Affiliation:
1. Russian Academy of Sciences , Institute of Computational Mathematics and Mathematical Geophysics , Novosibirsk , Russia
Abstract
Abstract
In this paper, we address a long-standing open problem in stochastic simulation: construction of a random walk on spheres (RWS) algorithm for solving a system of elasticity equations, known as the Lamé equation. Many attempts to generalize the classic probabilistic representations like the Kac formula for parabolic and scalar elliptic equations failed.
A different approach based on a branching random walk on spheres (BRWS) introduced in our paper of 1995
[K. K. Sabelfeld and D. Talay,
Integral formulation of the boundary value problems and the method of random walk on spheres,
Monte Carlo Methods Appl. 1 1995, 1, 1–34]
made little progress in solving this problem. In the present study, we further improve
the BRWS algorithm by a special implementation of a branching anisotropic random walk on spheres process.
Funder
Russian Science Foundation
Russian Foundation for Basic Research
Subject
Applied Mathematics,Statistics and Probability
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