A Monte Carlo method for Poisson's equation

DOI10.1016/0021-9991(90)90199-BzbMath0716.65105OpenAlexW2066820176MaRDI QIDQ753456

J. M. DeLaurentis, Louis A. Romero

Publication date: 1990

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9991(90)90199-b

zbMATH Keywords

Green's functionnumerical experimentsPoisson's equationMonte Carlo methodwalk on spheres

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Applications to the sciences (65Z05)

Related Items (13)

A Feynman-Kac path-integral implementation for Poisson's equation using an \(h\)-conditioned Green's function ⋮ A novel parallel adaptive Monte Carlo method for nonlinear Poisson equation in semiconductor devices ⋮ A derivative-free method for solving elliptic partial differential equations with deep neural networks ⋮ Solving elliptic equations with Brownian motion: bias reduction and temporal difference learning ⋮ A triangular mesh random walk for Dirichlet problems ⋮ Efficient Monte Carlo Method for Integral Fractional Laplacian in Multiple Dimensions ⋮ A modified walk‐on‐sphere method for high dimensional fractional Poisson equation ⋮ \(\varepsilon\)-shell error analysis for ``walk on spheres algorithms ⋮ Some new simulations schemes for the evaluation of Feynman–Kac representations ⋮ A random walk on rectangles algorithm ⋮ Monte Carlo methods for computing the capacitance of the unit cube ⋮ The simulation-tabulation method for classical diffusion Monte Carlo ⋮ A diffusion Monte Carlo method for charge density on a conducting surface at non-constant potentials

Cites Work

• Exact Monte Carlo solution of elliptic partial differential equations
• Regional Monte Carlo solution of elliptic partial differential equations
• Some Continuous Monte Carlo Methods for the Dirichlet Problem
• The Monte Carlo Method
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