[petsc-users] Fwd: Questions using PCFIELDSPLIT

[Jed Brown]

Adriano Côrtes <adrimacortes at gmail.com> writes:

> 2013/12/14 Jed Brown <jedbrown at mcs.anl.gov>
>>
>> See that "fieldsplit_p_" uses a MATSCHURCOMPLEMENT and actually iterates
>> on that reduced system.  This is different from what is typically done
>> in full-space iterative methods.
>>
>
> Dear Jed,
> Can you elaborate more this comment? What is a MATSCHURCOMPLEMENT
> object? You mean that S is built? Or is it matrix-free as you said
> bellow?

It is a special Mat type that applies the action of the Schur complement
via the definition rather than by explicitly computing its entries.
This is often referred to as "matrix-free", though it is still a Mat in
PETSc (Mat in PETSc means "finite-dimensional linear operator").

>> Use -ksp_converged_reason to find out why the linear solve above did not
>> converge.  Maybe due to an indefinite preconditioner?
>>
>
> This was there result of -ksp_converged_reason
>
> 0 SNES Function norm 9.644918978350e-02
>     0 KSP Residual norm 1.297271248442e-01
>   Linear solve did not converge due to DIVERGED_INDEFINITE_MAT iterations 1
>   1 SNES Function norm 9.644918978350e-02
> Nonlinear solve did not converge due to DIVERGED_LINEAR_SOLVE iterations 1
> SNES Object: 1 MPI processes
>
> This I didn't understand, because minres is supposed to work for
> symmetric indefinite matrices. Isn't it? What am I missing here?

MINRES requires an SPD preconditioner.  As I guessed earlier, you may
have just gotten the sign wrong for the preconditioner.

> I will take a look. Thanks. But just to know if I set
> -fieldsplit_p_ksp_type preonly -fieldsplit_p_pc_type ksp, how do I
> choose the ksp? 

-fieldsplit_p_ksp_ksp_type cg.

> Multigrid V-cycle as you said is the default in this case?

No, but it would be a good choice if the pressure Schur complement is
similar to a Laplacian.  For Stokes (as opposed to finite-time step or
Navier-Stokes), the Schur complement is spectrally equivalent to a
scaled mass matrix, so most people use Jacobi.
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