_TERM({pterm1,pterm2}); + +g3 = @(z,p,t,dat) cos(z); + +pterm1 = MASS(g3); +termE_z = SD_TERM({pterm1}); +termE1 = MD_TERM(num_dims,{termE_v,termE_z}); + +% eE/m sin(z)vdf/dz + +g1 = @(v,p,t,dat) p.e.*p.E*v./p.a.m; +g2 = @(z,p,t,dat) sin(z); +g3 = @(z,p,t,dat) z.*0 + 1; + +pterm1 = MASS(g1); +pterm2 = MASS(g2); +pterm3 = GRAD(num_dims,g3,-1,'N','N'); + +termE_v = SD_TERM({pterm1}); +termE_z = SD_TERM({pterm2,pterm3}); +termE2 = MD_TERM(num_dims,{termE_v,termE_z}); + +% termC == v.^2.*nu_D/(2*sin(z))*d/dz sin(z)*df/dz +% +% becomes +% +% termC == g1(v) g2(z) q(z) [mass, g1(p) = nu_D(v), g2(z) = 1/(2sin(z)) BC N/A] +% q(z) == d/dz g3(z) r(z) [grad, g3(z) = sin(z), BCL=D,BCR=D] +% r(z) == d/dp g4(z) f(z) [grad, g3(p) = 1, BCL=N,BCR=N] + +g1 = @(v,p,t,dat) p.nu_D(v,p.a,p.b)/2; +g2 = @(z,p,t,dat) 1./sin(z); +g3 = @(z,p,t,dat) sin(z); +g4 = @(z,p,t,dat) z.*0 + 1; +pterm1 = MASS(g1); +pterm2 = MASS(g2); +pterm3 = GRAD(num_dims,g3,+1,'D','N'); +pterm4 = GRAD(num_dims,g4,-1,'N', 'D',BCL,BCR); +termC_v = SD_TERM({pterm1}); +termC_z = SD_TERM({pterm2,pterm3,pterm4}); +termC = MD_TERM(num_dims,{termC_v,termC_z}); + + +% term V1 == 1/v^2 d/dv(v^3(m_a/(m_a + m_b))nu_s f)) +% term V1 == g(v) q(v) [mass, g(v) = 1/v^2, BC N/A] +% q(v) == d/dv(g2(v)f(v)) [grad, g2(v) = v^3(m_a/(m_a + m_b))nu_s, BCL= N, BCR=N] + +g1 = @(v,p,t,dat) 1./v.^2; +g2 = @(v,p,t,dat) v.^3*p.a.m.*p.nu_s(v,p.a,p.b)./(p.a.m + p.b.m); + +pterm1 = MASS(g1); +pterm2 = GRAD(num_dims,g2,-1,'N','D', BCL, BCR); +termV_s = SD_TERM({pterm1,pterm2}); +termV1 = MD_TERM(num_dims,{termV_s,[]}); + +% term V2 == 1/v^2 d/dv(v^4*0.5*nu_par*d/dv(f)) +% term V2 == g(v) q(v) [mass, g(v) = 1/v^2, BC N/A] +% q(v) == d/dv(g2(v)r(v)) [grad, g2(v) = v^4*0.5*nu_par, BCL= D, BCR=D] +% r(v) = d/dv(g3(v)f) [grad, g3(v) = 1, BCL=N, BCR=N] + +g1 = @(v,p,t,dat) 1./v.^2; +g2 = @(v,p,t,dat) v.^4.*0.5.*p.nu_par(v,p.a,p.b); +g3 = @(v,p,t,dat) v.*0 + 1; + +pterm1 = MASS(g1); +pterm2 = GRAD(num_dims,g2,-1,'D','N'); +pterm3 = GRAD(num_dims,g3,+1,'N','D', BCL, BCR); +termV_par = SD_TERM({pterm1,pterm2,pterm3}); +termV2 = MD_TERM(num_dims,{termV_par,[]}); + +terms = {termV1,termV2,termC,termE1,termE2}; + + +%% Define sources + +sources = {}; + +%% Define function to set time step + function dt=set_dt(pde,CFL) + Lmax = pde.dimensions{1}.max; + LevX = pde.dimensions{1}.lev; + dt = Lmax/2^LevX*CFL; + end + + +%% Construct PDE + +pde = PDE(opts,dimensions,terms,[],sources,params,@set_dt,[],initial_conditions,solutions); + +end diff --git a/pdes/mirror2_velocity_div.m b/pdes/mirror2_velocity_div.m new file mode 100644 index 00000000..6b8017f3 --- /dev/null +++ b/pdes/mirror2_velocity_div.m @@ -0,0 +1,252 @@ +function pde = mirror2_velocity_div(opts) +% Two-dimensional magnetic mirror from the FP paper - evolution of the ion velocity dependence +% of f in the presence of