[petsc-users] Development enquiry

[Matthew Knepley]

On Tue, Feb 8, 2022 at 9:29 AM Nadimy, Amin <amin.nadimy19 at imperial.ac.uk>
wrote:

> Dear Sir/Madam,
>
>
> We are developing a semi-structured code based on a triangular mesh. It
> has similarities to Adaptive Mesh refinement (AMR) in which from an initial
> mesh (in our case unstructured) a structured mesh is generated based on a
> refine-by-splitting strategy, ending up, like in AMR, with a
> semi-structured mesh.
>

I need to ask  some questions to make sure I understand.

First, the above sounds like a regular refinement of a triangular mesh. We
support that, in parallel, to any level of refinement. Is that correct?

Second, if instead you want a different level of regular refinement in each
cell, that is harder. If you obey the 2:1 balance constraint between
cells, then I think our current infrastructure (written by Toby Isaac) can
handle it. There is a new version of p4est that handles simplices in this
way, but we have not yet integrated it. If we need that, it might take a
little doing.

>
>    -
>
>    Effectively we need a CSR type storage for the coarse initial mesh and
>    a stencil-based storage for the internal, structured mesh. We have noticed
>    that you have some routines to deal with semi-structured meshes but they
>    specifically target AMR type meshes, which may not be useful in our case as
>    the stencil and neighbouring are different to that of a structured
>    grid-based mesh. Do you think these approaches could be used directly for
>    our case or with minor modifications?
>
> This should be automatic once we have the topology that you want.

>
>    -
>
>
>    -
>
>    Other possibilities that we have considered are the use of
>    block-structured solvers, however, in our case, the blocks are not dense
>    and therefore this approach will be worse.
>
> Yes, Rich Vuduc did a study of densifying blocks during his Phd, but my
memory of the results was that it did not often win.

>
>    -
>
>
>    -
>
>    Another alternative would be to develop our own multigrid based on
>    PETSc ensuring that there is communication between the different blocks
>    during the smoothing operation, could this also easily be done or would
>    effectively require applying the smoothers independently to the different
>    structured sections and us performing the communication and extra-smoothing
>    steps at the interface?
>
> My plan would be to keep track of the refinements. Smooth in a structured
way on the refinements, and then turn the original unstructured grid over
to GAMG.

What kind of physics is this for?

  Thanks,

     Matt


> Kind regards,
>
> --
> Amin Nadimy
>
> Applied Modelling and Computation Group (AMCG),
>
> Imperial College London
>


-- 
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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