[petsc-users] Preconditioner for Helmholtz-like problem

[Jed Brown]

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.Kozlov.2 at 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: akozlov at nd.edu