<html><head><meta http-equiv="Content-Type" content="text/html; charset=us-ascii"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div class=""><br class=""></div> These are small enough that likely sparse direct solvers are the best use of your time and for general efficiency. <div class=""><br class=""></div><div class=""> PETSc supports 3 parallel direct solvers, SuperLU_DIST, MUMPs and Pastix. I recommend configuring PETSc for all three of them and then comparing them for problems of interest to you.</div><div class=""><br class=""></div><div class=""> --download-superlu_dist --download-mumps --download-pastix --download-scalapack (used by MUMPS) --download-metis --download-parmetis --download-ptscotch </div><div class=""><br class=""></div><div class=""> Barry</div><div class=""><br class=""><div><br class=""><blockquote type="cite" class=""><div class="">On Sep 18, 2020, at 11:28 PM, Alexey Kozlov <<a href="mailto:Alexey.V.Kozlov.2@nd.edu" class="">Alexey.V.Kozlov.2@nd.edu</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div dir="ltr" class="">Thanks for the tips! My matrix is complex and unsymmetric. My typical test case has of the order of one million equations. I use a 2nd-order finite-difference scheme with 19-point stencil, so my typical test case uses several GB of RAM.<br class=""></div><br class=""><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Fri, Sep 18, 2020 at 11:52 PM Jed Brown <<a href="mailto:jed@jedbrown.org" class="">jed@jedbrown.org</a>> wrote:<br class=""></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">Unfortunately, those are hard problems in which the "good" methods are technical and hard to make black-box. There are "sweeping" methods that solve on 2D "slabs" with PML boundary conditions, H-matrix based methods, and fancy multigrid methods. Attempting to solve with STRUMPACK is probably the easiest thing to try (--download-strumpack).<br class="">
<br class="">
<a href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MATSOLVERSSTRUMPACK.html" rel="noreferrer" target="_blank" class="">https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MATSOLVERSSTRUMPACK.html</a><br class="">
<br class="">
Is the matrix complex symmetric?<br class="">
<br class="">
Note that you can use a direct solver (MUMPS, STRUMPACK, etc.) for a 3D problem like this if you have enough memory. I'm assuming the memory or time is unacceptable and you want an iterative method with much lower setup costs.<br class="">
<br class="">
Alexey Kozlov <<a href="mailto:Alexey.V.Kozlov.2@nd.edu" target="_blank" class="">Alexey.V.Kozlov.2@nd.edu</a>> writes:<br class="">
<br class="">
> Dear all,<br class="">
><br class="">
> I am solving a convected wave equation in a frequency domain. This equation<br class="">
> is a 3D Helmholtz equation with added first-order derivatives and mixed<br class="">
> derivatives, and with complex coefficients. The discretized PDE results in<br class="">
> a sparse linear system (about 10^6 equations) which is solved in PETSc. I<br class="">
> am having difficulty with the code convergence at high frequency, skewed<br class="">
> grid, and high Mach number. I suspect it may be due to the preconditioner I<br class="">
> use. I am currently using the ILU preconditioner with the number of fill<br class="">
> levels 2 or 3, and BCGS or GMRES solvers. I suspect the state of the art<br class="">
> has evolved and there are better preconditioners for Helmholtz-like<br class="">
> problems. Could you, please, advise me on a better preconditioner?<br class="">
><br class="">
> Thanks,<br class="">
> Alexey<br class="">
><br class="">
> -- <br class="">
> Alexey V. Kozlov<br class="">
><br class="">
> Research Scientist<br class="">
> Department of Aerospace and Mechanical Engineering<br class="">
> University of Notre Dame<br class="">
><br class="">
> 117 Hessert Center<br class="">
> Notre Dame, IN 46556-5684<br class="">
> Phone: (574) 631-4335<br class="">
> Fax: (574) 631-8355<br class="">
> Email: <a href="mailto:akozlov@nd.edu" target="_blank" class="">akozlov@nd.edu</a><br class="">
</blockquote></div><br clear="all" class=""><br class="">-- <br class=""><div dir="ltr" class="gmail_signature"><div dir="ltr" class=""><div class=""><div dir="ltr" class=""><div class=""><div dir="ltr" class=""><span style="color:rgb(0,0,255)" class=""><font size="4" class=""><span style="font-family:comic sans ms,sans-serif" class="">Alexey V. Kozlov</span></font><br class=""><br class="">Research Scientist<br class="">Department of Aerospace and Mechanical Engineering<br class="">University of Notre Dame<br class=""><br class="">117 Hessert Center<br class="">Notre Dame, IN 46556-5684<br class="">Phone: (574) 631-4335<br class="">Fax: (574) 631-8355<br class="">Email: <a href="mailto:akozlov@nd.edu" target="_blank" class="">akozlov@nd.edu</a></span><br class=""></div></div></div></div></div></div>
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