[petsc-users] Erro in solution

[Danesh Daroui]

Yes, My problem is originally dense. That's why I used LAPACK to solve
the equation. After some sparsifications, when the problem becomes
sparse, I use sparse solvers. As I wrote, I have successfully used
direct sparse solvers using other packages and now I am moving to
iterative solvers using PETSc. I expected ILU preconditioner to be
inappropriate for my needs and that explains slow convergence. I printed
out number of iterations and also normalized residual and in slowest
case the number of iterations was ~470 and the residual was 6.04524e-5.
I experienced faster convergence but with higher residual 0.0005. The
solution is also quite inaccurate in most cases and I guess the residual
is still high. That's what I guess and the remedy can be using a better
preconditioner. As I said, my problem is badly conditioned and this can
be observed by plotting eigenvalues spectrum which is not clustered at
all and therefore results to a high condition number.

Thanks,

D.


On Mon, 2011-05-09 at 19:57 +0200, Jed Brown wrote:
> 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?