结合斯洛博迪安斯基表示法、基本解法和随机投影法求解二维和三维域拉姆方程组的随机模拟算法

IF 0.4 Q4 MATHEMATICS, APPLIED Numerical Analysis and Applications Pub Date : 2024-05-28 DOI:10.1134/s1995423924020095

K. K. Sabelfeld, D. D. Smirnov

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引用次数: 0

摘要

摘要本文提出了一种基于 Slobodianskii 表示法求解 Lame 方程系统的新随机算法，其中利用基解法隐式地恢复所涉及谐函数的边界条件，而该方法中的未知系数则利用随机投影法计算。文中给出了几个二维和三维边界值问题实例的数值实验结果，证明了所提方法的高效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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

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.

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来源期刊

Numerical Analysis and Applications MATHEMATICS, APPLIED-

CiteScore

1.00

自引率

0.00%

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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.