Title: Designing tetrahedral meshes -- and putting them to good use
Dr. Mathieu Desbrun
Department of Computing and Mathematical SciencesCalifornia Institute of Technology
Date: April 16, 2010
Time: 11:00 am
Location: 3105 Egr (CSE conference room)
Hosts: Yiying Tong
Meshing lies at the heart of many computational techniques across a wide range of fields. The meshing task consists of finding a set of simple elements (typically vertices, edges, triangles, and tetrahedra) which best partition a given domain while nicely approximating its boundaries. However, meshing a domain is complicated by requirements on the "quality" of its elements: badly shaped elements (too flat, too stretched, etc.) must be avoided as the presence of even a single one can ruin the convergence and/or accuracy of a computational method. In this talk, we will focus on the simple yet common case of isotropic tetrahedral meshing, and present new results linking Delaunay/Voronoi tessellations to approximation theory. We will then briefly mention recent work on developing a geometry-based, principled approach to computational modeling that benefits from such meshes. Examples ranging from processing of scanned geometry to simulation of complex fluids will be used to illustrate the numerical benefits.
Mathieu Desbrun is a Professor at the California Institute of Technology (Caltech). After receiving his Ph.D. from the National Polytechnic Institute of Grenoble (INPG), he spent a year as a post-doctoral researcher at Caltech in the Multires Modeling Group before joining the Computer Science faculty at the University of Southern California from 2000 to 2004. He now leads the Applied Geometry lab at Caltech, focusing on discrete differential modeling---the development of differential, yet readily discretizable foundations for computational modeling---and a wide spectrum of applications, ranging from discrete geometry processing to solid and fluid mechanics and field theory. He is also the director of the Information Science and Technology initiative at Caltech.