Computational Geometry Aspects of MC Approaches to PDEs

Name:    Prof. Michael Mascagni                 
Address: Department of Computer Science and
         Department of Mathematics and
	 Department of Scientific Computing and
         Graduate Program in Molecular Biophysics	
         Florida State University
         Tallahassee, FL  32306-4530  USA
         AND
         Information Technology Laboratory
         Applied and Computational Mathematics Division
         100 Bureau Drive M/S 8910
         National Institute of Standards and Technology (NIST)
         Gaithersburg, MD  20899-8910  USA

Offices: 498 Dirac Science Library/207A Love Building (FSU) Building 225/Room B154 (NIST)
Phone:   +1.850.644.3290 (FSU) +1.301.975.2051 (NIST)
FAX:     +1.850.644.0058
e-mail:  mascagni@fsu.edu (FSU) mascagni@nist.gov (NIST)

Title: Computational Geometry Aspects of Monte Carlo Approaches to PDE Problems in Biology, Chemistry, and Materials

We will introduce at some Monte Carlo methods for solving problems in electrostatics. These rely on evaluating functionals of the first-passage time of Brownian motion on geometries defined by the system of interest. We will use the Walk on Spheres (WOS) algorithm to quickly evaluate these functionals, and we will show how a computational geometric computation dominates this computation in complexity. We then consider computing the capacitance of a complicated shape, and use this as our model problem to find an efficient serial and parallel implementation. The capacitance computation is prototypical of many Monte Carlo approaches to problems in biology, biochemistry, and materials science.

This is joint work with Drs. Walid Keyrouz and Derek Juba from the Information Technology Laboratory at NIST.