[petsc-users] Solving Laplacian on complicated domain

[Matthew Knepley]

On Mon, Jul 4, 2022 at 1:29 AM BOYD Andrew via petsc-users <
petsc-users at mcs.anl.gov> wrote:

> Dear PETSc users,
>
>
>
> I am a PhD student looking to solve a Laplacian on a 3D domain which
> consists of a volume with ellipsoid “holes” in it. I am a newcomer to
> PETSc, and would like advice on how to begin to write this code. I have
> studied the examples, and example no.12 in SNES seems to share some of the same
> characteristics that I need.
>
> I have also looked at the mail archives, but unfortunately couldn’t find
> too much on this problem – it may be that I lack the background to
> understand it properly.
>
> Thanks in advance for any advice, it is much appreciated.
>
> (As an aside, I am also planning to run this in Rust using the PETSc
> bindings – if anyone has any experience with this it would be interesting
> to hear from you as well!)
>

It seems job 1 for you is forming the matrix with the correct boundary
conditions. Ex 12 should be enough for that if you can input a mesh
with the boundaries marked as you wish. After that I would

1) Run with a direct solver like MUMPS or SuperLU_dist

2) Run with algebraic multigrid, like GAMG, or Hypre, or ML

3) If that is not enough, think about a few steps of geometric or
p-refinement.

  Thanks,

     Matt


> Sincerely,
>
> Andrew Boyd
> The University of Edinburgh is a charitable body, registered in Scotland,
> with registration number SC005336. Is e buidheann carthannais a th’ ann an
> Oilthigh Dhùn Èideann, clàraichte an Alba, àireamh clàraidh SC005336.
>


-- 
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/>
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