Fix Netgen permutation

[pbrubeck]

Description

Attempting to make find_permutation more robust by comparing reference coordinates and using numpy.argmin as opposed to taking an arbitary tolerance, which is now deprecated.

The correct fix is to use a PETSc Section: #5277

[UZerbinati]

@KarsKnook might be what you are looking for, can you take a look ? :)

[connorjward]

Isn't this undone in #5277?

Not sure what this brings to the table. Shouldn't we just finish and merge #5277?

[pbrubeck]

Isn't this undone in #5277?

Not sure what this brings to the table. Shouldn't we just finish and merge #5277?

#5277 targets #5215 but this problem with the tolerances is a real bug (some high-order netgen meshes end up with self-intersecting cells), so we should ideally be targeting release. Are you okay with a cython rework of high-order netgen meshes going into release?

[connorjward]

Are you okay with a cython rework of high-order netgen meshes going into release?

Of course not.

If this fixes a real bug in release then I don't mind this going in to it, which can be distinct from the changes to main. We should have a test in that case.

[pbrubeck]

If this fixes a real bug in release then I don't mind this going in to it, which can be distinct from the changes to main. We should have a test in that case.

Done

[connorjward]

Yes this much better. I think that this is not just me being picky. This is radically clearer for anyone else coming to this code for this first time.

[connorjward]

I still don't understand the maths, but that's a me issue. This is probably fine.

[UZerbinati]

I'm very very happy with this, it's nice to see that you find a better way to construct the mapping.
I was trying to do something similar here: https://github.com/firedrakeproject/firedrake/tree/uz/fix_permuation

[pbrubeck]

I'm very very happy with this, it's nice to see that you find a better way to construct the mapping.

This is just a patch. The correct approach is #5277