[petsc-users] Erro in solution

[RenZhengYong]

Hi,
I do not use preconditioners for the surface integral formula, because it it
well-conditioned.
I tested several preconditoners, the convergence rates by using
precoditioners are more or less the same as the one without preconditioners.



Zhengyong

On Tue, May 10, 2011 at 11:48 AM, Danesh Daroui <danesh.daroui at ltu.se>wrote:

>
> Hi,
>
> Yes this is more or less what I am using, however in addition to surface
> I use volume integrals too for current distributions. Well, I know that
> condition number should be decreased in general to improve the
> convergence, but can you please let me know what preconditioner did you
> use? I have not used Fast Multipole Method because of high
> approximations specially in lower frequencies.
>
> Regards,
>
> D.
>
>
> On Tue, 2011-05-10 at 01:38 +0200, Renzhengyong wrote:
> > HI，
> > I was working on solving Maxwell equations by surface integral
> > approaches. If you are working on this, try to decrease the condition
> > numbers of your integral operators so that it is reasonable to use
> > GMRES solver in a limited number of iterations, which is a need for
> > applying fast multipole method.
> >
> >
> >
> >
> > Zhengyong
> >
> > Zhengyong Ren,
> > Institute of Geophysics,
> > Department of Geoscience,
> > ETH Zurich, CH8092,
> > Zurich, Switzerland.
> >
> > On 2011-5-9, at 19:57, Jed Brown <jed at 59A2.org> 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?
> >
> >
>
>
>


-- 
Zhengyong Ren
AUG Group, Institute of Geophysics
Department of Geosciences, ETH Zurich
NO H 47 Sonneggstrasse 5
CH-8092, Zürich, Switzerland
Tel: +41 44 633 37561
e-mail: zhengyong.ren at aug.ig.erdw.ethz.ch
Gmail: renzhengyong at gmail.com
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