[petsc-users] Unique number in each element of a DMPlex mesh

[Matthew Knepley]

On Mon, Jan 22, 2024 at 10:49 AM Berend van Wachem <berend.vanwachem at ovgu.de>
wrote:

> Dear Petsc-Team,
>
> Is there a good way to define a unique integer number in each element
> (e.g. a cell) of a DMPlex mesh, which is in the same location,
> regardless of the number of processors or the distribution of the mesh
> over the processors?
>
> So, for instance, if I have a DMPlex box mesh, the top-right-front
> corner element (e.g. cell) will always have the same unique number,
> regardless of the number of processors the mesh is distributed over?
>
> I want to be able to link the results I have achieved with a mesh from
> DMPlex on a certain number of cores to the same mesh from a DMPlex on a
> different number of cores.
>
> Of course, I could make a tree based on the distance of each element to
> a certain point (based on the X,Y,Z co-ordinates of the element), and go
> through this tree in the same way and define an integer based on this,
> but that seems rather cumbersome.
>

I think this is harder than it sounds. The distance will not work because
it can be very degenerate.
You could lexicographically sort the coordinates, but this is hard in
parallel. It is fine if you are willing
to gather everything on one process. You could put down a p4est, use the
Morton order to number them since this is stable for a given refinement.
And then within each box lexicographically sort the centroids. This is
definitely cumbersome, but I cannot think of anything else. This also might
have parallel problems since you need to know how much overlap you need to
fill each box.

  Thanks,

      Matt


> Thanks and best regards, Berend.

-- 
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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