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

IF 0.8 Q3 STATISTICS & PROBABILITY
I. Shalimova, K. Sabelfeld
{"title":"Development and implementation of branching random walk on spheres algorithms for solving the 2D elastostatics Lamé equation","authors":"I. Shalimova, K. Sabelfeld","doi":"10.1515/mcma-2022-2131","DOIUrl":null,"url":null,"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.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Monte Carlo Methods and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/mcma-2022-2131","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
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.
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。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
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
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信