dolfin team mailing list archive

[Shawn Walker <walker@xxxxxxxxxxxxxxx>]

On Mon, 26 Jan 2009, Anders Logg wrote:

> On Mon, Jan 26, 2009 at 11:30:25AM -0500, Shawn Walker wrote:
> > Hello, I have a question on implementing the Laplace-Beltrami operator in
> > FFC/DOLFIN.  Can you do it?  If the domain is just a 2-D surface, then
> > maybe not; 2-D topological meshes in 3-D geometric space still needs to be
> > implemented right?
>
> The mesh class supports it (that's why you can extract the boundary
> mesh from a 3D mesh) but other pieces are missing.
>
> I suggest you try a very simple problem and try to track where things
> go wrong (I assume they will). It might be that major work will be
> needed to get it to work, but it might also be fixable.
>
> > What about if I just have a 2-D (flat) domain with a 1-D boundary.  Is
> > there a convenient way to define the surface (tangential) gradient in FFC?
> > It is just the derivative with respect to arc-length multiplied by the
> > tangent vector.  Can you define forms on the boundary like that?
>
> Do you want to have the tangent on the boundary? That's fairly easy,
> just do
>
> n = FacetNormal(mesh)
> t = [-n[0], n[1]]
>
> --
> Anders

But can I do the derivative with respect to arc-length?

Actually, another way to define the tangential gradient is to compute the 
full gradient project onto the tangent space.  Would that work for 
computing on the boundary of a flat 2-D domain?

- Shawn