Stochastic Simulation Algorithm for Solving the System of Lame Equations for Two- and Three-Dimensional Domains by Combining the Slobodianskii Representation, the Method of Fundamental Solutions and a Stochastic Projection Method
{"title":"Stochastic Simulation Algorithm for Solving the System of Lame Equations for Two- and Three-Dimensional Domains by Combining the Slobodianskii Representation, the Method of Fundamental Solutions and a Stochastic Projection Method","authors":"K. K. Sabelfeld, D. D. Smirnov","doi":"10.1134/s1995423924020095","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, a new stochastic algorithm for solving the system of Lame equations based on the Slobodianskii representation is proposed, in which the recovery of boundary conditions for the harmonic functions involved is carried out implicitly using the method of fundamental solutions, while the unknown coefficients in this method are calculated using a stochastic projection method. Results of numerical experiments for several examples of two- and three-dimensional boundary value problems are presented, which demonstrate the high efficiency of the proposed method.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"66 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Numerical Analysis and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1995423924020095","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
In this paper, a new stochastic algorithm for solving the system of Lame equations based on the Slobodianskii representation is proposed, in which the recovery of boundary conditions for the harmonic functions involved is carried out implicitly using the method of fundamental solutions, while the unknown coefficients in this method are calculated using a stochastic projection method. Results of numerical experiments for several examples of two- and three-dimensional boundary value problems are presented, which demonstrate the high efficiency of the proposed method.
期刊介绍：
Numerical Analysis and Applications is the translation of Russian periodical Sibirskii Zhurnal Vychislitel’noi Matematiki (Siberian Journal of Numerical Mathematics) published by the Siberian Branch of the Russian Academy of Sciences Publishing House since 1998.
The aim of this journal is to demonstrate, in concentrated form, to the Russian and International Mathematical Community the latest and most important investigations of Siberian numerical mathematicians in various scientific and engineering fields.
The journal deals with the following topics: Theory and practice of computational methods, mathematical physics, and other applied fields; Mathematical models of elasticity theory, hydrodynamics, gas dynamics, and geophysics; Parallelizing of algorithms; Models and methods of bioinformatics.
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