Hello, all. I've been thinking about this higher order mesh stuff, and I need to be more clear about what I want to do. I'm not sure it would be good to make an ultra-general higher order mesh format. It seems to be more trouble than it is worth (right now).
What I would like to have is a format for higher order meshes based on polynomial mappings (ONLY!). Currently, everything in FENICS assumes that a P1 map is used for each element in the mesh. Of course, this only requires knowledge of the vertex coordinates of the element. If a higher order polynomial map is used, all you need are the positions of the extra control points. And this would extend the P1 map quite naturally. For the .xml format, I think the data for the control points should contain the usual vertex coordinates also (not just the extra control points). This would be redundant, but a little simpler to read in from the XML file. Note that storing the coordinates for each element separately would not be good, because even the edge mid-point positions would be used by 2 (or more) elements, so you need to keep this connectivity information. One advantage of using a polynomial map (besides for free boundary problems) is that the element tensor can be computed exactly in some cases (but not for a stiffness matrix). This isn't bad. Anyway, I know this is probably boring some of you. And I know this is not a high priority, but I am willing to put in time implementing this (mostly because it would be useful to me). I will repost another format for the mesh.xml file and see what people think. - Shawn _______________________________________________ DOLFIN-dev mailing list [email protected] http://www.fenics.org/mailman/listinfo/dolfin-dev
