Hi Corrado! Sorry for the slow reply on here, I know we have discussed this privately, but of course this is the best place for discussion.
1. First half of the presentation; My understanding of the current 'PDE on Manifold' functionality in FEniCS is that the weak form cannot include terms relating to the geometry of the manifold. i.e. it would be natural to have terms such as the fundamental form expressed through UFL which you could then define the shell model. I have seen someone discuss this idea before here: http://www.mail-archive.com/[email protected]/msg08932.html albeit in the context of isoparametric mappings. I think though, that isoparametric mapping is just relating R^3->E^3 and the shell concept is relating R^2->E^3, the efforts towards shell models should work within bringing isoparametric mappings to FEniCS. @David Ham: I remember David Ham discussed with me that he had a student working isoparametric mappings, did anything come of it? 2. Second half of the presentation; local projections. As you can see I have done some simple local projections at the linear algebra level (ie. post assembly), but I do not think this is a suitable path for implementing the MITC operators which are significantly more complicated. One initial option would be to do the full mixed problem, at the expense of engendering extra unknowns. Also you suggested in our private email that we could do these local projections using a custom C++ kernel/assembly routine. I can see there are still some problems with the RT elements on manifolds, it would be important for this functionality to work first: http://fenicsproject.org/pipermail/fenics/2014-March/001340.html And only two threads up from this one, this discussion seems pertinent: http://fenicsproject.org/pipermail/fenics/2014-March/001371.html Another option is that we avoid this second piece of functionality and go with trying to get DG-Koiter shell models working first which work which are rotation-free and use standard element constructions. @Garth Wells: I know this is something Garth Wells is an expert on so perhaps it is the best path forward for now? 3. Generality. So I know a lot about shells, but not about other PDEs on manifolds. I remember Douglas Arnold mentioned that any approach implemented in FEniCS should be as general as possible. Any comments on this? Kind regards, ----- Dr. Jack S. Hale Research Associate University of Luxembourg Campus Kirchberg G005 Phone +352 44 66 44 5236 [email protected] Latest publications and conferences: http://goo.gl/rNiISG ORCID: http://orcid.org/0000-0001-7216-861X Google Scholar: http://scholar.google.com/citations?user=Fx9lQ7MAAAAJ&hl=de _______________________________________________ fenics mailing list [email protected] http://fenicsproject.org/mailman/listinfo/fenics
