Derek Gaston wrote: > On Nov 11, 2008, at 10:02 AM, Roy Stogner wrote: > >> On Tue, 11 Nov 2008, Norbert Stoop wrote: >> >>> To summarize, we abuse the traditional mesh as a control mesh. We define >>> a parametrization of the limit surface which naturally gives us the >>> needed mathematical objects such as derivatives, surface patches etc. >>> Since we *know* where each control point converges to in the limit, we >>> can assign back calculated nodal values to the control points and >>> assemble the system as usual. >>> >>> Hope this helps to clarify... > > It seems like if you could use Clough Touchers (or hermites) as the map > then that would solve this problem... but as you mentioned earlier > that's probably not doable with our current architecture.
>From an implementation point of view, the subdivision approach does not require this map, since you directly construct the element in the global system (as C1). The only map you have and need is the parametrization X(xi,eta) where X maps to the C1 surface in physical space. The jacobian at some point P(xi,eta) on the (C1!) element is then calculated from two basis vectors a_xi and a_eta of the tangent space at P, according to differential geometry: jac = | a_xi crossprod a_eta | Since you have X(xi,eta), the a_xi and a_eta follow by just differentiating X by xi or eta respectively. To put it in a sloppy way: Instead of defining everything on the master element, then find a transformation into global space, we do *define* the C1 element in global space and *there* construct the jacobian and all the other properties. We sort of go the other way around than how one typically does for FE. -Norbert ------------------------------------------------------------------------- This SF.Net email is sponsored by the Moblin Your Move Developer's challenge Build the coolest Linux based applications with Moblin SDK & win great prizes Grand prize is a trip for two to an Open Source event anywhere in the world http://moblin-contest.org/redirect.php?banner_id=100&url=/ _______________________________________________ Libmesh-users mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/libmesh-users
