[petsc-users] BiCGSTAB for general use

[Jed Brown]

On Fri, Aug 12, 2011 at 07:55, Paul Anton Letnes <
paul.anton.letnes at gmail.com> wrote:

> I am attempting to solve a large, dense equation system. I would like to
> try using the BiCGSTAB algorithm, and specifically, the petsc library, as it
> is open source and seems to be well supported. I take it petsc is primarily
> aimed at people solving partial differential equations by 'brute force' type
> methods.


If by "brute force", you mean volumetric discretizations of the differential
equations, then this is indeed the largest user base. But there are many
optimal methods in this category, such that I think "brute force" would be a
misnomer.

What sort of problem does your dense equation system come from? E.g. does it
come from a boundary element method? Can you give a rough estimate of the
condition number? Are the eigen/singular values well-clustered? For many
dense problems, a Krylov method alone won't beat a direct solver like
LAPACK, but if it has extra structure, and especially if it can be
stored/applied in less than O(n^2) work, then iterative methods may be
competitive.

How large are these matrices likely to be and about how many processors
would you like to run on?
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