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
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.