Change solver in mixed Poisson

[jorgensd]

"superlu_dist" fails with

Traceback (most recent call last):
  File "/root/shared/demo/demo_mixed-poisson.py", line 196, in <module>
    raise e
  File "/root/shared/demo/demo_mixed-poisson.py", line 189, in <module>
    w_h = problem.solve()
          ^^^^^^^^^^^^^^^
  File "/usr/local/dolfinx-real/lib/python3.12/dist-packages/dolfinx/fem/petsc.py", line 906, in solve
    self._solver.solve(self._b, self._x)
  File "petsc4py/PETSc/KSP.pyx", line 1782, in petsc4py.PETSc.KSP.solve
petsc4py.PETSc.Error: error code 71
[0] KSPSolve() at /usr/local/petsc/src/ksp/ksp/interface/itfunc.c:1075
[0] KSPSolve_Private() at /usr/local/petsc/src/ksp/ksp/interface/itfunc.c:826
[0] KSPSetUp() at /usr/local/petsc/src/ksp/ksp/interface/itfunc.c:415
[0] PCSetUp() at /usr/local/petsc/src/ksp/pc/interface/precon.c:1071
[0] PCSetUp_LU() at /usr/local/petsc/src/ksp/pc/impls/factor/lu/lu.c:121
[0] MatLUFactorNumeric() at /usr/local/petsc/src/mat/interface/matrix.c:3307
[0] MatLUFactorNumeric_SuperLU_DIST() at /usr/local/petsc/src/mat/impls/aij/mpi/superlu_dist/superlu_dist.c:561
[0] Zero pivot in LU factorization: https://petsc.org/release/faq/#zeropivot
[0] Zero pivot in row 1862

Changing to "mumps" resolves the issue.
Also adding assertion if ksp fails to demo to avoid this slipping in at a future release of mumps.

[jorgensd]

Mumps doesnt like int64, so either we skip int64 or change to an iterative solver?

[jhale]

Hasn't this been running ok for years?

[jorgensd]

Hasn't this been running ok for years?

That is unclear. We never had the ksp error if not converged on. We would have to work our way backwards on an int64 system to check that it actually converge

[garth-wells]

Hasn't this been running ok for years?

Yes, but the underlying solvers have changed and we never checked the correctness of the solution.

I've been planning to change this demo to using a block-preconditioned solver (perhaps alongside the direct solver). Will do as soon as I get a chance.