From: Roy Stogner <roystgnr@ic...>  20081111 21:26:47

On Tue, 11 Nov 2008, Benjamin Kirk wrote: > So why not compute instead > > phi(Xc) = phi(Xc(X)) = phi(Xc(X(xi))) and > (dphi/dXc)(Xc) = [(dphi/dxi)(dxi/dX)(dX/dXc)](Xc(X(xi))) > > Where Xc(X) is the C1 geometry representation provided by the "geometry > system" described previously. This is what I was thinking of when I said that arbitrary topologies would be the tricky part. X needs to be in the 2D plane for Xc(X) to make sense with our current setup. That's not even possible if your desired manifold Xc is closed and unbounded, which I'm guessing would be a pretty common case. My best idea right now is: let X be the "faceted" C0 representation of the manifold (which on any C1 element is already implicit as the first order Lagrange interpretation of the vertex dofs), and at every node or edge take some "average" of the surrounding elements to get a local coordinate system on which you can take welldefined derivatives. Easy to state, not quite as easy to picture, probably not easy at all to code. My second best idea: actually go back to the geometry literature and find out how this has been done in the past. I'd have done so already, but the only useful articles I can recall off the top of my head aren't online.  Roy 