Name: Prof. Michael Mascagni Address: Department of Computer Science and School of Computational Science Florida State University Tallahassee, FL 32306-4530 USA Offices: 498 Dirac Science Library/172 Love Building Phone: +1.850.644.3290 FAX: +1.850.644.0098 e-mail: email@example.com
Title: Monte Carlo Methods for Partial Differential Equations
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.
We also present the example of the "telegrapher's" equation, an hyperbolic equation, as solved stochastically, and some nonlinear PDE examples.
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