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Two stochastic algorithms for solving elastostatics problems governed by the Lamé equation. / Kireeva, Anastasiya; Aksyuk, Ivan; Sabelfeld, Karl K.

In: Monte Carlo Methods and Applications, Vol. 29, No. 2, 01.06.2023, p. 143-160.

Research output: Contribution to journal › Article › peer-review

Harvard

Kireeva, A, Aksyuk, I & Sabelfeld, KK 2023, 'Two stochastic algorithms for solving elastostatics problems governed by the Lamé equation', Monte Carlo Methods and Applications, vol. 29, no. 2, pp. 143-160. https://doi.org/10.1515/mcma-2023-2008

APA

Kireeva, A., Aksyuk, I., & Sabelfeld, K. K. (2023). Two stochastic algorithms for solving elastostatics problems governed by the Lamé equation. Monte Carlo Methods and Applications, 29(2), 143-160. https://doi.org/10.1515/mcma-2023-2008

Vancouver

Kireeva A, Aksyuk I, Sabelfeld KK. Two stochastic algorithms for solving elastostatics problems governed by the Lamé equation. Monte Carlo Methods and Applications. 2023 Jun 1;29(2):143-160. doi: 10.1515/mcma-2023-2008

Author

Kireeva, Anastasiya ; Aksyuk, Ivan ; Sabelfeld, Karl K. / Two stochastic algorithms for solving elastostatics problems governed by the Lamé equation. In: Monte Carlo Methods and Applications. 2023 ; Vol. 29, No. 2. pp. 143-160.

BibTeX

@article{51b429968e344b4ba3f067e12d74b2b4,
title = "Two stochastic algorithms for solving elastostatics problems governed by the Lam{\'e} equation",
abstract = "In this paper, we construct stochastic simulation algorithms for solving an elastostatics problem governed by the Lam{\'e} 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, global random walk, random walk on spheres, randomized algorithm for solving linear equations",
author = "Anastasiya Kireeva and Ivan Aksyuk and Sabelfeld, {Karl K.}",
note = "Support of the Russian Science Foundation, Grant 19-11-00019, is greatly acknowledged. Публикация для корректировки.",
year = "2023",
month = jun,
day = "1",
doi = "10.1515/mcma-2023-2008",
language = "English",
volume = "29",
pages = "143--160",
journal = "Monte Carlo Methods and Applications",
issn = "0929-9629",
publisher = "Walter de Gruyter GmbH",
number = "2",

}

RIS

TY - JOUR

T1 - Two stochastic algorithms for solving elastostatics problems governed by the Lamé equation

AU - Kireeva, Anastasiya

AU - Aksyuk, Ivan

AU - Sabelfeld, Karl K.

N1 - Support of the Russian Science Foundation, Grant 19-11-00019, is greatly acknowledged. Публикация для корректировки.

PY - 2023/6/1

Y1 - 2023/6/1

N2 - 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.

AB - 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.

KW - Meshless algorithms

KW - global random walk

KW - random walk on spheres

KW - randomized algorithm for solving linear equations

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85160849709&origin=inward&txGid=463940ebdf90d59f31b2caf0d108f6a1

UR - https://www.mendeley.com/catalogue/f5c0574f-83b8-31b1-93d4-f35dbb246738/

U2 - 10.1515/mcma-2023-2008

DO - 10.1515/mcma-2023-2008

M3 - Article

VL - 29

SP - 143

EP - 160

JO - Monte Carlo Methods and Applications

JF - Monte Carlo Methods and Applications

SN - 0929-9629

IS - 2

ER -

ID: 59278419