A fast approach evaluating origin intensity factors on Neumann boundary in the singular boundary method

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements Pub Date : 2025-02-15 DOI:10.1016/j.enganabound.2025.106160

Weiwei Li, Chenchen Yang

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引用次数: 0

Abstract

This study introduces a rapid methodology based on recursive skeletonization factorization (RSF), for the determination of origin intensity factors (OIFs) at Neumann boundaries within the framework of the singular boundary method (SBM). The conventional formula for OIFs, which is derived using the subtracting and adding-back technique (SABT), is reformulated into a matrix-vector product representation. The components of the matrix consist of the fundamental solutions of the double-layer potential that adhere to the governing equations. Consequently, the RSF facilitates the implicit construction of a hierarchically generalized LU decomposition of the matrix, producing decomposition factors that allow for efficient multiplication with any vector. This innovative approach significantly reduces the computational cost associated with the calculation of OIFs, thereby meeting the demands of simulating large-scale problems. Numerical results demonstrate that this method is both accurate and stable, and it is applicable to a variety of problems characterized by irregular geometries.

查看原文本刊更多论文

奇异边界法中求解Neumann边界上原点强度因子的快速方法

本文介绍了一种基于递归骨架分解（RSF）的快速方法，用于在奇异边界法（SBM）框架内确定Neumann边界处的原点强度因子（oif）。使用减法和反加法技术（SABT）导出的传统oif公式被重新表述为矩阵-向量乘积表示。矩阵的组成部分由遵循控制方程的双层势的基本解组成。因此，RSF促进了矩阵的层次上广义LU分解的隐式构造，产生了允许与任何向量进行有效乘法的分解因子。这种创新的方法大大降低了与oif计算相关的计算成本，从而满足了模拟大规模问题的需求。数值结果表明，该方法精度高，稳定性好，适用于各种不规则几何问题。

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.