Hello;

What is a good criteria for a triangular face of a tetrahedron unstructured cell to be swapped? Any information on tetrahedron face swapping is greatly appreciated. Thank You, Saied

(1). I am not sure whether we are talking about the same thing or not. (2). If you have a pair of triangular surfaces sharing a long common edge, then the skewness of both triangles will be high. (3). By swapping the diagonal common edge, the resultant triangles will have lower skewness, still using the same original four vertices. (4). If this is not your question, then please define the "swapping" more clearly.

Dear John, thank you for respondig. Yes, we are talking about the same thing. 1- replacing a common face between two tetrahedral cells 2- by connecting the opposite (diagonal) vertices to form a new edge and 3- creating three new faces that all share this new edge. The question is: When do we do this? What should be the criteria to swap? should I only consider the skewness of the face? or its relation with other faces has to be taken into account

(1). To make it simple, you can go through the loop once. And then come back second time to do the second loop, and so on. Until, there is no more triangles to swap. (based on the skewness, I hope. Unless you have some new ideas?)

How can we be certain that the new edge passes through the original face? Would the three new cells replacing the two old cells have equivelent total volume? How is a skewed face defined?(two edges being larger than a third edge by a factor for example. If so what is a good factor?)

(1). Well, if a trangle has three equal edges, then it it not skewed. The angle between two edges is 60 degrees. (2). Sometimes it is easier to use the minimum angle to set the requirement, for example, 20 degrees as a minimum. I guess, it depends on the solver, whether it can handle it accurately or not with certain skewness. (3). You may have to read the user's manual of a particular code to find out the specific definition of the skewness. (4). In 2-D, when you swap the edges, the two new triangles are brand new. So, they will have completely different properties of their own. (hopefully better than the original triangles.)

Dear John, I am intrested in 3-d, thank you

Hi,

I am still working on the 2-D swapping problem. It appears to me that edge swapping in 2-D is a very sensitive process. For example, if I have an isotropic mesh, and then introduce a matrix which can result in grids at any aspect ratio I need. I find that for aspect ratio >10, edge swapping itself can result in a very bad mesh, while AR < 10, it works pretty well together with edge splitting and node removal.

I don't which kind of application you are doing, hope it helps.

Guoping

Hi,

Paul Louis George's book on Delaunay triangulation might be interesting for you:

Paul-Louis George, Houman Borouchaki: Delaunay Triangulation and meshing. Editions Hermes (1998), ISBN 2-86601-692-0. http://www.editions-hermes.fr/Wlivre.asp?qid=934

Best regards,

Robert

Robert Schneiders MAGMA Giessereitechnologie GmbH D-52072 Aachen Kackertstr. 11 Germany Tel.: +49-241-88901-13 email: R.Schneiders@magmasoft.de www: http://www-users.informatik.rwth-aachen.de/~roberts/