Schur complement system

[Matthew Knepley]

On Sun, Mar 9, 2008 at 3:25 PM, Kathrin Burckhardt
<tribur at vision.ee.ethz.ch> wrote:
> Hi Matt,
>
>  1. Where do I integrate the application of the Schur system using
>     MATSHELL? Can I use KSP?

Here is a sketch:

MatShellSetLOperation(S, MATOP_MULT, myApply);

PetscErrorCode myApply(Mat S, Vec x, Vec y) {
  <Get temp vectors, matrices, and KSP from shell context>
  MatMult(B, x, tmp1);
  KSPSetOperators(ksp, A, A);
  KSPSolve(ksp, tmp1, tmp2);
  MatMultTranspose(B, tmp2, y);
}

>  2. I already have the local Schur complements computed. Is it advisable
>     to once setup the global Schur matrix using MATIS and then use KSP,
>     instead of the application of the Schur complement, i.e. the two
>     MatMult() and the KSPSolve(), at each iteration?

It depends on how dense the Schur complement is.

   Matt

>  Thank you,
>  Kathrin
>
>
>  > Yes, you can certainly solve this system. Normally, you would just create a
>  > simple MATSHELL to apply the Schur complement, which does two MatMult()s
>  > and one KSPSolve(). We are integrating specific support for this, but it will
>  > not be released until the summer I think.
>  >
>  >  Thanks,
>  >
>  >     Matt
>  >
>  > On Fri, Mar 7, 2008 at 5:50 AM, Kathrin Burckhardt
>  > <tribur at vision.ee.ethz.ch> wrote:
>  >> Dear nice people,
>  >>
>  >>  Did you ever try to solve a Schur complement system using PETSc?
>  >>
>  >>
>  >
>  >
>  >
>  >
>
>



-- 
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