A general algorithm for the numerical evaluation of nearly singular integrals on 3D boundary element

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:235

Article

Qin, Xianyun¹  Zhang, Jianming¹  Xie, Guizhong¹  Zhou, Fenglin¹  Li, Guanyao¹ 

[1] Hunan Univ, Coll Mech & Vehicle Engn, State Key Lab Adv Design & Mfg Vehicle Body, Changsha 410082, Hunan, Peoples R China

关键词: Nearly singular integrals;    Numerical integration;    Boundary integral equations;    Distance transformation technique;   

DOI  :  10.1016/j.cam.2011.03.012

来源: Elsevier

【 摘 要 】

A general numerical method is proposed to compute nearly singular integrals arising in the boundary integral equations (BIEs). The method provides a new implementation of the conventional distance transformation technique to make the result stable and accurate no matter where the projection point is located. The distance functions are redefined in two local coordinate systems. A new system denoted as (alpha, beta) is introduced here firstly. Its implementation is simpler than that of the polar system and it also performs efficiently. Then a new distance transformation is developed to remove or weaken the near singularities. To perform integration on irregular elements, an adaptive integration scheme is applied. Numerical examples are presented for both planar and curved surface elements. The results demonstrate that our method can provide accurate results even when the source point is very close to the integration element, and can keep reasonable accuracy on very irregular elements. Furthermore, the accuracy of our method is much less sensitive to the position of the projection point than the conventional method. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free