A new global and direct integral formulation for 2D potential problems

Chao Zhang; Zhuojia Fu; Yaoming Zhang

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A new global and direct integral formulation for 2D potential problems

机译：用于2D潜在问题的新全球和直接组成的制定

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摘要

A new global and direct integral formulation (GDIF) is presented for 2D potential problems. The 'global' and 'direct' mean that Gaussian quadrature can be applied directly to the entire body surface if its geometry description is mathematically available. This concept is simple and time-honored. The method has been long pursued by several researchers thanks to its accuracy and efficiency. However, the GDIF is based on the boundary integral equations (BIEs). The most crucial but difficult part in this method is to eliminate the singularities in BIEs, especially the source singularity. In this study, new non-singular boundary integral equations (NSBIEs) with indirect unknowns are developed in association with the average source technique without using the equi-potential method for source singularity. The integrands of all integrals in the NSBIEs are finite at any point on the body surface, which allows them to be considered as a normal function for computation. Based on this, with collocation points chosen in the NSBIEs being exactly the same as Gaussian points, an arbitrary order Gaussian quadrature can be directly applied to evaluate the integrals over the global elements. Three benchmark examples are tested to verify the efficiency and convergence of the proposed scheme.

机译：为2D潜在问题提供了新的全局和直接组成的制定（GDIF）。 “全局”和“直接”意味着如果在数学上可用的几何描述，高斯正交可以直接应用于整个车身表面。这个概念很简单又令人愉快。由于其准确性和效率，几位研究人员长期以来，该方法已经长期追求。然而，GDIF基于边界积分方程（偏见）。这种方法中最重要但困难的部分是消除偏见的奇点，尤其是源奇点。在本研究中，具有间接未知的新的非奇异边界积分方程（NSBIE）与平均源技术相关联，而不使用源奇异性的Equi-Polysit方法。 NSBIE中所有积分的整体在体表上的任何点都是有限的，这允许它们被认为是用于计算的正常功能。基于这一点，利用在NSBIE中选择的搭配点与高斯点完全相同，可以直接应用任意顺序高斯正交以评估全局元素上的积分。测试了三个基准示例以验证所提出的方案的效率和收敛性。

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来源
《Engineering analysis with boundary elements》 |2021年第4期|233-240|共8页
作者
Chao Zhang; Zhuojia Fu; Yaoming Zhang;
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作者单位

College of Mechanics and Materials Hohai University Nanjing Jiangsu 211100 China;

College of Mechanics and Materials Hohai University Nanjing Jiangsu 211100 China State Key Laboratory of Mechanics and Control of Mechanical Structures Nanjing University of Aeronautics & Astronautics Nanjing Jiangsu 210016 China;

Institute of Applied Mathematics Shandong University of Technology Zibo Shandong 255049 China;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Global element; Direct integration; Non-singular boundary integral equation; Potential problems;

机译：全球元素;直接整合;非奇异边界积分方程;潜在问题;

A new global and direct integral formulation for 2D potential problems

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