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On Mon, 25 Aug 2008, Jed Brown wrote:
It would be nice to store and manipulate the coordinates just like any other Function. Suppose the basis operations accept (in some way) a NULL coordinate vector which means that the element Jacobian is the identity everywhere. That way you could manipulate mesh geometry by evaluating forms to construct a new geometry Function. Then register this new Function (i.e. compute associated element Jacobians, required facet normals).
I agree it would be nice. But this function would need to feed into various routines, like Tabulate_Tensor. Would this just become part of the `w' coefficient vector? Or would there need to be another input to these routines? Or could the cell class contain this? I will have to think about it some more...
- Shawn
Not all operations make sense without coordinates, but basis evaluation, derivatives, and integration in the element interior still do. I think treating the coordinates as a special case would duplicate a lot of code. Of course in the pre- and post-processing you still need to be able to handle `normal' mesh descriptions. For preprocessing, this means projecting nodal coordinates into the finite element basis. They will normally be exactly representable in the FE basis so an elementwise (DG) projection would be sufficient (in the nodal case, it can just be evaluation). Going the other way is just point evaluation (or a continuous Galerkin projection). Thoughts? Jed
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