[petsc-users] Preconditioner for Helmholtz-like problem

[Mark Adams]

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.Kozlov.2 at nd.edu>
wrote:

> 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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