CSE Symposium Keynote
The Poisson-Boltzmann Equation: Some Unfinished Business
Tuesday, April 10, 2007, 9:00 A.M.
2240 DCL, 1304 W. Springfield Ave., Urbana, IL
Abstract
We examine a nonlinear PDE model of electrostatics phenomena arising in
biophysics. Through use of a two-scale expansion we establish a number
of new results for the PDE itself, such as a priori max-norm
estimates. These results are then used to derive a priori and a
posteriori estimates of various types for Galerkin approximations.
This collection of results for the continuous and discretized problems
leads to the design of a particular nonlinear approximation algorithm
based on error indicators and local refinement. We prove that the
adaptive algorithm converges, establishing one of only a handful of
rigorous results of this type for nonlinear elliptic equations. We
then shift gears and describe a somewhat strange parallelization scheme
for these types of adaptive algorithms that appears to scale linearly
with the number of processors. We prove that in fact this is the case
(with some caveats). We finish by illustrating the adaptive algorithm
with examples using the Finite Element ToolKit (FETK). This is joint
work with a number of collaborators.
Biography
Professor Michael Holst received his Ph.D. in Computer Science from the
University of Illinois at Urbana-Champaign in 1993. He was a Prize
Research Fellow and a von Karman Instructor of Applied Mathematics at
the California Institute of Technology 1993-1997, Assistant Professor
at UC Irvine 1997-1998, and joined the Department of Mathematics at
UCSD in 1998, where he was promoted to Associate Professor in 2000 and
Full Professor in 2003. He was a UCSD Hellman Fellow in 1999, and was
the recipient of an NSF CAREER Award 1999-2004 for his research in
computational and applied mathematics. He is currently PI, Co-PI,
and/or on the steering committees for a number of interdisciplinary
research projects and centers at UCSD and elsewhere.