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
Offices: 498 Dirac Science Library/207A Love Building
Phone: +1.850.644.3290
FAX: +1.850.644.0058
e-mail: mascagni@fsu.edu
Title: Monte Carlo Methods for Partial Differential Equations: A Personal Journey
Abstract:
We give a brief overview of the early history of the Monte Carlo
method. We
then give a quick review of the Feynman-Kac equations; these allow one
to represent the solution of linear elliptic and parabolic partial
differential equations (PDEs) as expected values over stochastic
processes. The particular stochastic process for a given PDE is
the solution to a stochastic differential equation defined via the
elliptic operator in the PDE. We then return to elliptic PDEs
and discuss, in detail, several acceleration techniques that are widely
applicable Monte Carlo methods. We begin with the "walk on
spheres" algorithm, followed by the the "Greens function first-passage"
method, the "simulation-tabulation" method, "last passage" methods, the
"walk on the boundary" method, and finally the "walk on subdomains"
method. These various Monte Carlo methods are presented within
the context of various problems that arise in flow through porous
media, electrostatics, and continuum biochemistry that were researched
and published by Prof. Mascagni and his group over the years.
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