[petsc-users] Nullspaces for schur complement PCs

[Dmitry Karpeyev]

I'm actually not proposing putting extra intelligence into the DM, but into
the ApplicationCtx
and the associated callbacks that the user can write.  The DM is used to
propagate this information
to the deeper levels of a nested solver hierarchy by "restricting" the
relevant ctx/callbacks to the split's subdm.
Restriction is a standard PETSc way of propagating information through the
solver hierarchy (e.g., MG, (N)ASM),
but it hasn't been used in the FieldSplit context.

Currently even a user-defined preconditioner for a Schur complement that
sits at a deeper level in the hierarchy
cannot be set very easily, especially when the solvers are configured
dynamically.

Yes, this does place a greater emphasis on DM, but not overly so, in my
view.

On Wed Nov 12 2014 at 8:39:23 PM Jed Brown <jed at jedbrown.org> wrote:

> Dmitry Karpeyev <karpeev at mcs.anl.gov> writes:
>
> > I think the problem-specific solver configuration can be carried out by
> an
> > additional user-specified callback (attached, e.g., using
> PCSetUserSetUp())
> > called from PCSetUp().
> > The problem of propagating it down the hierarchy can be solved by using
> DMs
> > (even DMShell would do, as it carries an ApplicationCtx) and a consistent
> > use of DMFieldSplitRestrictHook (by analogy with other restriction hooks,
> > like DMSubDomainRestrictHook).  DMFieldSplitRestrict() would be called
> when
> > creating each split and one of the restriction hooks would transfer the
> > necessary contexts.
> >
> > This is a bit heavyweight, but flexible and logically consistent, it
> seems
> > to me, and no worse that what has to be done to propagate things like
> > DMSNES/DMKSP through the MG hierarchy. (N)ASM uses something similar,
> too.
>
> Previously discussed.
>
> http://lists.mcs.anl.gov/pipermail/petsc-dev/2012-August/009291.html
>
> It makes things more dependent on DM, but that may be less bad than the
> alternatives.
>
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