[petsc-users] Solver/Preconditioner suggestions

[Alfredo J Duarte Gomez]

Hello,

Yes, the boundary layer is important to the problem and is resolved by the
mesh, although it is a very small part of the mesh.

Thanks,

-Alfredo

On Thu, May 19, 2022 at 1:03 PM Matthew Knepley <knepley at gmail.com> wrote:

> On Thu, May 19, 2022 at 8:00 AM Alfredo J Duarte Gomez <
> aduarteg at utexas.edu> wrote:
>
>> Hello Matthew,
>>
>> Thank you for your suggestion on the Laplace solver.
>>
>> About the other systems I would say B and C are mostly dominated by
>> advection, except for diffusive layers at the boundaries.
>>
>> A is a bit more difficult to judge, although it can be expected to have a
>> very large advective component, it also has a large reactive component, and
>> the diffusion dominated layers at the boundaries.
>>
>
> Is your mesh resolving the boundary layers?
>
>   Thanks,
>
>      Matt
>
>
>> Thank you,
>>
>> -Alfredo
>>
>> On Thu, May 19, 2022 at 12:31 PM Matthew Knepley <knepley at gmail.com>
>> wrote:
>>
>>> On Thu, May 19, 2022 at 7:27 AM Alfredo J Duarte Gomez <
>>> aduarteg at utexas.edu> wrote:
>>>
>>>> Good afternoon PETSC users,
>>>>
>>>> I am looking for some suggestions on preconditioners/solvers.
>>>>
>>>> Currently, I have a custom preconditioner that solves 4 independent
>>>> systems, let's call them A,B,C, and D.
>>>>
>>>> A is an advective, diffusive, reactive system, although due to some
>>>> coefficient it is the system with the highest condition number and
>>>> therefore the most difficult to solve.
>>>>
>>>> B and C, are more "standard" advective, diffusion, reactive systems.
>>>> The condition number is not as high as A.
>>>>
>>>> D is simply the laplacian used to solve an elliptic Poisson equation.
>>>>
>>>> For more context, A,B, and C need to be recomputed about once every
>>>> time step, while D is a one time cost.
>>>>
>>>> The problem is 2-D, sizes are on the order of 1-10 million grid points,
>>>> and I am using a structured grid. These usually run on somewhere between
>>>> 100-400 processors.
>>>>
>>>> Currently  I am solving A,B, and C with the HYPRE Euclid algorithm
>>>> ILU(1), and D is solved with the direct solver MUMPS.
>>>>
>>>> While these were very useful to get the code working, I am now trying
>>>> to get better parallel scaling/efficiencies and performance. HYPRE euclid
>>>> does not seem to scale super well beyond like 60 procs, and MUMPS has very
>>>> large memory requirements.
>>>>
>>>> Does anyone have suggestions on more scalable ILU algorithms for A,B,
>>>> and C, or any other good alternatives?
>>>>
>>>
>>> Are these advectively dominated?
>>>
>>>
>>>> From what I have read, multigrid methods are probably the best
>>>> alternative for D, but I have very little experience with these and they
>>>> seem to require a lot of parameters. Does anyone have pointers on a good
>>>> setup for a multigrid preconditioner?
>>>>
>>>
>>> This is the easy one. If you are using DMDA, just turn on -pc_type mg
>>> and give a number of levels and it should be fine. If not, then use GAMG
>>> and it
>>> should be fine, You could also use Hypre Boomeramg for this since it is
>>> optimized for the 2D Laplacian.
>>>
>>>   Thanks,
>>>
>>>     Matt
>>>
>>>
>>>> Thank you and have a good day,
>>>>
>>>> -Alfredo
>>>>
>>>> --
>>>> Alfredo Duarte
>>>> Graduate Research Assistant
>>>> The University of Texas at Austin
>>>>
>>>
>>>
>>> --
>>> What most experimenters take for granted before they begin their
>>> experiments is infinitely more interesting than any results to which their
>>> experiments lead.
>>> -- Norbert Wiener
>>>
>>> https://www.cse.buffalo.edu/~knepley/
>>> <http://www.cse.buffalo.edu/~knepley/>
>>>
>>
>>
>> --
>> Alfredo Duarte
>> Graduate Research Assistant
>> The University of Texas at Austin
>>
>
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> experiments lead.
> -- Norbert Wiener
>
> https://www.cse.buffalo.edu/~knepley/
> <http://www.cse.buffalo.edu/~knepley/>
>


-- 
Alfredo Duarte
Graduate Research Assistant
The University of Texas at Austin
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