Coulomb collisions with background electrons +% Also applied to the 2D test for CQL4D equations + +% df/dt == -1/v^2 d(v^2 ZeE/m cos(th) f)/dv + 1/(vsin(th)) d(sin(th) ZeE/m sin(th) f)/dth +% + sum_{b} ( nu_D/(2*sin(th)) d/dth ( sin(th) 1/v d (v f) /dth ) + +% 1/v^2 (d/dv(v^2[(m_a/(m_a + m_b))v nu_s f) + 0.5*nu_par*v^2*d/dv(f)]) +% +% v,th are spherical coordinates (v,th,phi), so the div and grad look like +% +% div[] = 1/v^2 * d/dv * v^2[] + 1/sin(th) d/dth (sin(th)[]), grad[] = +% d/dv[],1/v * d/dth[] +% +% and the volument_element dV = v^2 sin(th) +% + +% df/dt == -1/v^2 d(v^2 ZeE/m cos(th) f)/dv %term1 +% + 1/(vsin(th)) d(sin(th) ZeE/m sin(th) f)/dth %term2 +% + % sum_b (( 1/v^2 (d/dv (v^2[0.5*nu_par*v^2*d/dv(f)]) %%term3 +% + 1/v^2 (d/dv(v^2[v (m_a/(m_a + m_b))nu_s f)]) %%term4 +% + nu_D/(2 sin(z)) d/dth ( sin(th) df/dth )) %%term5 +% +% split into five div terms (term1,term2, term3, term4, and term5) +% +% term1 is done combining mass and div defining F(th) = -ZeE/m cos(th) and +% G(v) = 1 +% +% eq1 : df/dt == div(F(th) f) [pterm1: div(g(v)=G(v),-1, BCL=D,BCR=N)] +% +% term2 is a simple div term, defining K(th) = ZeE/m sin(th) +% +% eq1 : df/dt == div(K(th) f) [pterm1:div(g(th)=K(th),-1, BCL=N,BCR=N)] +% +% term3 is done combining mass and div defining C(v) = (nu_D(v)/2) +% +% eq1 : df/dt == div( q) [pterm1: div (g(v)=D(v),+1, BCL=D, BCR=D] +% eq2 : q == C(v) grad(f) [pterm2: grad(g(v)=D(v),-1, BCL=N, BCR=N] +% +% term4 is a div using B(v) = v (m_a/(m_a + m_b))nu_s +% +% eq1 : df/dt == div(B(v) * f) [pterm1: div(g(p)=B(v),+1, BCL=?, BCR=?] +% +% +% term5 is done using SLDG defining C(v) = sqrt(v*nu_D(v)/2) +% +% eq1 : df/dt == div(C(v) * q) [pterm1: div (g(v)=C(v),+1, BCL=D, BCR=D] +% eq2 : q == C(v) * grad(f) [pterm2: grad(g(v)=C(v),-1, BCL=N, BCR=N] +% Run with +% +% asgard(@mirror2_velocity_div,'timestep_method','BE','case',3, 'grid_type','SG', 'lev', 3, 'deg', 3,'num_steps', 10, 'dt',5e-5, 'normalize_by_mass', true, 'calculate_mass', true,'save_output',true,'update_params_each_timestep', true) + +% Run with +% +% asgard(@mirror2_velocity_div,'timestep_method','BE','case',3,'dt',1e-6) + +params = mirror_parameters(opts); + + +%% Define the dimensions + +dim_v = DIMENSION(0,5*params.a.vth); +dV_v = @(x,p,t,d) x.^2; +dim_v.moment_dV = dV_v; + +dim_th = DIMENSION(0,pi); +dV_th = @(x,p,t,d) sin(x); +dim_th.moment_dV = dV_th; + +dimensions = {dim_v, dim_th}; +num_dims = numel(dimensions); + +%% Define the analytic solution (optional) + +soln1 = new_md_func(num_dims,{ ... + params.soln_v, ... + params.soln_z, ... + }); +solutions = {soln1}; + +%% Define the initial conditions + +ic1 = new_md_func(num_dims,{params.init_cond_v,params.init_cond_z,params.init_cond_t}); +initial_conditions = {ic1}; + +%% Define the boundary conditions + +BCL = new_md_func(num_dims,{... + params.boundary_cond_v, ... + params.boundary_cond_z, ... %params.boundary_cond_z, ... + params.boundary_cond_t}); + +BCR = new_md_func(num_dims,{... + params.boundary_cond_v, ... + params.boundary_cond_z, ... + params.boundary_cond_t}); + +%% Define the terms of the PDE + +% termE1a is done combining mass and div defining F(th) = (ZeE/m cos(th)) and +% G(v) = 1 +% +% eq1 : df/dt == div(F(th) f) [pterm1: div(g(v)=G(v),-1, BCL=D,BCR=N)] + + dV_v = @(x,p,t,d) x.^2; + dV_th = @(x,p,t,d) sin(x); + +F = @(x,p) -cos(x).*p.a.Z.*p.e.*p.E./p.a.m; +g1 = @(x,p,t,dat) F(x,p).*(x>pi/2); +pterm1 = MASS(g1,'','',dV_th); +termE1_th = SD_TERM({pterm1}); + +G = @(v,p) v.*0 + 1; +g2 = @(v,p,t,dat) G(v,p); +pterm1 = DIV(num_dims,g2,'',+1,'D','N',BCL,'','',dV_v); +termE1_v = SD_TERM({pterm1}); +termE1a = MD_TERM(num_dims,{termE1_v,termE1_th}); + +%termE1b is the same form as term1 but accounting for the flow in the +%opposite direction + +F = @(x,p) -cos(x).*p.a.Z.*p.e.*p.E./p.a.m; +g1 = @(x,p,t,dat) F(x,p).*(xpi/2); +pterm1 = MASS(g1,'','',dV_th); +termE1_th = SD_TERM({pterm1}); + +G = @(v,p) v.*0 + 1; +g2 = @(v,p,t,dat) G(v,p); +pterm1 = DIV(num_dims,g2,'',-1,'N','D','',BCR,'',dV_v); +termE1_v = SD_TERM({pterm1}); +termE1a = MD_TERM(num_dims,{termE1_v,termE1_th}); + +%termE1b is the same form as term1 but accounting for the flow in the +%opposite direction + +F = @(x,p) -cos(x).*params.a.Z.*params.e.*params.E./params.a.m; +g1 = @(x,p,t,dat) F(x,p).*(xpi/2); +pterm1 = MASS(g1,'','',dV_th); +termE1_th = SD_TERM({pterm1}); + +G = @(v,p) v.*0 - params_si.a.Z.*params_si.e.*params_si.E./params_si.a.m; +g2 = @(v,p,t,dat) G(v,p); +pterm1 = DIV(num_dims,g2,'',+1,'D','N',BCL,'','',dV_v); +termE1_v = SD_TERM({pterm1}); +termE1a = MD_TERM(num_dims,{termE1_v,termE1_th,[]}); + +%termE1b is the same form as term1 but accounting for the flow in the +%opposite direction + +F = @(x,p) cos(x); +g1 = @(x,p,t,dat) F(x,p).*(x Q(x) = k, Q'(x) = -k^2*sin(k*x) == 0 - pterm2 = GRAD(num_dims,g2,0,'D','D'); % f = sin(k*x) => Q(x)=0 - case 2 - pterm1 = GRAD(num_dims,g1,+1,'D','D'); - pterm2 = GRAD(num_dims,g2,-1,'N','N'); - case 3 - pterm1 = GRAD(num_dims,g1,+1,'D','N'); % if you switch the signs of the fluxes this will fail on the right - pterm2 = GRAD(num_dims,g2,-1,'N','D'); - case 4 - pterm1 = GRAD(num_dims,g1,-1,'N','D'); % if you switch the signs of the fluxes this will pass - pterm2 = GRAD(num_dims,g2,+1,'D','N'); - case 5 - pterm1 = GRAD(num_dims,g1,0,'D','N'); - pterm2 = GRAD(num_dims,g2,0,'N','D'); - case 6 - pterm1 = GRAD(num_dims,g1,0,'N','D'); - pterm2 = GRAD(num_dims,g2,0,'D','N'); -end +pterm1 = DIV(num_dims,g1,'',0,'N','N','',dV); +pterm2 = GRAD(num_dims,g2,'',0,'D','D',BCL,BCR,'',dV); term1_x = SD_TERM({pterm1,pterm2}); term1 = MD_TERM(num_dims,{term1_x}); @@ -132,3 +101,4 @@ end + diff --git a/pdes/projecti_test.m