[petsc-dev] chebychev method

[Stefano Zampini]

2013/11/18 Jed Brown <jedbrown at mcs.anl.gov>

> Stefano Zampini <s.zampini at cineca.it> writes:
>
> > Currently, the man page for
> > chebychev<
> http://www.mcs.anl.gov/petsc/petsc-dev/docs/manualpages/KSP/KSPCHEBYSHEV.html
> >states
> > that it will only work for symmetric positive (semi-)definite
> > systems, but the chebychev code has support for nonsymmetric systems
> using
> > the hybrid approach. Is the hybrid branch still a work in progress?
>
> The "hybrid" in cheby.c is nothing special for nonsymmetric problems.
> In the paper, it just means that Arnoldi is used instead of Lanczos, but
> the spectrum still has to be near the real line for it to be any good.
> The tests in the paper are not so strongly nonsymmetric, and the most
> nonsymmetric (Problem 4) performs better with Orthomin.
>
> Cheby is fine more mildly nonsymmetric problems and inadequate for
> strongly nonsymmetric.
>
>
In case of BDDC coarse problem, I will not expect strongly unymmetricity.
The coarse problem is also structurally symmetric.


> > Who can give me some quick hints on how to work with it?
> >
> > I wish to make Chebychev the default KSP for the coarse problem of the
> > BDDC, and I'd wish to know in which cases it will work or not.
>
> Actually, I would rather you not change the defaults unless it is
> clearly better to the extent we should change other coarse level solvers
> in PETSc.  It is confusing for users when every component chooses its
> own defaults for similar concepts seemingly-arbitrarily.
>

Sorry, my fault. I didn't explain completely my point. My intent is not of
changing the default of the coarse solver (which is
ksppreonly+pcredundant), but to find a good ksp in case the user requests a
multilevel bddc, i.e. to solve the coarse problem with another level of
BDDC. In that case, I would choose very few iterations of a cheap ksp (like
richardson or cheby).

It seems to me that the rational can be: use cheby if the problem is
positive (semi-) definite, and gmres if not. Suggestions?




-- 

Ph. D. Stefano Zampini
CINECA
SuperComputing Applications and Innovations Department - SCAI
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