[petsc-dev] chebychev method

[Jed Brown]

Stefano Zampini <s.zampini at cineca.it> writes:
> In case of BDDC coarse problem, I will not expect strongly unymmetricity.
> The coarse problem is also structurally symmetric.

Okay, Chebyshev should just work.  I recommend not turning on the
"hybrid" stuff because that makes the operator nonlinear and doesn't
help much in my experience, particularly as a coarse solver.

> 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).

Okay.

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

Sure, but note that GMRES is a nonlinear operator unless you converge it
to high accuracy.  Better is to recursively restrict the coarse space to
smaller process sets (like we do in PCGAMG).
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