Regarding the issue of the iterative solver not working

General
1

I am trying to use an iterative solver to solve the Navistox equation.
Refer to it：
https://docs.fenicsproject.org/dolfinx/main/python/demos/demo_navier-stokes.html

I will replace the solver with gmres.
PCtype is ILU. ILU preprocessing does not allow diagonal 0 to appear.

Therefore, I added a rearrangement of the 0 diagonal elements to avoid this issue.

opts[“pc_factor_nonzeros_along_diagonal”]=10**(-8)

The solver as follow:

ksp = PETSc.KSP().create(msh.comm) # type: ignore
ksp.setOperators(A)

ksp.setInitialGuessNonzero(True)
ksp.setConvergenceHistory(reset=True)
ksp.setType(“gmres”)
ksp.getPC().setType(“ilu”)

opts = PETSc.Options() # type: ignore
opts[“ksp_rtol”] = 1.0e-10
opts[“ksp_atol”] = 1.0e-3
opts[“ksp_max_it”] = 800
opts[“pc_factor_nonzeros_along_diagonal”]=10**(-8)
ksp.setFromOptions()

errors：

petsc4py.PETSc.Error: error code 73
[0] KSPSolve() at /usr/local/petsc/src/ksp/ksp/interface/itfunc.c:1082
[0] KSPSolve_Private() at /usr/local/petsc/src/ksp/ksp/interface/itfunc.c:836
[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:1068
[0] PCSetUp_ILU() at /usr/local/petsc/src/ksp/pc/impls/factor/ilu/ilu.c:135
[0] MatILUFactorSymbolic() at /usr/local/petsc/src/mat/interface/matrix.c:6939
[0] MatILUFactorSymbolic_SeqAIJ() at /usr/local/petsc/src/mat/impls/aij/seq/aijfact.c:1678
[0] Object is in wrong state
[0] Matrix is missing diagonal entry 2624

2

The zero terms on the diagonal are probably due to the bottom right block.
A simple is solution is to replace None in

a = fem.form([[a_00, a_01], [a_10, None]])

with a Constant(mesh, 0)*p*q*dx to allocate zero explicitly on the diagonal