[petsc-dev] chebychev method

[Jed Brown]

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.

> 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.
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