From 5afd98e150c60a77b59fa975daf5052aba1ceac9 Mon Sep 17 00:00:00 2001 From: Peter Brady Date: Fri, 9 Aug 2024 14:06:35 -0500 Subject: [PATCH 1/6] add time offset for LowStorageIntegrator --- .../low_storage_integrator.cpp | 19 +++++++++++++++++++ src/time_integration/staged_integrator.hpp | 1 + 2 files changed, 20 insertions(+) diff --git a/src/time_integration/low_storage_integrator.cpp b/src/time_integration/low_storage_integrator.cpp index d833ddd8ad20..4d30e70fa97c 100644 --- a/src/time_integration/low_storage_integrator.cpp +++ b/src/time_integration/low_storage_integrator.cpp @@ -57,11 +57,13 @@ LowStorageIntegrator::LowStorageIntegrator(const std::string &name) beta.resize(nstages); gam0.resize(nstages); gam1.resize(nstages); + c.resize(nstages); delta[0] = 1.0; beta[0] = 1.0; gam0[0] = 0.0; gam1[0] = 1.0; + c[0] = 0.0; } else if (name_ == "rk2") { nstages = 2; nbuffers = 2; @@ -69,16 +71,19 @@ LowStorageIntegrator::LowStorageIntegrator(const std::string &name) beta.resize(nstages); gam0.resize(nstages); gam1.resize(nstages); + c.resize(nstages); delta[0] = 1.0; beta[0] = 1.0; gam0[0] = 0.0; gam1[0] = 1.0; + c[0] = 0.0; delta[1] = 0.0; beta[1] = 0.5; gam0[1] = 0.5; gam1[1] = 0.5; + c[1] = 1.0; } else if (name_ == "vl2") { nstages = 2; nbuffers = 2; @@ -86,16 +91,19 @@ LowStorageIntegrator::LowStorageIntegrator(const std::string &name) beta.resize(nstages); gam0.resize(nstages); gam1.resize(nstages); + c.resize(nstages); delta[0] = 1.0; beta[0] = 0.5; gam0[0] = 0.0; gam1[0] = 1.0; + c[0] = 0.0; delta[1] = 0.0; beta[1] = 1.0; gam0[1] = 0.0; gam1[1] = 1.0; + c[1] = 0.5; } else if (name_ == "rk3") { nstages = 3; nbuffers = 2; @@ -103,21 +111,25 @@ LowStorageIntegrator::LowStorageIntegrator(const std::string &name) beta.resize(nstages); gam0.resize(nstages); gam1.resize(nstages); + c.resize(nstages); delta[0] = 1.0; beta[0] = 1.0; gam0[0] = 0.0; gam1[0] = 1.0; + c[0] = 0.0; delta[1] = 0.0; beta[1] = 0.25; gam0[1] = 0.25; gam1[1] = 0.75; + c[1] = 1.0; delta[2] = 0.0; beta[2] = 2.0 / 3.0; gam0[2] = 2.0 / 3.0; gam1[2] = 1.0 / 3.0; + c[2] = 0.5; } else if (name_ == "rk4") { // Classic 5-stage SSPRK(5)4 in low-storage form // ceff = 0.377 @@ -128,31 +140,38 @@ LowStorageIntegrator::LowStorageIntegrator(const std::string &name) beta.resize(nstages); gam0.resize(nstages); gam1.resize(nstages); + c.resize(nstages); delta[0] = 1.0; beta[0] = 0.357534921136978; gam0[0] = 0.0; gam1[0] = 1.0; + c[0] = 0.0; delta[1] = 0.0; beta[1] = 2.364680399061355; gam0[1] = -3.666545952121251; gam1[1] = 4.666545952121251; + c[1] = 0.357534921136978; delta[2] = 0.0; beta[2] = 0.016239790859612; gam0[2] = 0.035802535958088; gam1[2] = 0.964197464041912; + c[2] = 1.0537621812245777; delta[3] = 0.0; beta[3] = 0.498173799587251; gam0[3] = 4.398279365655791; gam1[3] = -3.398279365655790; + c[3] = 0.05396714924417825; delta[4] = 0.0; beta[4] = 0.433334235669763; gam0[4] = 0.770411587328417; gam1[4] = 0.229588412671583; + c[4] = 0.7355363985311864; + } else { throw std::invalid_argument("Invalid selection for the time integrator: " + name_); } diff --git a/src/time_integration/staged_integrator.hpp b/src/time_integration/staged_integrator.hpp index 329f69bc294b..10389bb6d8f7 100644 --- a/src/time_integration/staged_integrator.hpp +++ b/src/time_integration/staged_integrator.hpp @@ -55,6 +55,7 @@ class LowStorageIntegrator : public StagedIntegrator { std::vector beta; std::vector gam0; std::vector gam1; + std::vector c; // time offset of each stage }; // TODO(JMM): Should this be named ButcherTableauIntegrator? From 8ea6f8769766bd9b7c63e6c528bc2b3a9a952343 Mon Sep 17 00:00:00 2001 From: Peter Brady Date: Wed, 14 Aug 2024 14:57:05 -0500 Subject: [PATCH 2/6] Add docs for `c` in `LowStorageIntegrator` --- CHANGELOG.md | 1 + doc/sphinx/src/integrators.rst | 18 ++++++++++++------ 2 files changed, 13 insertions(+), 6 deletions(-) diff --git a/CHANGELOG.md b/CHANGELOG.md index c404edb308a7..006d85fc561b 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -3,6 +3,7 @@ ## Current develop ### Added (new features/APIs/variables/...) +- [[PR 1151]]((https://github.com/parthenon-hpc-lab/parthenon/pull/1151)) Add time offset `c` to LowStorageIntegrator - [[PR 1143]](https://github.com/parthenon-hpc-lab/parthenon/pull/1143) Add tensor indices to VariableState, add radiation constant to constants, add TypeLists, allow for arbitrary containers for solvers - [[PR 1140]](https://github.com/parthenon-hpc-lab/parthenon/pull/1140) Allow for relative convergence tolerance in BiCGSTAB solver. - [[PR 1047]](https://github.com/parthenon-hpc-lab/parthenon/pull/1047) General three- and four-valent 2D forests w/ arbitrary orientations. diff --git a/doc/sphinx/src/integrators.rst b/doc/sphinx/src/integrators.rst index 8e035832f473..be5d4bf63b2e 100644 --- a/doc/sphinx/src/integrators.rst +++ b/doc/sphinx/src/integrators.rst @@ -32,15 +32,17 @@ described in `Ketchson (2010)`_. These integrators are of the classic .. math:: u^{(0)} &= u^n \\ - u^{(i)} &= \sum_{k=0}^{i-1} (\alpha_{i,k} u^{(k)} + \Delta t \beta_{i, k} F(u^{(k)})\\ + u^{(i)} &= \sum_{k=0}^{i-1} (\alpha_{i,k} u^{(k)} + \Delta t \beta_{i, k} F(t^n+c_k \Delta t, u^{(k)}))\\ u^{n+1} &= u^{(m)} where superscripts in parentheses mean subcycles in a Runge-Kutta -integration and :math:`F` is the right-hand-side of ODE system. The +integration and :math:`F` is the right-hand-side of ODE system. Note +that the time dependence of :math:`F` is explicitly included in the above +formulation. The difference between these low-storage methods and the classic SSPK methods is that the low-storage methods typically have sparse :math:`\alpha` and :math:`\beta` matrices, which are replaced by -diagonal termes, named :math:`\gamma_0` and :math:`\gamma_1` +diagonal terms, named :math:`\gamma_0` and :math:`\gamma_1` respectively. These methods can be generalized to support more general methods with @@ -52,11 +54,15 @@ The full update then takes the form: .. math:: u^{(1)} &:= u^{(1)} + \delta_s u^{(0)} \\ - u^{(0)} &:= \gamma_{s0} u^{(0)} + \gamma_{s1} u^{(1)} + \beta_{s,s-1} \Delta t F(u^{(0)}) + u^{(0)} &:= \gamma_{s0} u^{(0)} + \gamma_{s1} u^{(1)} + \beta_{s,s-1} \Delta t F(t^n+c_s\Delta t, u^{(0)}) where here :math:`u^{(0)}` and :math:`u^{(1)}` are the two storage buffers required to compute the update for a given Runge-Kutta stage -:math:`s`. +:math:`s`. While the :math:`delta`, :math:`beta`, :math:`gamma_0` and :math:`gamma_1` +associated with a particular scheme are published in the literature, :math:`c` is not. +Instead, :math:`c` is computed following the procedure outlined in +`Ketchson (2010)`_ for obtaining the Butcher coefficients from their low-storage +counterparts. .. _Ketchson (2010): https://doi.org/10.1016/j.jcp.2009.11.006 @@ -65,7 +71,7 @@ buffers required to compute the update for a given Runge-Kutta stage .. _Athena++ paper: https://doi.org/10.3847/1538-4365/ab929b The ``LowStorageIntegrator`` contains arrays for ``delta``, ``beta``, -``gam0``, and ``gam1``. Available integration methods are: +``gam0``, ``gam1``, and ``c``. Available integration methods are: * ``RK1``, which is simply forward Euler. From 4d2bc6017f320dfc7660c2c70d1487b25771b146 Mon Sep 17 00:00:00 2001 From: Peter Brady Date: Wed, 14 Aug 2024 15:32:12 -0500 Subject: [PATCH 3/6] Fix math expressions in docs --- doc/sphinx/src/integrators.