This article is cited in 3 papers

Random walk-on-spheres algorithms for solving mixed and Neumann boundary-value problems

N. A. Simonov

Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences

Abstract: We propose a new approach to constructing Monte Carlo methods for solving mixed boundary value problems for elliptic equations with constant coefficients. We derived a mean-value relation for point values of the solution. As a consequence, the walk-on-spheres algorithm can still be used even after a trajectory hits the reflecting boundary. Such an approach is significantly more efficient than the standard one.

Key words: Monte Carlo, random walk, walk-on-spheres, mixed boundary-value problem, Poisson equation, mean value theorem.

UDC: 519.245

Received: 06.12.2005
Revised: 28.04.2006