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