b/pdes/projecti_test.m index 63bcbec4..b2aec4f4 100644 --- a/pdes/projecti_test.m +++ b/pdes/projecti_test.m @@ -17,34 +17,4 @@ function pi_diff_test(testCase) rel_err = err / norm(fval); verifyLessThan(testCase,rel_err,1e-5); -opts.case_=2; -pde = projecti_diff1(opts); -[err,fval,fval_realspace,nodes,err_realspace] = asgard_run_pde(opts,pde); -rel_err = err / norm(fval); -verifyLessThan(testCase,rel_err,1e-5); - -opts.case_=3; -pde = projecti_diff1(opts); -[err,fval,fval_realspace,nodes,err_realspace] = asgard_run_pde(opts,pde); -rel_err = err / norm(fval); -verifyLessThan(testCase,rel_err,1e-5); - -opts.case_=4; -pde = projecti_diff1(opts); -[err,fval,fval_realspace,nodes,err_realspace] = asgard_run_pde(opts,pde); -rel_err = err / norm(fval); -verifyLessThan(testCase,rel_err,1e-5); - -opts.case_=5; -pde = projecti_diff1(opts); -[err,fval,fval_realspace,nodes,err_realspace] = asgard_run_pde(opts,pde); -rel_err = err / norm(fval); -verifyLessThan(testCase,rel_err,2e-5); - -opts.case_=6; -pde = projecti_diff1(opts); -[err,fval,fval_realspace,nodes,err_realspace] = asgard_run_pde(opts,pde); -rel_err = err / norm(fval); -verifyLessThan(testCase,rel_err,2e-5); - end \ No newline at end of file diff --git a/pdes/seperable_adapt_test_2d.m b/pdes/seperable_adapt_test_2d.m index ebdffc1e..89338f26 100644 --- a/pdes/seperable_adapt_test_2d.m +++ b/pdes/seperable_adapt_test_2d.m @@ -21,7 +21,9 @@ %% Define the dimensions dim_x = DIMENSION(-10,+10); +dim_x.moment_dV = @(x,p,t,dat) 0*x+1; dim_y = DIMENSION(-1,+1); +dim_y.moment_dV = @(x,p,t,dat) 0*x+1; dimensions = {dim_x,dim_y}; num_dims = numel(dimensions); @@ -54,8 +56,10 @@ % % d/dx g1(x) f(x,y) [grad,g1(x)=-1, BCL=P, BCR=P] +dV = @(x,p,t,dat) 0*x+1; + g1 = @(x,p,t,dat) x*0-1; -pterm1 = GRAD(num_dims,g1,0,'D','D'); +pterm1 = DIV(num_dims,g1,'',0,'D','D','','','',dV); term1_x = SD_TERM({pterm1}); term1 = MD_TERM(num_dims,{term1_x,[]}); diff --git a/pdes/spacetime2.m b/pdes/spacetime2.m index d5370fe8..aeeffd78 100644 --- a/pdes/spacetime2.m +++ b/pdes/spacetime2.m @@ -10,7 +10,9 @@ %% Define the dimensions dim_x = DIMENSION(0,+1); +dim_x.moment_dV = @(x,p,t,dat) 0*x+1; dim_y = DIMENSION(0,+1); +dim_y.moment_dV = @(x,p,t,dat) 0*x+1; dimensions = {dim_x,dim_y}; num_dims = numel(dimensions); @@ -35,13 +37,15 @@ % % Here we have 2 terms, having only nDims=2 (x,y) operators. +dV = @(x,p,t,dat) 0*x+1; + %% % -df/dx which is % % d/dx g1(x) f(x,y) [grad,g1(x)=-1, BCL=D, BCR=N] g1 = @(x,p,t,dat) x*0-1; -pterm1 = GRAD(num_dims,g1,0,'D','N'); +pterm1 = DIV(num_dims,g1,'',0,'D','N',BCL,'','',dV); term1_x = SD_TERM({pterm1}); term1 = MD_TERM(num_dims,{term1_x,[]}); @@ -52,7 +56,7 @@ % g1 = @(y,p,t,dat) y*0-1; -pterm1 = GRAD(num_dims,g1,0,'D','N',BCL); +pterm1 = DIV(num_dims,g1,'',0,'D','N',BCL,'','',dV); term2_y = SD_TERM({pterm1}); term2 = MD_TERM(num_dims,{[],term2_y}); diff --git a/pdes/vlasov2.m b/pdes/vlasov2.m new file mode 100644 index 00000000..94c2dcd0 --- /dev/null +++ b/pdes/vlasov2.m @@ -0,0 +1,110 @@ +function pde = vlasov2(opts) +% 2D test case using continuity equation, i.e., +% +% df/dt == -ydf/dx +% +% Run with +% +% explicit +% asgard(@vlasov2,'lev',3,'deg',3,'CFL',0.1) +% +% implicit +% asgard(@vlasov2,'timestep_method','CN') +% +% with adaptivity +% asgard(@vlasov2,'timestep_method','CN','adapt',true) + +% pde.CFL = 0.1; + +soln_x = @(x,p,t) 0*x+1; +soln_y = @(y,p,t) 0*y+1; +soln_t = @(t,p) 0*t+1; + +%% Define the dimensions +% +% Here we setup a 2D problem (x,y) + +dim_x = DIMENSION(-1,+1); +dim_x.moment_dV = @(x,p,t,dat) 0*x+1; +dim_y = DIMENSION(-1,+1); +dim_y.moment_dV = @(y,p,t,dat) 0*y+1; +dimensions = {dim_x,dim_y}; +num_dims = numel(dimensions); + +%% Define the analytic solution (optional). + +soln1 = new_md_func(num_dims,{soln_x,soln_y,soln_t}); +solutions = {soln1}; + +%% Initial conditions +ic1 = new_md_func(num_dims,{soln_x,soln_y,soln_t}); +initial_conditions = {ic1}; + +BCL = soln1; +BCR = soln1; + +%% Define the terms of the PDE +% +% Here we have 2 terms, having only nDims=2 (x,y) operators. + +dV = @(x,p,t,dat) 0*x+1; + +%% +% -df/dx which is +% +% d/dx g1(x) f(x,y) [grad,g1(x)=-1, BCL=P, BCR=P] + +g1 = @(x,p,t,dat) x*0-1; +pterm1 = DIV(num_dims,g1,'',-1,'D','N',BCL,'','',dV); +term1_x = SD_TERM({pterm1}); + +g1 = @(x,p,t,dat) x.*(x>0); +pterm1 = MASS(g1,'','',dV); +term1_y = SD_TERM({pterm1}); + +term1 = MD_TERM(num_dims,{term1_x,term1_y}); + +%% +% -df/dy which is +% +% d/dy g1(y) f(x,y) [grad,g1(y)=-1, BCL=P, BCR=P] + +g1 = @(x,p,t,dat) x*0-1; +pterm1 = DIV(num_dims,g1,'',+1,'N','D','',BCR,'',dV); +term2_x = SD_TERM({pterm1}); + +g1 = @(x,p,t,dat) x.*(x<0); +pterm1 = MASS(g1,'','',dV); +term2_y = SD_TERM({pterm1}); + +term2 = MD_TERM(num_dims,{term2_x,term2_y}); + +terms = {term1,term2}; + +%% Define some parameters and add to pde object. +% These might be used within the various functions below. + +params.parameter1 = 0; +params.parameter2 = 1; + +%% Define sources + +sources = {}; + +%% Define function to set dt + + function dt=set_dt(pde,CFL) + + Lmax = pde.dimensions{1}.max; + Lmin = pde.dimensions{1}.min; + LevX = pde.dimensions{1}.lev; + dt = (Lmax-Lmin)/2^LevX*CFL; + end + +%% Construct PDE + +pde = PDE(opts,dimensions,terms,[],sources,params,@set_dt,[],initial_conditions,solutions); + +end + + diff --git a/plot_fval.m b/plot_fval.m index 9d15d0a2..fb140096 100644 --- a/plot_fval.m +++ b/plot_fval.m @@ -40,16 +40,19 @@ function plot_fval(pde,nodes,f_nD,f_nD_analytic,element_coordinates,window_title %% % Plot a 1D line through the solution - sy = max(1,floor(ny/2)); + sy = max(1,floor(ny)); if ny > 2 - sy = sy+2; % just to get off the exact middle + sy = sy-1; % just to get off the exact middle