> 2.) *Any* refinement pattern for the pyramid will likely involve a
> splitting where some children have a different type than the parent.
> Since this would be the only element with such an inhomogeneous
> splitting, I'd like to discuss the best way to do this in the present
> context of the embedding matrix.  Since embedding_matrix() is a
> virtual function, it can be redefined in Pyramid sub-classes to do
> whatever we want, e.g. we could place -1 entries in the actual tables
> and just ensure, through embedding_matrix(), that those entries are
> never accessed.  The real issue seems to be determining where in the
> library, if anywhere, we've assumed that all the children have the
> same geometric type.  I'd be glad to hear your comments there.

I'll have to look way back in the logs.  Before the embedding_matrix we
actually did pyramids with the first split you proposed.  I'd rather go to
the second (only sub-pyramids on the base) for a reimplementation.

One issue which has to be addressed is the recursive sideset stuff.  That is
why the pyramid has a 'nonstandard' side numbering: 0,1,2,3 are the
triangular sides, and 4 is the square base.  It has to be that way so the
child tets (which only have 4 sides) can inherit bcs from the same side in
the parent.  So that is not a problem, but an issue that must be addressed.

The only other thing that comes to mind is places like constraint
calculation where we compute on a parent and child.  We just need to be
careful there is no assumption that they are the same type...  I don't think
this is an issue at all for Lagrange elements, because constraints are only
calculated using the sides, which are of the same type.  But perhaps some of
Roy's more exotic FE spaces?

-Ben




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