Integral and geometrical means in the analytical evaluation of the BEM integrals for a 3D Laplace equation

被引：8
作者：
Jablonski, Pawel [1 ]
机构：
[1] Czestochowa Tech Univ, Fac Elect Engn, PL-42200 Czestochowa, Poland
来源：
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS | 2010年 / 34卷 / 03期
关键词：
Boundary element method; Analytical integration; Nearly singular integrals; Laplace equation; SINGULAR-INTEGRALS; FORMULATIONS; ELEMENTS;
D O I：
10.1016/j.enganabound.2009.10.002
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
By using integral theorems and geometrical interpretations, the analytical formulas for the coefficients occurring in boundary element method (BEM) equations for a 3D Laplace equation were found for arbitrary planar polygonal boundary elements with constant approximation. Closed forms for the gradients of the coefficients were also obtained. In addition, an analytical formula for planar triangular boundary elements with a linear approximation of potential was given. The formulas obtained are appropriate especially in singular and nearly singular cases. (C) 2009 Elsevier Ltd. All rights reserved.
引用
收藏
页码：264 / 273
页数：10
相关论文
共 50 条
[21]   A binary-tree subdivision method for evaluation of singular integrals with discontinuous kernel in 3D BEM [J].
Ju, Chuanming ;
Chen, Jiehao ;
Li, Ning ;
Du, Xianfeng .
ENGINEERING COMPUTATIONS, 2025, 42 (01) :301-336
[22]   Analytical removal of singularity and direct evaluation of singular integrals in 3-D elastoplastic finite deformation analysis by BEM [J].
Lu, Shan ;
Ye, Tian-Qi ;
Chen, Bai-Ping .
Acta Mechanica Solida Sinica, 1993, 6 (04) :387-399
[23]   The solution to an elliptic partial differential equation for facilitating exact volume integral transformation in the 3D BEM analysis [J].
Shiah, Y. C. ;
Li, Meng-Rong .
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2015, 54 :13-18
[24]   Analytical transformation of the volume integral in the boundary integral equation for 3D anisotropic elastostatics involving body force [J].
Shiah, Y. C. .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2014, 278 :404-422
[25]   Analytical expressions for singular integrals arising from the 3D Laplace and Stokes kernels when using constant or linear triangular and quadrilateral boundary elements [J].
Ravnik, Jure .
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2023, 154 :47-53
[26]   Use of the sinh transformation for evaluating 2D nearly singular integrals in 3D BEM [J].
XiaoChao Li ;
Yaoming Zhang ;
Yanpeng Gong ;
Yu Su ;
Xiaowei Gao .
Acta Mechanica, 2015, 226 :2873-2885
[27]   Use of the sinh transformation for evaluating 2D nearly singular integrals in 3D BEM [J].
Li, XiaoChao ;
Zhang, Yaoming ;
Gong, Yanpeng ;
Su, Yu ;
Gao, Xiaowei .
ACTA MECHANICA, 2015, 226 (09) :2873-2885
[28]   Vertex Singularities Associated with Conical Points for the 3D Laplace Equation [J].
Zaltzman, T. ;
Yosibash, Z. .
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2011, 27 (03) :662-679
[29]   A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains [J].
Ying, Lexing ;
Biros, George ;
Zorin, Denis .
JOURNAL OF COMPUTATIONAL PHYSICS, 2006, 219 (01) :247-275
[30]   Causality condition relevant functions-orientated analytical treatment on in 3D TD-BEM [J].
Lei, Weidong ;
Qin, Xiaofei ;
Li, Hongjun ;
Fan, Youhua .
APPLIED MATHEMATICS AND COMPUTATION, 2022, 427
12345