[petsc-users] Erro in solution

[Jed Brown]

On Mon, May 9, 2011 at 19:06, Danesh Daroui <danesh.daroui at ltu.se> wrote:

> Thanks for the tip, but I already have two different version of my
> solver with PARDISO and MUMPS. Sparse Direct Solvers gave us a great
> contribution but I need to move to O(n^2) time complexity, So I really
> need to employ iterative solvers! :)
>

I'm confused. Is your problem dense? If so, then it doesn't make sense to
use sparse solvers. If it is sparse, then the asymptotics for a direct
solver are O(n^{3/2}) flops and O(n log n) space in two dimensions and
O(n^2) flops and O(n^{4/3}) spare in three dimensions.

You can still use PETSc, but sparse preconditioners won't help you. In
particular, ILU is just a really crappy direct solver if you use it on a
dense matrix. Are there preconditioners for your problem in the literature?
Can it be done with a hierarchical method like FMM?
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