[Libmesh-users] patch for XYZ basis functions

[Lorenzo A. B. <bot...@gm...>]

Hi All,
I'm submitting a patch with improvements and bug fixes for XYZ basis functions.

I haven't been able to test it against the svn head because I had compilation issues. See the error file.
However, since the patch is only related to fe_xyz*.C, it should work.

The major change is related to a scaling introduced to improve the condition number on small and big elements (small and big compared to the reference element).
With such a scaling on linear hexs the XYZ is equivalent to a MONOMIAL basis, independently of the element size.
On curved elements the approximation properties of this scaled XYZ should be better than MONOMIAL and should allow to go up to a third or fourth degree approximation without any trouble.
Another step would be to introduce a rotation in order to define the XYZ basis using a frame oriented with the principal axis of inertia of the mesh element. This might help on stretched elements.

I hope that the patch will be included in future libMesh releases.