Stochastic Simulation Algorithms for Iterative Solution of the Lamé Equation

In this paper, iterative stochastic simulation algorithms for the Lamé 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 a...

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Bibliographic Details
Published in:Numerical analysis and applications Vol. 16; no. 4; pp. 299 - 316
Main Authors: Aksyuk, I. A., Kireeva, A. E., Sabelfeld, K. K., Smirnov, D. D.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.12.2023
Springer Nature B.V
Subjects:
Algorithms
Approximation
Boundary conditions
Boundary value problems
Elastic bodies
Iterative methods
Iterative solution
Lame functions
Linear equations
Mathematics
Mathematics and Statistics
Numerical Analysis
Random variables
Random walk
global random walk algorithm
randomized algorithm for solving linear equations
grid-free stochastic algorithm
random walk on spheres
ISSN:1995-4239, 1995-4247
Online Access:Get full text
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Summary:In this paper, iterative stochastic simulation algorithms for the Lamé 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.
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ISSN:1995-4239
1995-4247
DOI:10.1134/S199542392304002X