[petsc-users] Block preconditioning for 3d problem

[Dave Lee]

Hi PETSc,

I have a nonlinear 3D problem for a set of uncoupled 2D slabs. (Which I
ultimately want to couple once this problem is solved).

When I solve the inner linear problem for each of these 2D slabs
individually (using KSPGMRES) the convergence of the outer nonlinear
problem is good. However when I solve the inner linear problem as a single
3D problem (with no coupling between the 2D slabs, so the matrix is
effectively a set of uncoupled blocks, one for each 2D slab) the outer
nonlinear convergence degrades dramatically.

Note that I am not using SNES, just my own quasi-Newton approach for the
outer nonlinear problem.

I suspect that the way to recover the convergence for the 3D coupled
problem is to use some sort of PCBJACOBI or PCFIELDSPLIT preconditioner,
but I'm not entirely sure. I've tried following this example:
https://www.mcs.anl.gov/petsc/petsc-current/src/ksp/ksp/examples/tutorials/ex7.c.html
but without any improvement in the convergence.

On each processor the slab index is the major index and the internal slab
DOF index is the minor index. The parallel decomposition is within the 2D
slab dimensions only, not between slabs.

I'm configuring the 3D inner linear solver as

KSPGetPC(ksp, &pc);
PCSetType(pc, PCBJACOBI);
PCBJacobiSetLocalBlocks(pc, num_slabs, NULL);
KSPSetUp(ksp);
PCBJacobiGetSubKSP(pc, &nlocal, &first_local, &subksp);
for(int ii = 0; ii < nlocal; ii++) {
    KSPGetPC(subksp[ii], &subpc);
    PCSetType(subpc, PCJACOBI);
    KSPSetType(subksp[ii], KSPGMRES);
    KSPSetTolerances(subksp[ii], 1.e-12, PETSC_DEFAULT, PETSC_DEFAULT,
PETSC_DEFAULT);
}

However this does not seem to change the outer nonlinear convergence. When
I run with ksp_view the local block sizes look correct - number of local 2D
slab DOFs for each block on each processor.

Any ideas on what sort of KSP/PC configuration I should be using to recover
the convergence of the uncoupled 2D slab linear solve for this 3D linear
solve? Should I be rethinking my node indexing to help with this?

Cheers, Dave.
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