As Jed said high frequency is hard. AMG, as-is, can be adapted ( https://link.springer.com/article/10.1007/s00466-006-0047-8) with parameters. AMG for convection: use richardson/sor and not chebyshev smoothers and in smoothed aggregation (gamg) don't smooth (-pc_gamg_agg_nsmooths 0). Mark
On Sat, Sep 19, 2020 at 2:11 AM Alexey Kozlov <alexey.v.kozlo...@nd.edu> wrote: > 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 >
