SPEAKER: Benoit Hudson
TIME: Wednesday 12-1pm, February 7, 2007
PLACE: NSH 1507
TITLE: Three Recent Mesh Refinement Results
ABSTRACT:
Mesh refinement is the first step in running a finite element simulation: we take an input geometry (points, segments, polygons, …) and output a mesh of triangles and tetrahedra.
I’ll report on three exciting new mesh refinement results our group have come up with in the past year. First, for the benefit of those who didn’t see Todd’s talk last semester, I’ll reiterate (without proof) our optimal-time algorithm for mesh refinement. Next, I’ll show how to work-efficiently parallelize our algorithm to within a log factor of optimal depth. Finally, I’ll show how to dynamically maintain a mesh as we add or remove points to/from it, in optimal time. There were no known fast algorithms for any of these problems before except in two dimensions.
Our work opens up a vast number of open problems, both geometric and algorithmic; I’ll make sure to leave some for the audience to ponder.
