A Feynman-Kac path-integral implementation for Poisson's equation using an \(h\)-conditioned Green's function

DOI10.1016/S0378-4754(02)00224-0zbMath1025.65006OpenAlexW2124222311WikidataQ57553652 ScholiaQ57553652MaRDI QIDQ1873035

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

Publication date: 19 May 2003

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0378-4754(02)00224-0

zbMATH Keywords

Dirichlet problemBrownian motionPoisson's equationnumerical experimentwalk on spheresBrownian trajectories\(h\)-conditioned Green's functionFeynmann-Kac path-integral

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Brownian motion (60J65) Integral representations of solutions to PDEs (35C15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Boundary element methods for boundary value problems involving PDEs (65N38)

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Cites Work

• A Monte Carlo method for Poisson's equation
• Exact Monte Carlo solution of elliptic partial differential equations
• Regional Monte Carlo solution of elliptic partial differential equations
• Integral and probabilistic representations for systems of elliptic equations
• Some Continuous Monte Carlo Methods for the Dirichlet Problem
• Functional Integration and Partial Differential Equations. (AM-109)
• From Brownian Motion to Schrödinger’s Equation
• The simulation-tabulation method for classical diffusion Monte Carlo
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