A feynman-kac path-integral implementation for poisson’s equation

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 the Poisson kernel instead of simulating Brownian trajectories in detail to implement the path-integral computation.We derive this approach and provide results from a numerical experiment on a two-dimensional problem as verification of the method.