Thanks a lot! I'll check them out. On Sat, Sep 19, 2020 at 1:41 AM Barry Smith <bsm...@petsc.dev> wrote:
> > These are small enough that likely sparse direct solvers are the best > use of your time and for general efficiency. > > 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. > > --download-superlu_dist --download-mumps --download-pastix > --download-scalapack (used by MUMPS) --download-metis --download-parmetis > --download-ptscotch > > Barry > > > On Sep 18, 2020, at 11:28 PM, Alexey Kozlov <alexey.v.kozlo...@nd.edu> > wrote: > > 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. > > On Fri, Sep 18, 2020 at 11:52 PM Jed Brown <j...@jedbrown.org> wrote: > >> 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). >> >> >> https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MATSOLVERSSTRUMPACK.html >> >> Is the matrix complex symmetric? >> >> 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. >> >> Alexey Kozlov <alexey.v.kozlo...@nd.edu> writes: >> >> > Dear all, >> > >> > I am solving a convected wave equation in a frequency domain. This >> equation >> > is a 3D Helmholtz equation with added first-order derivatives and mixed >> > derivatives, and with complex coefficients. The discretized PDE results >> in >> > a sparse linear system (about 10^6 equations) which is solved in PETSc. >> I >> > am having difficulty with the code convergence at high frequency, skewed >> > grid, and high Mach number. I suspect it may be due to the >> preconditioner I >> > use. I am currently using the ILU preconditioner with the number of fill >> > levels 2 or 3, and BCGS or GMRES solvers. I suspect the state of the art >> > has evolved and there are better preconditioners for Helmholtz-like >> > problems. Could you, please, advise me on a better preconditioner? >> > >> > Thanks, >> > Alexey >> > >> > -- >> > Alexey V. Kozlov >> > >> > Research Scientist >> > Department of Aerospace and Mechanical Engineering >> > University of Notre Dame >> > >> > 117 Hessert Center >> > Notre Dame, IN 46556-5684 >> > Phone: (574) 631-4335 >> > Fax: (574) 631-8355 >> > Email: akoz...@nd.edu >> > > > -- > Alexey V. Kozlov > > Research Scientist > Department of Aerospace and Mechanical Engineering > University of Notre Dame > > 117 Hessert Center > Notre Dame, IN 46556-5684 > Phone: (574) 631-4335 > Fax: (574) 631-8355 > Email: akoz...@nd.edu > > > -- Alexey V. Kozlov Research Scientist Department of Aerospace and Mechanical Engineering University of Notre Dame 117 Hessert Center Notre Dame, IN 46556-5684 Phone: (574) 631-4335 Fax: (574) 631-8355 Email: akoz...@nd.edu
