The random walk on the boundary method for calculating capacitance

Authors:
Michael Mascagni;Nikolai A. Simonov
Affiliations:
Department of Computer Science and School of Computational Science and Information Technology, Florida State University, Tallahassee, FL;Institute of Computational Mathematics and Mathematical Geophysics, Novosibirsk, Russia
Venue:
Journal of Computational Physics
Year:
2004

Citing 5
Cited 2

Extrapolated surface charge method for capacity calculation of polygons and polyhedra

Journal of Computational Physics
Improved extrapolation technique in the boundary element method to find the capacitances of the unit square and cube

Journal of Computational Physics
Algorithm 806: SPRNG: a scalable library for pseudorandom number generation

ACM Transactions on Mathematical Software (TOMS)
The simulation-tabulation method for classical diffusion Monte Carlo

Journal of Computational Physics
Continuous Path Brownian Trajectories for Diffusion Monte Carlo via First- and Last-Passage Distributions

LSSC '01 Proceedings of the Third International Conference on Large-Scale Scientific Computing-Revised Papers

Estimation of Fekete points

Journal of Computational Physics
Review: Monte Carlo methods for computing the capacitance of the unit cube

Mathematics and Computers in Simulation

Quantified Score

Hi-index	31.47

Visualization

Abstract

In this paper we present the "random walk on the boundary" method for the rapid solution of integral equations that arise in electrostatics and related areas. This method is a Monte Carlo method based on the construction of a Markov chain that is readily interpreted as a random walk along the boundary over which integration in the integral equation is taken. To illustrate the usefulness of this technique, we apply it to the computation of the capacitance of the unit cube. Obtaining the capacitance of the cube usually requires computing the charge density, and this problem has been used as a benchmark by many in the field for algorithms of this kind. Here, the "random walk on the boundary" method does not require charge density computation, and obtains the capacitance of the cube within a statistical error of 2.7 × 10-7, the most accurate estimate to date.