<div class="gmail_quote">On Fri, Aug 12, 2011 at 07:55, Paul Anton Letnes <span dir="ltr"><<a href="mailto:paul.anton.letnes@gmail.com">paul.anton.letnes@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
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.</blockquote>
</div><br><div>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.</div>
<div><br></div><div>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.</div>
<div><br></div><div>How large are these matrices likely to be and about how many processors would you like to run on?</div>