[petsc-users] ASM for Saddle-point problems

Matthew Knepley knepley at gmail.com
Wed Feb 26 09:39:41 CST 2014

On Wed, Feb 26, 2014 at 6:25 AM, Jed Brown <jed at jedbrown.org> wrote:

> Adriano Côrtes <adrimacortes at gmail.com> writes:
> > Dear all,
> >
> > I'm solving a saddle-point problem coming from a 2d stokes problem
> > discretized by an inf-sup stable mixed element.
> > By now I'm playing in serial, because I want to understand the
> > behavior of the solver. I have the whole matrix assembled in memory.
> > After playing with GMRES and ILU with different fill-ins,
> ILU is typically terrible for saddle point problems.
> > I started playing with ASM to see if I can get better results. By
> > using -pc_asm_blocks and -pc_asm_overlap I tried some variations none
> > giving better results.
> >
> > My questions are
> >
> > 1. how the blocks are built by PETSc, since my problem is a saddle-point
> one?
> It starts with the set of owned variables and adds overlap by taking all
> neighbors represented in the graph.  You generally need a minimum
> overlap of 1 for saddle point problems.
> > 2. From the theoretical point-of-view, block-factorizations, that is
> > using PCFieldsplit, are in general the best we can have in terms of
> > performance (number of iterations and scalability)?
> There is no consensus on this and I'm actually fond of "monolithic"
> multigrid methods, but it is harder to reuse components and harder to
> debug convergence.  PCFieldSplit is a good methodology.  Some of my
> talks have a comparison slide.  Here is a high-level one from last week.
> http://59a2.org/files/20140221-ExploitsInImplicitness.pdf

More specifically, you can use -pc_fieldsplit_detect_saddle_point on your
matrix, and then construct any of the block methods from options. I list
of the interesting ones in the Paris Tutorial on our website.


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
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20140226/5636eb7c/attachment.html>

More information about the petsc-users mailing list