On Fri, 12 Feb 2010 10:23:24 -0600, John Peterson <[email protected]>
wrote:
> Many thanks for your explanation, it clears up my confusion quite
> well. It definitely seems that one should always monitor the
> unpreconditioned residual as a general practice...
It costs extra for many methods because it's not computed as part of the
algorithm (it costs a lot to build for left-preconditioned GMRES), but
you definitely want to make sure that the preconditioner you are using
exhibits predictable behavior.
> Can you also comment briefly on the use of the sparse direct class of
> solvers (MUMPS/superLU/etc.) for indefinite problems? I.e. are they
> suitable for such problems or should I expect to run into similar
> issues? I did some tests with MUMPs on ex13 and it appeared to work
> fine.
Direct solvers with robust ordering schemes tend to do fine. It's
always worth checking, but I've found MUMPS and SuperLU to be quite
reliable (and the former much faster).
> In my present problem I have a Stokes (symmetric, indefinite) operator
> with multiple right-hand sides to solve. Bjacobi+ILU works but is a
> little slower than I'd like. I thought boomerAMG was working, but of
> course it wasn't. MUMPS seems like it would be ideal but I was having
> a bit of trouble getting it to work for the largest problem size I was
> interested in trying (not sure if it was out of memory or what).
I assume you're in 3D, so the memory demands go up quickly.
> If you happen to be aware of what the "latest and greatest" in
> preconditioning/solving techniques for Stokes is I'd be very grateful
> to have some clue as well!
Heh, this is a very active field. The two schools of thought are
Schur-complement methods where you perform a block (incomplete)
factorization of the fields and precondition the Schur complement with
something based on approximate commutators (though constant-viscosity
Stokes simplifies somewhat), the other is to carefully construct
subdomains and coarse spaces that are compatible with the divergence
theorem.
@article{elman2008tcp,
title={{A taxonomy and comparison of parallel block multi-level
preconditioners for the incompressible Navier-Stokes equations}},
author={Elman, H.C. and Howle, V.E. and Shadid, J. and Shuttleworth, R. and
Tuminaro, R.},
journal={Journal of Computational Physics},
volume={227},
number={1},
pages={1790--1808},
year={2008},
publisher={Academic Press}
}
http://ftp.cs.nyu.edu/web/Research/TechReports/TR2005-861/TR2005-861.pdf
Jed
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