Hi, <br>I do not use preconditioners for the surface integral formula, because it it well-conditioned. <br>I tested several preconditoners, the convergence rates by using precoditioners are more or less the same as the one without preconditioners. <br>
<br><br>Zhengyong<br><br><div class="gmail_quote">On Tue, May 10, 2011 at 11:48 AM, Danesh Daroui <span dir="ltr"><<a href="mailto:danesh.daroui@ltu.se">danesh.daroui@ltu.se</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin: 0pt 0pt 0pt 0.8ex; border-left: 1px solid rgb(204, 204, 204); padding-left: 1ex;">
<br>
Hi,<br>
<br>
Yes this is more or less what I am using, however in addition to surface<br>
I use volume integrals too for current distributions. Well, I know that<br>
condition number should be decreased in general to improve the<br>
convergence, but can you please let me know what preconditioner did you<br>
use? I have not used Fast Multipole Method because of high<br>
approximations specially in lower frequencies.<br>
<br>
Regards,<br>
<font color="#888888"><br>
D.<br>
</font><div><div></div><div class="h5"><br>
<br>
On Tue, 2011-05-10 at 01:38 +0200, Renzhengyong wrote:<br>
> HI，<br>
> I was working on solving Maxwell equations by surface integral<br>
> approaches. If you are working on this, try to decrease the condition<br>
> numbers of your integral operators so that it is reasonable to use<br>
> GMRES solver in a limited number of iterations, which is a need for<br>
> applying fast multipole method.<br>
><br>
><br>
><br>
><br>
> Zhengyong<br>
><br>
> Zhengyong Ren,<br>
> Institute of Geophysics,<br>
> Department of Geoscience,<br>
> ETH Zurich, CH8092,<br>
> Zurich, Switzerland.<br>
><br>
> On 2011-5-9, at 19:57, Jed Brown <jed@59A2.org> wrote:<br>
><br>
><br>
><br>
> > On Mon, May 9, 2011 at 19:06, Danesh Daroui <<a href="mailto:danesh.daroui@ltu.se">danesh.daroui@ltu.se</a>><br>
> > wrote:<br>
> > Thanks for the tip, but I already have two different version<br>
> > of my<br>
> > solver with PARDISO and MUMPS. Sparse Direct Solvers gave us<br>
> > a great<br>
> > contribution but I need to move to O(n^2) time complexity,<br>
> > So I really<br>
> > need to employ iterative solvers! :)<br>
> ><br>
> > I'm confused. Is your problem dense? If so, then it doesn't make<br>
> > sense to use sparse solvers. If it is sparse, then the asymptotics<br>
> > for a direct solver are O(n^{3/2}) flops and O(n log n) space in two<br>
> > dimensions and O(n^2) flops and O(n^{4/3}) spare in three<br>
> > dimensions.<br>
> ><br>
> ><br>
> > You can still use PETSc, but sparse preconditioners won't help you.<br>
> > In particular, ILU is just a really crappy direct solver if you use<br>
> > it on a dense matrix. Are there preconditioners for your problem in<br>
> > the literature? Can it be done with a hierarchical method like FMM?<br>
><br>
><br>
<br>
<br>
</div></div></blockquote></div><br><br clear="all"><br>-- <br>Zhengyong Ren<br>AUG Group, Institute of Geophysics<br>Department of Geosciences, ETH Zurich<br>NO H 47 Sonneggstrasse 5<br>CH-8092, Zürich, Switzerland<br>Tel: +41 44 633 37561<br>
e-mail: <a href="mailto:zhengyong.ren@aug.ig.erdw.ethz.ch">zhengyong.ren@aug.ig.erdw.ethz.ch</a><br>Gmail: <a href="mailto:renzhengyong@gmail.com">renzhengyong@gmail.com</a><br>