Method of fundamental solutions formulations for biharmonic problems

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements Pub Date : 2025-03-06 DOI:10.1016/j.enganabound.2025.106180

Csaba Gáspár , Andreas Karageorghis

引用次数: 0

Abstract

We consider various method of fundamental solution (MFS) formulations for the numerical solution of two-dimensional boundary value problems (BVPs) governed by the homogeneous biharmonic equation. The motivation for employing the proposed techniques comes from the corresponding boundary integral representations. These are carefully analyzed in the case the domain of the BVP under consideration is a disk. The results of this analysis detect a potentially troublesome case in one of the proposed MFS approaches. Numerical results confirm the analytical findings for more general domains.

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双调和问题的基本解公式方法

本文考虑了齐次双调和方程下二维边值问题数值解的各种基本解（MFS）公式。采用所提出的技术的动机来自于相应的边界积分表示。在考虑的BVP域是磁盘的情况下，对这些进行仔细分析。这一分析的结果发现了MFS方法中一个潜在的麻烦情况。数值结果证实了更一般的分析结果。

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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来源期刊

Engineering Analysis with Boundary Elements 工程技术-工程：综合

CiteScore

5.50

自引率

18.20%

发文量

368

审稿时长

56 days

期刊介绍： This journal is specifically dedicated to the dissemination of the latest developments of new engineering analysis techniques using boundary elements and other mesh reduction methods. Boundary element (BEM) and mesh reduction methods (MRM) are very active areas of research with the techniques being applied to solve increasingly complex problems. The journal stresses the importance of these applications as well as their computational aspects, reliability and robustness. The main criteria for publication will be the originality of the work being reported, its potential usefulness and applications of the methods to new fields. In addition to regular issues, the journal publishes a series of special issues dealing with specific areas of current research. The journal has, for many years, provided a channel of communication between academics and industrial researchers working in mesh reduction methods Fields Covered: • Boundary Element Methods (BEM) • Mesh Reduction Methods (MRM) • Meshless Methods • Integral Equations • Applications of BEM/MRM in Engineering • Numerical Methods related to BEM/MRM • Computational Techniques • Combination of Different Methods • Advanced Formulations.