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/doc/sphinx/src/integrators.rst b/doc/sphinx/src/integrators.rst index be5d4bf63b2e..9197656abe68 100644 --- a/doc/sphinx/src/integrators.rst +++ b/doc/sphinx/src/integrators.rst @@ -58,7 +58,7 @@ The full update then takes the form: where here :math:`u^{(0)}` and :math:`u^{(1)}` are the two storage buffers required to compute the update for a given Runge-Kutta stage -:math:`s`. While the :math:`delta`, :math:`beta`, :math:`gamma_0` and :math:`gamma_1` +:math:`s`. While the :math:`\delta`, :math:`\beta`, :math:`\gamma_0` and :math:`\gamma_1` associated with a particular scheme are published in the literature, :math:`c` is not. Instead, :math:`c` is computed following the procedure outlined in `Ketchson (2010)`_ for obtaining the Butcher coefficients from their low-storage From 8cf2a6a1af38ce7bd208af0939bf045c99bf77ef Mon Sep 17 00:00:00 2001 From: Peter Brady Date: Fri, 23 Aug 2024 15:23:31 -0500 Subject: [PATCH 4/6] add notebook for sparse time levels --- scripts/sparseIntegrators.nb | 7543 ++++++++++++++++++++++++++++++++++ 1 file changed, 7543 insertions(+) create mode 100644 scripts/sparseIntegrators.nb diff --git a/scripts/sparseIntegrators.nb b/scripts/sparseIntegrators.nb new file mode 100644 index 000000000000..d81623b3a938 --- /dev/null +++ b/scripts/sparseIntegrators.nb @@ -0,0 +1,7543 @@ +(* Content-type: application/vnd.wolfram.mathematica *) + +(*** Wolfram Notebook File ***) +(* http://www.wolfram.com/nb *) + +(* CreatedBy='Mathematica 13.2' *) + +(*CacheID: 234*) +(* Internal cache information: +NotebookFileLineBreakTest +NotebookFileLineBreakTest +NotebookDataPosition[ 158, 7] +NotebookDataLength[ 401150, 7535] +NotebookOptionsPosition[ 397281, 7463] +NotebookOutlinePosition[ 397679, 7479] +CellTagsIndexPosition[ 397636, 7476] +WindowFrame->Normal*) + +(* Beginning of Notebook Content *) +Notebook[{ + +Cell[CellGroupData[{ +Cell["Computing Butcher Coefficients", "Chapter", + CellChangeTimes->{{3.933340025507483*^9, + 3.933340039642274*^9}},ExpressionUUID->"da94eb33-72d4-4c5a-bfbb-\ +d9684d02fbee"], + +Cell[TextData[{ + "The goal is to compute the time offset, \[ScriptC], associated with the \ +stages of a low storage RK integrator. 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See scripts/mathematica/sparse_integrators.nb + std::vector c; }; // TODO(JMM): Should this be named ButcherTableauIntegrator? diff --git a/tst/regression/test_suites/particle_leapfrog/parthinput.particle_leapfrog b/tst/regression/test_suites/particle_leapfrog/parthinput.particle_leapfrog index f91bec8010bd..5a9d2ea2e5e9 100644 --- a/tst/regression/test_suites/particle_leapfrog/parthinput.particle_leapfrog +++ b/tst/regression/test_suites/particle_leapfrog/parthinput.particle_leapfrog @@ -61,3 +61,7 @@ swarm_variables = id, v, vv file_type = rst dt = 1.0 + + +file_type = openpmd +dt = 1.0 From 02b0bb459e71f63c72cd838fdbcae9c22ff51261 Mon Sep 17 00:00:00 2001 From: Philipp Grete Date: Mon, 26 Aug 2024 09:50:10 +0200 Subject: [PATCH 6/6] Oops. Fixed mixed files. --- doc/sphinx/src/integrators.rst | 2 ++ .../particle_leapfrog/parthinput.particle_leapfrog | 4 ---- 2 files changed, 2 insertions(+), 4 deletions(-) diff --git a/doc/sphinx/src/integrators.rst b/doc/sphinx/src/integrators.rst index 9197656abe68..53b67b7a19e0 100644 --- a/doc/sphinx/src/integrators.rst +++ b/doc/sphinx/src/integrators.rst @@ -63,6 +63,8 @@ associated with a particular scheme are published in the literature, :math:`c` i Instead, :math:`c` is computed following the procedure outlined in `Ketchson (2010)`_ for obtaining the Butcher coefficients from their low-storage counterparts. +A Mathematica notebook to calculate :math:`c` is provided +`here `__. .. _Ketchson (2010): https://doi.org/10.1016/j.jcp.2009.11.006 diff --git a/tst/regression/test_suites/particle_leapfrog/parthinput.particle_leapfrog b/tst/regression/test_suites/particle_leapfrog/parthinput.particle_leapfrog index 5a9d2ea2e5e9..f91bec8010bd 100644 --- a/tst/regression/test_suites/particle_leapfrog/parthinput.particle_leapfrog +++ b/tst/regression/test_suites/particle_leapfrog/parthinput.particle_leapfrog @@ -61,7 +61,3 @@ swarm_variables = id, v, vv file_type = rst dt = 1.0 - - -file_type = openpmd -dt = 1.0