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 _______________________________________________ DOLFIN-dev mailing list [email protected] http://www.fenics.org/mailman/listinfo/dolfin-dev
