[petsc-users] Nullspaces for schur complement PCs

Matthew Knepley knepley at gmail.com
Tue Nov 11 05:45:12 CST 2014

On Mon, Nov 10, 2014 at 10:28 PM, Jed Brown <jed at jedbrown.org> wrote:

> Matthew Knepley <knepley at gmail.com> writes:
> >> at which point the nullspace is not attached, no?
> >>
> >
> > Crap, that is right. I think we should propagate the nullspace from
> pmat[1].
> Uh, there is no reason pmat[1] can be expected to have the same null
> space.  pmat[1] is the zero matrix in some important cases, and the null
> space of the Schur complement (or its SIMPLE-type approximation) depends
> on boundary conditions in a different block (thus problematic for
> segregated assembly).  I've been unsuccessful so far in my search for an
> elegant solution, but passing the null space along in this way is
> encouraging overt lying and can be expected to break other algorithms as
> well as any consistency tests we might add in the future.

I know it can break, however here is my thinking. The user is completely in
here, and this is the only channel we have to pass the information. So I
would make
them responsible for breakage. We have excellent diagnostics here, so we
can tell
who has a null space right away. We have a lot of interface that allow a
user to break
PETSc in order to allow them to customize it sufficiently.



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
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