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ICCS
2001
Springer

A Feynman-Kac Path-Integral Implementation for Poisson's Equation

9 years 7 months ago
A Feynman-Kac Path-Integral Implementation for Poisson's Equation
This study presents a Feynman–Kac path-integral implementation for solving the Dirichlet problem for Poisson’s equation. The algorithm is a modified “walk on spheres” (WOS) that includes the Feynman–Kac path-integral contribution for the source term. In our approach, we use an h-conditioned Green’s function instead of simulating Brownian trajectories in detail to implement this path-integral computation. The h-conditioned Green’s function allows us to represent the integral of the right-hand-side function from the Poisson equation along Brownian paths as a volume integral with respect to a residence time density function: the h-conditioned Green’s function. The h-conditioned Green’s function allows us to solve the Poisson equation by simulating Brownian trajectories involving only large jumps, which is consistent with both WOS and our Green’s function first-passage (GFFP) method [J. Comput. Phys. 174 (2001) 946]. As verification of the method, we tabulate the h-...
Chi-Ok Hwang, Michael Mascagni
Added 29 Jul 2010
Updated 29 Jul 2010
Type Conference
Year 2001
Where ICCS
Authors Chi-Ok Hwang, Michael Mascagni
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