A Feynman-Kac Path-Integral Implementation for Poisson's Equation
نویسندگان
چکیده
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 FeynmanKac 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.
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A Feynman-Kac path-integral implementation for Poisson's equation using an h-conditioned Green's function
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 co...
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