Date:

Monday, February 4, 2002

Speaker:

Ben Fox

Affiliation:

SIM-OPT Consulting, Boulder, CO.

e-mail:

bfox@carbon.cudenver.edu

Title:

Fast Heat-Equation Solvers

Abstract:

I give fast solvers for the heat equation based on formulas of Feynman-Kac type for the pointwise solution. In spatial dimension one, my solvers have about the same computational complexity as conventional solvers. In spatial dimension d greater than one, my schemes win -- the difference increasing quickly with d. This is far better than folklore has it for simulation schemes, which generally indicates simulation winning somewhere around spatial dimension five or more. Feynman-Kac formulas involve so-called path integrals of functions of Brownian motion. I give enough background so that the meaning of the formulas can be understood by non-probabilists. My methods blend classical methods (Simpson & Hermite) in deterministic numerical integration with a simulation method, called randomized quasi-Monte Carlo, that is much more efficient than the usual Monte Carlo. My talk gives only an outline of my methods. For details, see my paper FILTERING THE FEYNMAN-KAC FORMULA, to appear in SINUM.