[petsc-dev] Bordered systems and low-rank corrections

[Jed Brown]

On Sat, Nov 5, 2011 at 10:02, Mark F. Adams <mark.adams at columbia.edu> wrote:

> FYI: the yellow SIAM book on mixed FE methods by Brezi and Fortin has an
> excellent 2 page section on Uzawa that give, among other things, a precise
> recipe for Uzawa (page 99 I think) including preconditioning and a non-zero
> RHS for the constraint part.


You can run Uzawa with -pc_fieldsplit_type schur and Richardson.

As a practical matter, I don't see any complication for Woodbury
with/without nonzero RHS. I would do the Schur complement in the other
direction and and as the preconditioner for the Schur complement that came
from eliminating the (small number of) augmented variables, I would use the
Woodbury formula with only a preconditioner for the A^{-1} that appear in
that formula.

If that inner preconditioner was a full solve, then this would provide the
exact inverse, but that wouldn't gain anything because then CG on the Schur
complement _in_ the augmented variables would converge without
preconditioning in the same number of iterations.
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