[petsc-users] shell preconditioner for Schur complement

[Matthew Knepley]

On Wed, Feb 10, 2021 at 11:51 AM Matteo Semplice <
matteo.semplice at uninsubria.it> wrote:

> Dear PETSc users,
>      we are trying to program a preconditioner for the Schur complement
> of a Stokes system, but it seems that the r.h.s. for the Schur
> complement system differs from what we expect by a scale factor, which
> we don't understand.
>
> Our setup has a system matrix A divided in 2x2 blocks for velocity and
> pressure variables. We have programmed our preconditioner in a routine
> PrecondSchur and in the main program we do
>
> PC pc;
> KSPGetPC(kspA,&pc);
> PCSetFromOptions(pc);
> KSPSetOperators(kspA, A, A);
> KSPSetInitialGuessNonzero(kspA,PETSC_FALSE);
> KSPSetFromOptions(kspA);
> KSP *subksp;
> PetscInt nfield;
> PCSetUp(pc);
> PCFieldSplitGetSubKSP(pc, &nfield, &subksp);
> PC pcSchur;
> KSPGetPC(subksp[1],&pcSchur);
> PCSetType(pcSchur,PCSHELL);
> PCShellSetApply(pcSchur,PrecondSchur);
> KSPSetFromOptions(subksp[1]);
>
> and eventually
>
> KSPSolve(A,b,solution);
>
> We run the code with options
>
>   -ksp_type fgmres \
>   -pc_type fieldsplit -pc_fieldsplit_type schur \
>   -pc_fieldsplit_schur_fact_type full \
>
> and, from reading section 2.3.5 of the PETSc manual, we'd expect that
> the first r.h.s. passed to PrecondSchur be exactly
>      b_1-A_10*inv(A_00)*b_0
>
> Instead (from a monitor function attached to the subksp[1] solver), the
> first r.h.s. appears to be scalar multiple of the above vector; we are
> guessing that we should take into account this multiplicative factor in
> our preconditioner routine, but we cannot understand where it comes from
> and how its value is determined.
>
> Could you explain us what is going on in the PC_SCHUR exactly, or point
> us to some working code example?
>

1) It is hard to understand solver questions without the output of -ksp_view

2) The RHS will depend on the kind of factorization you are using for the
system


https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCFieldSplitSetSchurFactType.html#PCFieldSplitSetSchurFactType

    I can see which one in the view output

  Thanks,

    Matt


> Thanks in advance!
>
>      Matteo
>
>

-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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