Random walk method for the two- and three-dimensional Laplace, Poisson andHelmholtz's equations

Citation
Mk. Chati et al., Random walk method for the two- and three-dimensional Laplace, Poisson andHelmholtz's equations, INT J NUM M, 51(10), 2001, pp. 1133-1156
Citations number
20
Categorie Soggetti
Engineering Mathematics
Journal title
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
ISSN journal
00295981 → ACNP
Volume
51
Issue
10
Year of publication
2001
Pages
1133 - 1156
Database
ISI
SICI code
0029-5981(20010810)51:10<1133:RWMFTT>2.0.ZU;2-N
Abstract
The random walk method (RWM) is developed here for solving the Laplace, Poi sson, and Helmholtz equations in two and three dimensions. The RWM is a loc al method, i.e. the solution at an arbitrary point can be determined withou t having to obtain the complete field solution. The method is based on the properties of diffusion processes, the Ito formula, the Dynkin formula, the Feynman-Kac functional, and Monte Carlo simulation. Simplicity, stability, accuracy, and generality are the main features of the proposed method. The RWK is inherently parallel and this fact has been fully exploited in this paper. Extensive numerical results have been presented in order to understa nd the various parameters involved in the method. Copyright (C) 2001 John W iley & Sons, Ltd.