[petsc-users] DMPlex higher order elements

[Andrew Ho]

>
> Philosophically it's certainly part of the job of the mesh generator, but
> realistically I don't think there are any really viable high-order mesh
> generators or even file formats right now (correct me if I'm wrong). And as
> Matthew put, the mesh generator has no business telling us what our
> function basis should be, and by extension has no basis telling us where we
> should place our face nodes.
>

The mesh surface nodes have no correspondence to the basis set I use for
expanding my solution on; i.e. I could use sub/super parametric mappings. I
think this is why Exodus II doesn't support any elements higher than 6-node
triangles; I believe these are sufficient for representing conics sections
(not entirely sure about this).

This comes up a lot in high order mesh discussions, but I always wonder
> when do you *not* have access to the original geometric representation? If
> you've generated the mesh yourself you must have the geometry.


Yes, I have the original CAD files, but there are a few issues:

1. I don't have any code for reading in the CAD format (not entirely sure
how difficult this is)
2. I don't know of any easy way to correspond a given element in the mesh
with a surface in the CAD file, as in what part of the original surface is
my element on. I could do some "geometric tolerance" based approach, but I
don't know how robust this is especially near where two surfaces join
together.
3. Why do I need to add this complexity to all of my simulation codes? The
mesh generator already knows how to understand the geometry, and output
meshes which conform to the curved surface. I simply want to use this
existing feature and have my simulation code deal entirely with performing
the simulation, not deal with having to handle NURBS surfaces, conics
section, surface mapping, etc.

-- 
Andrew Ho
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