Name: Prof. Michael Mascagni Address: Department of Computer ScienceandSchool of Computational Science Florida State University Tallahassee, FL 32306-4530USAOffices: 498 Dirac Science Library/172 Love Building Phone: +1.850.644.3290 FAX: +1.850.644.0098 e-mail: mascagni@fsu.edu

**Title: Using
Simple SDEs (Stochastic Differential Equations) to Solve Complicated PDEs
(Partial Differential Equations)**

**Abstract:**

**This talk begins with an overview of
methods to solve PDEs based on the representation of point solutions of the PDEs
as expected values of functionals of stochastic processes defined by the
Feynman-Kac formula. The particular stochastic processes that arise in the
Feynman-Kac formula are solutions to specific SDEs defined by the
characteristics of the differential operator in the PDE. The Feynman-Kac
formula is applicable to wide class of linear initial and initial-boundary value
problems for elliptic and parabolic PDEs. We then concentrate our
attention on elliptic boundary value problems that arise in applications in
materials science and biochemistry. These problems are similar in that the
PDEs to be solved are rather simple, and hence the associated SDEs that arise in
the Feynman-Kac formula are likewise simple. However, the geometry of the
problem is often complicated and amenable to several acceleration approaches
particular to these simple SDEs. We will specifically describe the walk on
spheres, Greens function first passage, last passage, walk on the boundary, and
walk on subdomains methods in this context. These methods will be
presented in the setting of several applications studied by the author and his
research collaborators.**

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