A Feynman–Kac path-integral implementation for Poisson’s equation using an h-conditioned Green’s function

Chi-Ok Hwang, Michael Mascagni and James A. Given

Mathematics and Computers in Simulation (MATCOM), 2003, vol. 62, issue 3, 347-355

Abstract: 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-conditioned Green’s function for Brownian motion starting at the center of the unit circle and making first-passage on the boundary of the circle, find an analytic expression fitting the h-conditioned Green’s function, and provide results from a numerical experiment on a two-dimensional Poisson problem.

Keywords: Walk on spheres; h-Conditioned Green’s function; Poisson’s equation (search for similar items in EconPapers)
Date: 2003
References: View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:62:y:2003:i:3:p:347-355

DOI: 10.1016/S0378-4754(02)00224-0

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