[petsc-dev] help for use PETSc

[Jed Brown]

On Tue, Jun 28, 2011 at 11:55, tuane <tuane at lncc.br> wrote:

> cg+redundant-PC give us the best result, similar to out original direct
> solver. we don't be sure what “redundant” is.
>

Redundant means that the whole problem is solved redundantly (using a direct
solver by default) on every process. It only makes sense as a coarse level
solver.


> Our response are beeing too dependent of these parameters:
>
>   1. iterative solver (CG, GMRES, BCGS)
>   2. preconditioners (jacobi, redundant, ILU)
>   3. tolerance
>   4. number of processors
>

At this point, you should always run with -ksp_monitor_true_residual to make
sure that it is really converging.

We also tried to use the Algebraic Multigrid, but without success. An error
> occurs in the program execution.  We used the routines:
> call PCSetType (pc, PCMG, ierr)
>

This is not algebraic multigrid, it is geometric multigrid. If you use DMDA
to manage the grid, then you could use geometric multigrid here.

But I think you are using a Raviart-Thomas mixed space in which case the
default interpolants from DMDA are not going to work for you.

The simplest thing you can do is to use PCFieldSplit to eliminate the fluxes
such that the preconditioner can work with the non-mixed (H^1-conforming)
operator defined in the potential/pressure space.


The following won't work right now, but it should work soon. I'm describing
it here for the others on petsc-dev. If you call

PCFieldSplitSetIS(pc,"u",is_fluxes);
PCFieldSplitSetIS(pc,"p",is_potential);

and

-pc_type fieldsplit -pc_fieldsplit_type schur
-fieldsplit_u_pc_type jacobi # The (u,u) block is diagonal for lowest order
RT spaces
-fieldsplit_p_pc_type ml # or other multigrid, uses SIMPLE approximation of
the Schur complement which happens to be exact because the (u,u) block is
diagonal.


This won't work right now because PCFieldSplit does not actually call
MatGetSchurComplement() is designed. It would simplify fieldsplit.c to use
MatGetSchurComplement(), but then MatGetSubMatrix() would be called twice
for certain blocks in the matrix, once inside the Schur complement and once
directly from fieldsplit.c. This is why I so want to make a mode in which
the parent retains ownership and the caller gets a (intended to be)
read-only reference when MatGetSubMatrix() and MatGetSchurComplement() are
called.
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