Development and implementation of branching random walk on spheres algorithms for solving the 2D elastostatics Lamé equation

IF 0.8 Q3 STATISTICS & PROBABILITY Monte Carlo Methods and Applications Pub Date : 2023-01-10 DOI:10.1515/mcma-2022-2131
I. Shalimova, K. Sabelfeld
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引用次数: 1

Abstract

Abstract In this paper, we address a long-standing open problem in stochastic simulation: construction of a random walk on spheres (RWS) algorithm for solving a system of elasticity equations, known as the Lamé equation. Many attempts to generalize the classic probabilistic representations like the Kac formula for parabolic and scalar elliptic equations failed. A different approach based on a branching random walk on spheres (BRWS) introduced in our paper of 1995 [K. K. Sabelfeld and D. Talay, Integral formulation of the boundary value problems and the method of random walk on spheres, Monte Carlo Methods Appl. 1 1995, 1, 1–34] made little progress in solving this problem. In the present study, we further improve the BRWS algorithm by a special implementation of a branching anisotropic random walk on spheres process.
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求解二维弹性静力学lam方程的球上分支随机行走算法的开发与实现
摘要在本文中,我们解决了随机模拟中一个长期存在的开放问题:构造求解弹性方程组(即Lamé方程)的随机球上行走(RWS)算法。许多推广经典概率表示的尝试,如抛物型和标量椭圆方程的Kac公式,都失败了。我们在1995年的论文[K.K.Sabelfeld和D.Talay,边值问题的积分公式和球上随机行走方法,蒙特卡罗方法应用1 1995,1,1–34]中介绍了一种基于分支随机行走(BRWS)的不同方法,在解决这个问题方面进展甚微。在本研究中,我们通过一个特殊的分支各向异性球体随机行走过程来进一步改进BRWS算法。
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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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