[Libmesh-users] Subdivision surface based FEM

[Norbert S. <no...@st...>]

Hi,

Recently, subdivision surfaces were suggested as an alternative way to
construct C1 (and higher) conforming surface meshes for finite element
simulations. Now, I'm wondering how hard it would be to implement such
elements in libmesh:
Assuming triangular elements, the subdivision surface approach results
in 12 b-spline shape functions per element. The isoparametric map to
real space is a combination of them multiplied with the real space
position of the triangle's nodes *and* its next neighbor nodes (the
1-ring of triangles around the element).
Looking at existing libmesh elements (lagrange, clough), I see that only
the ::shape, ::shape_deriv and ::shape_second_deriv are typically
overwritten, and the mapping to real space is done by libmesh
(fe_base.C, I think).
As pointed out above, the subdivision elements have a special mapping to
real space, which needs to take the neighboring nodes' position into
account. Is there a way to accomplish this in the current code or would
it be possible to extend it in that way?

Thanks in advance,
Norbert