Semi-analytic integration of hypersingular Galerkin BIEs for three-dimensional potential problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:231

Article

Fata, S. Nintcheu¹  Gray, L. J.¹ 

[1] Oak Ridge Natl Lab, Div Math & Comp Sci, Oak Ridge, TN 37831 USA

关键词: Analytic integration;    Galerkin approximation;    Singular integrals;    Hypersingular integrals;    Boundary element method;    Triangular boundary;    Potential theory;   

DOI  :  10.1016/j.cam.2009.04.003

来源: Elsevier

【 摘 要 】

An accurate and efficient semi-analytic integration technique is developed for three-dimensional hypersingular boundary integral equations of potential theory. Investigated in the context of a Galerkin approach, surface integrals are defined as limits to the boundary and linear surface elements are employed to approximate the geometry and field variables on the boundary. In the inner integration procedure, all singular and non-singular integrals over a triangular boundary element are expressed exactly as analytic formulae over the edges of the integration triangle. In the outer integration scheme, closed-form expressions are obtained for the coincident case, wherein the divergent terms are identified explicitly and are shown to cancel with corresponding terms from the edge-adjacent case. The remaining surface integrals, containing only weak singularities, are carried out successfully by use of standard numerical cubatures. Sample problems are included to illustrate the performance and validity of the proposed algorithm. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free