This article is cited in 1 paper

Stochastic simulation algorithms for iterative solution of the Lame equation

I. A. Aksyuk, A. E. Kireeva, K. K. Sabelfeld, D. D. Smirnov

Institute of Computational Mathematics and Mathematical Geophysics of Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russia

Abstract: In this paper, iterative stochastic simulation algorithms for the Lame equation describing the displacements of an isotropic elastic body are constructed. Three different stochastic methods are proposed: the first one is based on a global algorithm of random walk on spheres to compute the solution and its derivatives for an anisotropic diffusion equation. It does not use grids and does not require large amounts of RAM. The second method is based on a randomized algorithm for solving large systems of linear equations and requires the introduction of a grid. The third method is also grid-based and uses a random walk algorithm. All three methods implement an iterative process, at each step of which anisotropic diffusion equations are solved. The paper provides a comparative analysis of the proposed methods and discusses the limits of applicability of each of them.

Key words: meshless stochastic algorithm, random walk on spheres, global random walk algorithm, randomized algorithm for solving linear equations.

UDC: 519.676

Received: 13.04.2023
Revised: 02.06.2023
Accepted: 05.09.2023

DOI: 10.15372/SJNM20230402

 English version: Numerical Analysis and Applications, 2023, 16:4, 299–316