Wednesday, December 04, 2002
Hewlett Packard Auditorium, 306 Soda Hall
4:00-5:00 p.m.

Professor Peter Schröder

Depts. of Computer Science &
Applied and Computational Mathematics,
California Institute of Technology

Subdivision for Modeling and Simulation

Abstract:

Subdivision surfaces are now solidly established as a major modeling primitive for free-form design. As it turns out they also have very favorable qualities when it comes to solving 4th order PDEs such as the thin-shell equations. The latter describe the behavior of thin flexible structures as they appear in all areas of engineering design. In this way subdivision surfaces are highly suited for integrated engineering design, removing the usual troubles associated with converting geometric representations to a form more suitable for finite element analysis.

My talk covers two subjects from this area. In a first part I will describe some recent developments in the construction of subdivision schemes based on repeated averaging. As it turns out, primal/dual mesh averaging operators are sufficient to build large families of classical as well as new subdivision schemes for a variety of possible topological split operators. Among them primal and dual quad schemes and more exotic dual Sqrt(3) schemes (among many others). In the second part I will review some of the work on thin-shell modeling with the Subdivision Element Method and discuss strategies for the simple (in terms of data structures) construction of adaptive solvers.

Peter Schröder is Professor of Computer Science and Applied and Computational Mathematics at the California Institute of Technology where he began his academic career in 1995. Prior to Caltech and a short stint as postdoctoral research fellow at Interval Corporation (summer 1995) he was a postdoctoral research fellow at the University of South Carolina department of mathematics and a lecturer in the computer science department, where he worked with Prof. Björn Jawerth and Dr. Wim Sweldens. He received his PhD in computer science from Princeton University in 1994 for work on "Wavelet Methods for Illumination Computations." Prior to Princeton he was a member of the technical staff at Thinking Machines, where he worked on graphics algorithms for massively parallel computers. In 1990 he received an MS degree from MIT's Media Lab. He did his undergraduate work at the Technical University of Berlin in computer science and pure mathematics. He has also held an appointment as a visiting researcher with the German national computer science research lab (GMD) and its visualization group.