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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Kireeva Anastasiya & Aksyuk Ivan & Sabelfeld Karl K., 2023. "Two stochastic algorithms for solving elastostatics problems governed by the Lamé equation," Monte Carlo Methods and Applications, De Gruyter, vol. 29(2), pages 143-160, June.
    • Handle: RePEc:bpj:mcmeap:v:29:y:2023:i:2:p:143-160:n:1
    DOI: 10.1515/mcma-2023-2008
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