Development and implementation of branching random walk on spheres algorithms for solving the 2D elastostatics Lamé equation

Shalimova Irina () and Sabelfeld Karl K. ()
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Shalimova Irina: Russian Academy of Sciences, Institute of Computational Mathematics and Mathematical Geophysics, Novosibirsk, Russia
Sabelfeld Karl K.: Russian Academy of Sciences, Institute of Computational Mathematics and Mathematical Geophysics, Novosibirsk, Russia

Monte Carlo Methods and Applications, 2023, vol. 29, issue 1, 79-93

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.

Keywords: Lamé equation; branching random walk on spheres; mean number of steps; variance estimation (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1515/mcma-2022-2131

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