On Wed, Mar 24, 2010 at 2:49 PM, Pablo Angulo <pablo.ang...@uam.es> wrote: > Hello, Ondrej: > >> Do you have some example worksheet doing this? That's the exact same >> workflow that we want to use in FEMhub --- only we want to use our C++ >> PDE solvers (http://hpfem.org/ >> <http://www.google.com/url?sa=D&q=http://hpfem.org/&usg=AFQjCNGeqv6JoTc2MKrXb5G6x8cbvLNKXg>), >> that we wrapped in Python. > I've taken a look around your place, and I'm impressed. I'm working on > such a worksheet, it should be ready by the weekend. Maybe when I've > finished my worksheet I can borrow one of yours to have more examples. > Do you have a license policy regarding the published worksheets.
I actually don't know. I think one should ask the one who did the worksheets, but I think you can use it under the same conditions as hermes, e.g. hermes1d is BSD, hermes2d is GPL. Our goal is to eventually ship nice worksheets directly with femhub (http://femhub.org), so I guess they would use the same license as femhub, which uses the same license as Sage, e.g. GPL. > >> > By the way, Ondrej Certik just mentioned he's using Flex to work in a >> > mesh editor: >> > >> http://groups.google.com/group/sage-devel/browse_thread/thread/c26290... >> <http://www.google.com/url?sa=D&q=http://groups.google.com/group/sage-devel/browse_thread/thread/c262901cfafd3f45&usg=AFQjCNH505zaCxBLUuEZrzLwRORSaox3GQ> >> >> >> Yes, Aayush in our group in Reno knows flex, so he started to develop >> the mesh editor in that. Just yesterday I have discovered the graph >> editor and realized that it does exactly what we need. > Honestly, I'd like SAGE not to depend on Flash, if at all possible. With > the awesome javascript libraries now available, and the graph_editor > lightning the way, I think I can produce a good-enough widget, with some > guidance from your team and other users. I totally agree, also flash doesn't work on my phone, but the graph editor does. As I said, it's just Aayush already knew flex, so we could get some results quickly. > >> I have one more question --- does your code produce elements? >> > The output is a list of coordinates, a list of tuples with the indices > of the triangles. That's how the people that taught me used to work. > Then I take it from there to build the elements at plain sight. It's > only for instructional use. Ok. > >> I was thinking yesterday, that if I take the graph (generated using >> the graph editor), I have vertices (and their coordinates), and then I >> have a set of edges (pairs of vertices, connected by a line). How can >> I convert this to a FE mesh? FE mesh is a set of triangles and quads. >> > In my limited knowledge of FE, I thought a mesh was either a set of > triangles, or a set of quads. I haven't read about mixing both. Yes, they can be mixed. We actually prefer quads to triangles, because it's easier to handle (refine, integrate, ...) and also in 3d hexes are easier to handle than other elements. The mesh should (eventually) allow both triangles and quads. > >> So here is a crude algorithm, that we have in mind: >> >> 1) find some boundary edge >> 2) get neighboring vertices (follow edges) and try to construct a >> triangle, that contains the edge. If success, cut the triangle out >> (add it to the list of triangles) and go to 1) >> 3) try to construct a quad, make sure it is not composed of two >> triangles. If success (e.g. either a quad, or two triangles), cut it >> out (add it to the list of quads or triangles) and go to 1) >> >> Isn't this already implemented in Sage somewhere? >> > Well, I'd rather adapt the code. The graph editor has a lot of stuff > that is only going to confuse the users. In the editor I wrote, there is > no posible way of introducing a graph with crossings. The only possible Yes, I agree. The graph editor was just the initial way to get something working. It should be modified specifically for FEM. > way that you can produce a wrong triangulation is that there is a vertex > in the boundary of several triangles, with gaps between the triangles. > To me, the goal is to have a 2D SimplicialComplex such that all faces > are triangles, and every point (of the underlying topological space) has > a neighborhood that is either a ball or a circular sector. > >> In any case, your code (which just produces triangles) would also be >> fine, at the beginning. >> > I can add quads, if we decide a good way to add it to the GUI. > > Please let me ask you two questions: > * I added some javascript code I found (from some Joshua Bell) to > compute the Delaunay triangulation. This speeds up the process, as you > only have to drop the points, and hit the "delaunay" button. Then you > can remove some triangles if needed (for example, if you're working with > a non-convex domain). Do you approve of this methodology? I CCed to our femhub list to see what other people think. Aayush, Pavel, any opinions? > * Do you think that circular arcs are important to add? It would work Yes! Our FE solver can do circular arcs (any nurbs curve actually, but arcs seem to be enough). > this way: in the initial triangulation, you mark an edge as circular > (with a certain center). In the triangulation, this edge is straight, > but the information that it was circular is used when the mesh is > refined. Otherwise, if you approximate a curve by straight segments, the > approximation will not improve when you refine. 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