Startseite Two stochastic algorithms for solving elastostatics problems governed by the Lamé equation
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Two stochastic algorithms for solving elastostatics problems governed by the Lamé equation

  • Anastasiya Kireeva ORCID logo EMAIL logo , Ivan Aksyuk und Karl K. Sabelfeld ORCID logo
Veröffentlicht/Copyright: 23. Mai 2023

Abstract

In this paper, we construct stochastic simulation algorithms for solving an elastostatics problem governed by the Lamé equation. Two different stochastic simulation methods are suggested: (1) a method based on a random walk on spheres, which is iteratively applied to anisotropic diffusion equations that are related through the mixed second-order derivatives (this method is meshless and can be applied to boundary value problems for complicated domains); (2) a randomized algorithm for solving large systems of linear algebraic equations that is the core of this method. It needs a mesh formation, but even for very fine grids, the algorithm shows a high efficiency. Both methods are scalable and can be easily parallelized.

MSC 2010: 65C05; 65C40; 65Z05

Award Identifier / Grant number: 19-11-00019

Funding statement: Support of the Russian Science Foundation, Grant 19-11-00019, is greatly acknowledged.

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Received: 2023-01-07
Revised: 2023-05-02
Accepted: 2023-05-04
Published Online: 2023-05-23
Published in Print: 2023-06-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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