end +% sy=ny; f_slice = f_nD(sy,:); x = nodes{1}; y = nodes{2}; ax1 = subplot(2,2,1); plot(x,f_slice,'-o'); + %xlim([0,10]) + %ylim([1e-5,1]) title('1D slice (horizontal)'); %% @@ -63,7 +66,6 @@ function plot_fval(pde,nodes,f_nD,f_nD_analytic,element_coordinates,window_title end sx = max(1,floor(nx/2)); - sx = 2; if nx > 2 sx = sx+2; % just to get off the exact middle end diff --git a/pterm_coeff_matrix.m b/pterm_coeff_matrix.m index 988f61e5..c22bbb65 100644 --- a/pterm_coeff_matrix.m +++ b/pterm_coeff_matrix.m @@ -6,15 +6,17 @@ [L,L_not_rotated] = coeff_matrix(deg,t,dim,pterm,params,FMWT_blocks,coeff_level); % note that dV is applied in here % Get the LHS mass matrix (M) for this pterm - -lhs_mass_pterm = MASS(pterm.LHS_mass_g,'','',pterm.dV); -[M,M_not_rotated] = coeff_matrix(deg,t,dim,lhs_mass_pterm,params,FMWT_blocks,coeff_level); % note that dV is applied in here +% this mass matrix needs to have the volume jacobian incorporated instead +% of the possibly different surface jacobian. +lhs_mass_pterm = MASS(pterm.LHS_mass_g,'','',dim.moment_dV); +[M,M_not_rotated] = coeff_matrix(deg,t,dim,lhs_mass_pterm,params,FMWT_blocks,coeff_level); % Move M to the RHS pterm.mat = inv(M) * L; pterm.mat_unrotated = inv(M_not_rotated) * L_not_rotated; + % Store M for use in application to the BC pterm.LHS_mass_mat = M; diff --git a/save_output.m b/save_output.m index 373a979c..85c38f2a 100644 --- a/save_output.m +++ b/save_output.m @@ -5,6 +5,7 @@ outputs.time_array(L+1) = t+dt; outputs.wall_clock_time(L+1) = toc; outputs.dt = dt; + outputs.hash_table = hash_table; f_realspace_nD = singleD_to_multiD(num_dims,fval_realspace,nodes); if strcmp(opts.output_grid,'fixed') || strcmp(opts.output_grid,'elements') @@ -21,19 +22,9 @@ if opts.save_output && (mod(L,opts.save_freq)==0 || L==opts.num_steps) [status, msg, msgID] = mkdir([root_directory,'/output']); - if isempty(opts.output_filename_id) - adapt_str = 'n'; - if opts.adapt; adapt_str=num2str(opts.adapt_threshold,'%1.1e'); end - filename_str = ['-l',replace(num2str(opts.lev),' ','') ... - '-d',num2str(opts.deg),'-',opts.grid_type,'-dt',num2str(dt),... - '-adapt-',adapt_str]; - else - filename_str = opts.output_filename_id; - end - output_file_name = append(root_directory,"/output/asgard-out",filename_str,".mat"); - outputs.output_file_name = output_file_name; - - save(output_file_name,'pde','opts','outputs','nodes','hash_table'); + + outputs.output_file_name = create_output_filename(opts); + save(outputs.output_file_name,'pde','opts','outputs'); end diff --git a/sd_term_coeff_matrix.m b/sd_term_coeff_matrix.m index cb453c9a..21f5d508 100644 --- a/sd_term_coeff_matrix.m +++ b/sd_term_coeff_matrix.m @@ -1,6 +1,6 @@ function [term_1D] = sd_term_coeff_matrix(deg,t,dim,term_1D,params,FMWT_blocks,coeff_level) -if ~exist('lev','var') || isempty(coeff_level) +if