[petsc-users] Preconditioner for Helmholtz-like problem

[Alexey Kozlov]

Thanks a lot! I'll check them out.

On Sat, Sep 19, 2020 at 1:41 AM Barry Smith <bsmith at 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.Kozlov.2 at 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 <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
>
>
>

-- 
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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