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

Kireeva Anastasiya (), Aksyuk Ivan () and Sabelfeld Karl K. ()
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Kireeva Anastasiya: Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, Novosibirsk, Russia
Aksyuk Ivan: Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, Novosibirsk, Russia
Sabelfeld Karl K.: Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences; and Novosibirsk State University, Novosibirsk, Russia

Monte Carlo Methods and Applications, 2023, vol. 29, issue 2, 143-160

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.

Keywords: Meshless algorithms; random walk on spheres; global random walk; randomized algorithm for solving linear equations (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1515/mcma-2023-2008

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