isempty(coeff_level) %Removed the lack of 'lev' or 'var' variable?? --SRS coeff_level = dim.lev; end diff --git a/Test_SeperableCoefficient2D_cleanup.m b/separable/Test_SeperableCoefficient2D_cleanup.m similarity index 100% rename from Test_SeperableCoefficient2D_cleanup.m rename to separable/Test_SeperableCoefficient2D_cleanup.m diff --git a/time_advance.m b/time_advance.m index 55a5f99e..df332238 100644 --- a/time_advance.m +++ b/time_advance.m @@ -208,16 +208,19 @@ f1 = expm(A*dt)*f0; end - function ret = rhs_integrand(u) - s = source_vector(pde,opts,hash_table,u); - bc = boundary_condition_vector(pde,opts,hash_table,u); - uu = t+dt-u; - if applyLHS - ret = ALHS\(expm(uu*(ALHS\A)) * (s+bc)); - else - ret = expm(uu*A) * (s+bc); - end +Q = A*f0; + + +function ret = rhs_integrand(u) + s = source_vector(pde,opts,hash_table,u); + bc = boundary_condition_vector(pde,opts,hash_table,u); + uu = t+dt-u; + if applyLHS + ret = ALHS\(expm(uu*(ALHS\A)) * (s+bc)); + else + ret = expm(uu*A) * (s+bc); end +end rhs_integral = integral(@rhs_integrand,t,t+dt,'ArrayValued',true);%,'RelTol',1e-5,'AbsTol',1e-5); f1 = f1 + rhs_integral; diff --git a/two_scale/two_scale_rel_1.mat b/two_scale/two_scale_rel_1.mat new file mode 100644 index 00000000..4391584a Binary files /dev/null and b/two_scale/two_scale_rel_1.mat differ diff --git a/two_scale/two_scale_rel_10.mat b/two_scale/two_scale_rel_10.mat new file mode 100644 index 00000000..90b52aef Binary files /dev/null and b/two_scale/two_scale_rel_10.mat differ diff --git a/two_scale/two_scale_rel_2.mat b/two_scale/two_scale_rel_2.mat new file mode 100644 index 00000000..0b76791c Binary files /dev/null and b/two_scale/two_scale_rel_2.mat differ diff --git a/two_scale/two_scale_rel_3.mat b/two_scale/two_scale_rel_3.mat new file mode 100644 index 00000000..417fb787 Binary files /dev/null and b/two_scale/two_scale_rel_3.mat differ diff --git a/two_scale/two_scale_rel_4.mat b/two_scale/two_scale_rel_4.mat new file mode 100644 index 00000000..f8fa0c0f Binary files /dev/null and b/two_scale/two_scale_rel_4.mat differ diff --git a/two_scale/two_scale_rel_5.mat b/two_scale/two_scale_rel_5.mat new file mode 100644 index 00000000..2eea2880 Binary files /dev/null and b/two_scale/two_scale_rel_5.mat differ diff --git a/two_scale/two_scale_rel_6.mat b/two_scale/two_scale_rel_6.mat new file mode 100644 index 00000000..7052f48c Binary files /dev/null and b/two_scale/two_scale_rel_6.mat differ diff --git a/two_scale/two_scale_rel_7.mat b/two_scale/two_scale_rel_7.mat new file mode 100644 index 00000000..1f1a32f7 Binary files /dev/null and b/two_scale/two_scale_rel_7.mat differ diff --git a/two_scale/two_scale_rel_8.mat b/two_scale/two_scale_rel_8.mat new file mode 100644 index 00000000..eb3d6704 Binary files /dev/null and b/two_scale/two_scale_rel_8.mat differ