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 > <mailto: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 > > <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 <mailto: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 <mailto: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 <mailto:akoz...@nd.edu>
