[petsc-dev] Preconditioner for Schur complement (pcfieldsplit)

[Jed Brown]

On Wed, Apr 6, 2011 at 11:36, Thomas Witkowski <
thomas.witkowski at tu-dresden.de> wrote:

> This brings me back to the starting point of my current problem: how to set
> splits for MatNest correctly? PCFieldSplitSetFields seems not to work in my
> case.


PCFieldSplitSetFields() is a special case that only works when fields are
interlaced. I would like to get rid of it, but there are still some cases
where it can provide a faster implementation in the special case so we'll
wait until the faster implementation can be accessed through the generic
interface.


> When I want to make use of PCFieldSplitSetIS for splitting MatNest, which
> indices should I provide? The MatNest I've created consists of the to main
> diagonal blocks with indices 0 to n and 0 to m.


This does not make sense because these index sets overlap. Maybe you want to
use (0:m) and (m:m+n), then these are the index sets you pass to
PCFieldSplitSetIS(). With two processes, you would usually have

is0 = [(0:m0), (m0+n0:m0+n0+m1)]
is1 = [(m0:m0+n0), (m0+n0+m1:m0+n0+m1+n1)]

This is the decomposition that is set up automatically by MatCreateNest when
you pass PETSC_NULL for the index sets.

You should be able to retrieve the index sets that MatNest created using
MatNestGetSubMats(), but this is not implemented (Dave and I discussed it
and agree, but a patch has not been pushed yet).
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