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Updated: Sep 27, 2026

Finite Element Modelling of a Cellular Electric Microenvironment
Published on: May 18, 2021
First- and last-passage Monte Carlo algorithms for the charge density distribution on a conducting surface
James A Given1, Chi-Ok Hwang, Michael Mascagni
1Naval Research Laboratory, 4555 Overlook Avenue SW, Washington, DC 20375, USA. JAGiven137@aol.com
Abstract:
Recent research shows that Monte Carlo diffusion methods are often the most efficient algorithms for solving certain elliptic boundary value problems. In this paper, we extend this research by providing two efficient algorithms based on the concept of "last-passage diffusion." These algorithms are qualitatively compared with each other (and with the best first-passage diffusion algorithm) in solving the classical problem of computing the charge distribution on a conducting disk held at unit voltage. All three algorithms show detailed agreement with the known analytic solution to this problem.
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