<html><body bgcolor="#FFFFFF"><div><div><div>HI，</div><div>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. </div><div><br></div><div><br></div><div>Zhengyong<br><br><div>Zhengyong Ren,</div>Institute of Geophysics, <div>Department of Geoscience,</div><div>ETH Zurich, CH8092,</div><div>Zurich, Switzerland. </div></div><div><br>On 2011-5-9, at 19:57, Jed Brown <<a href="mailto:jed@59A2.org"></a><a href="mailto:jed@59A2.org"><a href="mailto:jed@59A2.org">jed@59A2.org</a></a>> wrote:<br><br></div><div></div><blockquote type="cite"><div><div class="gmail_quote">On Mon, May 9, 2011 at 19:06, Danesh Daroui <span dir="ltr"><<a href="mailto:danesh.daroui@ltu.se"></a><a href="mailto:danesh.daroui@ltu.se"></a><a href="mailto:danesh.daroui@ltu.se"><a href="mailto:danesh.daroui@ltu.se">danesh.daroui@ltu.se</a></a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
<div id=":4xf">Thanks for the tip, but I already have two different version of my<br>
solver with PARDISO and MUMPS. Sparse Direct Solvers gave us a great<br>
contribution but I need to move to O(n^2) time complexity, So I really<br>
need to employ iterative solvers! :)</div></blockquote></div><br><div>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.</div>
<div><br></div><div>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?</div>
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