[petsc-users] Preconditioner for Helmholtz-like problem

[Alexey Kozlov]

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 <jed at 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.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
>


-- 
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
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