An advanced fast multipole BEM for analyzing 2D heat conduction problems in multi-notched structures

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements Pub Date : 2024-10-19 DOI:10.1016/j.enganabound.2024.105995

Bin Hu , Cong Li , Zhongrong Niu , Lei Chen , Shijie Tang

引用次数: 0

Abstract

A new fast multipole boundary element method (FMBEM) is developed for heat conduction in multi-notched structures. To address the heat flux singularity occurring at the tips of cracks or sharp notches, a novel variable-order asymptotic element (VAE) is proposed. The VAE offers the flexibility to represent various singular orders through a simple adjustment of the exponent, and it is designed to be compatible with conventional elements, whether they are discontinuous or continuous. Subsequently, the VAE is integrated into the FMBEM framework, and several algorithms are established to deal with the singularity problems of boundary integrals on the VAE. Compared to the conventional FMBEM with quadratic elements, the present method achieves more precise results with a very low computational cost, which proves to be accurate and efficient for heat analysis of porous structures containing non-conductive cracks and polygonal pores.

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用于分析多缺口结构中二维热传导问题的先进快速多极 BEM

针对多缺口结构中的热传导问题开发了一种新的快速多极边界元法（FMBEM）。针对裂缝或尖锐缺口顶端出现的热通量奇异性，提出了一种新型变阶渐近元素（VAE）。通过简单调整指数，VAE 可以灵活地表示各种奇异阶数，其设计与传统元素兼容，无论是非连续元素还是连续元素。随后，VAE 被集成到 FMBEM 框架中，并建立了几种算法来处理 VAE 上边界积分的奇异性问题。与使用二次元素的传统 FMBEM 相比，本方法以极低的计算成本获得了更精确的结果，证明了它在包含非导电裂缝和多边形孔隙的多孔结构的热分析中的精确性和高效性。

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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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.