Hi again,

Okay, the basic functionality for subdivision surface FEM should be
implemented now, but I have a question regarding proper integration into
libmesh:
These elements need some additional variables to store
subdivision surface properties. For example, a vector of the 1-ring of
neighbors is needed. Some of these properties also need to be accessible
from the application code, for example to create a local coordinate
system from the surface tangents.

Now, which class should I derive the elements from? Somehow, I feel that
FE<2,SUBDIV> does not make too much sense since it has no containers for
the extra variables. On the other hand, all other libmesh machinery
relies on fe.h only and it's probably not the idea to change that.

Thanks in advance,
Norbert

Norbert Stoop wrote:
> 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
> 
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