Steven Pav, Mathematics, University of Califoria, San Diego
"Quality Delaunay Meshing in 3D"
Finite element simulations require decomposition of the problem domain into a collection of simplices known as a mesh. A good meshing algorithm should accept any reasonable input and output a mesh with a modest number of "high quality" (i.e. nearly regular) simplices. The quality restriction is imposed because near-regular simplices are essential for interpolation. A good meshing algorithm should also produce meshes where output simplex size is sensitive to the local sizing of the input. While this problem has been essentially solved in two dimensions, all previous attempts in three dimensions have been deficient in one respect or another: existing algorithms make restrictive assumptions on the input, require computationally expensive searches, or have very weak quality guarantees.
In this talk I discuss recent advances made on the problem in joint work with Noel Walkington. Our algorithm meets all the requirements of a good mesher, and may be the first practical, robust, conforming Delaunay meshing algorithm.
TUESDAY, September 14, 2004