Interaction between `fem.petsc.LinearProblem` and setting a nullspace

[francesco-ballarin]

The logic in fem.petsc.LinearProblem is currently the following

1. initialize the matrix A and vector b data structure, in __init__
2. assemble the matrix and vector values, in solve
3. call KSP to solve the linear system, in solve.

I think this makes sense for most of the cases. However, there is a limit case in which the user would need to interact with the matrix/vector between steps 2 and 3, which is the case of setting a nullspace, doing something like

assert nullspace.test(A)
A.setNullSpace(nullspace)
nullspace.remove(b)

• What we currently do is to do A.setNullSpace(nullspace) after step 1. See e.g.

  dolfinx/python/demo/demo_stokes.py

  Line 248 in a6dc610

  problem.A.setNullSpace(nsp)

  . This works perfectly, even when A is still zero.
• What we currently do is to do assert nullspace.test(A) after step 3. See e.g.

  dolfinx/python/demo/demo_stokes.py

  Line 261 in a6dc610

  assert nsp.test(problem.A)

  . IMHO, this is hard to understand for a end-user: arguably, the logical order would be first to test the nullspace, if the test passes then to set it to the matrix, and finally to solve. Unfortunately, we cannot do it in this way because the test would need to happen between steps 2 and 3, at

  dolfinx/python/dolfinx/fem/petsc.py

  Line 968 in a6dc610
  .
• We currently cannot have nullspace.remove(b) . Again, it would need to happen between steps 2 and 3.

Opening this issue as an enhancement just in case we can work out a slightly modified design, or determine that this is not worth it. I like fem.petsc.LinearProblem as it currently is and I would refrain from making it much more involved for the end-user just to support this.