[petsc-users] ASM for Saddle-point problems

[Jed Brown]

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
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