求解Lamé方程弹性静力学问题的两种随机算法

IF 0.8 Q3 STATISTICS & PROBABILITY Monte Carlo Methods and Applications Pub Date : 2023-05-23 DOI:10.1515/mcma-2023-2008
A. Kireeva, Ivan Aksyuk, K. Sabelfeld
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引用次数: 1

摘要

摘要本文构造了求解由lam方程控制的弹性静力学问题的随机模拟算法。提出了两种不同的随机模拟方法:(1)基于球上随机游走的方法,该方法迭代应用于通过混合二阶导数关联的各向异性扩散方程(该方法无网格,可应用于复杂域的边值问题);(2)求解大型线性代数方程组的随机算法,这是该方法的核心。它需要网格的形成,但即使是非常精细的网格,该算法也显示出很高的效率。这两种方法都是可伸缩的,可以很容易地并行化。
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Two stochastic algorithms for solving elastostatics problems governed by the Lamé equation
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.
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来源期刊
Monte Carlo Methods and Applications
Monte Carlo Methods and Applications STATISTICS & PROBABILITY-
CiteScore
1.20
自引率
22.20%
发文量
31
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