A new method for numerical evaluation of nearly singular integrals over high-order geometry elements in 3D BEM

被引：22

作者：

Zhang, Yaoming ^{[1
,2
]}

Li, Xiaochao ^{[3
]}

Sladek, Vladimir ^{[4
]}

Sladek, Jan ^{[4
]}

Gao, Xiaowei ^{[2
]}

机构：

[1] Shandong Univ Technol, Inst Appl Math, Zibo 255049, Peoples R China

[2] Dalian Univ Technol, State Key Lab Struct Anal Ind Equipment, Dalian 116024, Peoples R China

[3] Beijing Inst Technol, Sch Aerosp Engn, Dept Mech, Beijing 100081, Peoples R China

[4] Slovak Acad Sci, Inst Construct & Architecture, Bratislava 84503, Slovakia

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2015年 / 277卷

关键词：

BEM; Nearly singular integrals; High-order geometry elements; Transformation; 3D potential problems; PRINCIPAL VALUE INTEGRALS; GENERAL ALGORITHM; BOUNDARY INTEGRALS; DISTANCE TRANSFORMATION; SINH TRANSFORMATION; THIN STRUCTURES; REGULARIZATION; FORMULATION; FIELD;

D O I：

10.1016/j.cam.2014.08.027

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This work presents a new method for numerical computation of the two-dimensional nearly singular integrals by using the eight-node second-order quadrilateral surface elements in 3D BEM. A new indirect regularized boundary element formulation excluding the CPV (Cauchy Principal Value) and HFP (Hadamard-Finite-Part) integrals is proposed. Based on this, a new approximation formula of the distance from the fixed calculation point to a generic point of the aforementioned surface geometry elements is developed firstly, and then the exponential transformation, which has been widely employed in 2D BEM, is extended to 3D BEM to remove the near singularities of integrands for considered integrals. Several numerical examples are given to verify the high efficiency and the stability of the proposed scheme. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：57 / 72

页数：16

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