Add support for deflation via firedrake.DeflatedSNES

[pefarrell]

Description

This PR adds support for deflation in Firedrake via a custom SNES solver (firedrake.DeflatedSNES) and an object storing the solutions to be deflated (firedrake.Deflation). Deflation is a numerical technique for computing multiple solutions of a nonlinear problem. A general introduction to the idea can be found in

https://pefarrell.org/files/talks/deflation.pdf

This PR adapts and updates some code I've had in defcon (https://bitbucket.org/pefarrell/defcon) for many years.

The user interface can be seen in the tests in this PR, but the basic idea is sketched below.

    deflation = Deflation()  # by default, deflate no solutions
    appctx = {"deflation": deflation}

    # Find the first solution
    u.interpolate(guess)
    solver = NonlinearVariationalSolver(problem, solver_parameters=sp, appctx=appctx)
    solver.solve()

    # Now deflate the first solution found, restore initial guess, and
    # find second solution
    first = Function(u)
    deflation.append(first)
    u.interpolate(guess)  # start from the same initial guess as before
    solver.solve()  # if this converges, it converges to something different

The VI support requires a small PR in petsc4py to wrap SNESVIGetVariableBounds, which I will submit presently.

[pefarrell]

The petsc4py MR is at https://gitlab.com/petsc/petsc/-/merge_requests/8701.

[pefarrell]

The petsc4py MR has now been merged to PETSc main.

[pbrubeck]

Can we store this method as an attribute to avoid the weakref?

[pefarrell]

I confess I don't understand. Won't that keep a strong reference?

[pbrubeck]

Is this still necessary?

[pefarrell]

It's convenient to have, if not necessary.