Roy Stogner wrote:
>
> On Tue, 18 Nov 2008, Norbert Stoop wrote:
>
>> 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.
>
> Does this have to be stored as a vector? Or stored at all?
> Patch::add_point_neighbors() should do what you want on the fly. If
> it's worthwhile a caching version of that could be created.
Hm, the patch needs a special numbering scheme, which should look like this
N+4 - N+1 - N+2
/ \ / \ / \
/ \ / \ / \
N+5 -- N --- 1 -- N+3
\ / \ e / \ /
\ / \ / \ /
N-1--- 0 --- 2
\ /|\ /
\ / | \ /
5 -4- 3
where e is the element we consider and N is the valence of vertex 0
(which is irregular in this example).
>> 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.
>
> Could you describe this in more detail? Do you just need the FE
> object to be able to fill in xyz/dxyz/d2xyz properly, or is it more
> than that?
What I need in particular, and probably all people solving stuff on a
manifold, is the local surface metric at the quadrature points.
To get this, one needs the C1 parametrization x(eta,xi). The derivatives
wrt xi and eta give two tangents, from which the normal can be
constructed. Together they basically define the metric.
The problem is, x(xi,eta) is given as a sum of
phi(i)*nodal_xyz_position(i) where i goes over all vertices of the above
patch.
Now, either the finite element class exposes an interface to the
parametrization x(xi,eta) (and its derivatives) and the metric, or the
node patch is exposed and the user constructs what actually is needed
(since the phi's are already at hand).
-Norbert
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