Semi-Analytic Integration of Hypersingular Galerkin BIEs for 3D Potential Problems

Journal Article · Thu Jan 01 04:00:00 EST 2009 · Journal of Computational and Applied Mathematics

DOI:https://doi.org/10.1016/j.cam.2009.04.003· OSTI ID:963915

Nintcheu Fata, Sylvain ^[1]; Gray, Leonard J ^[1]

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1. ORNL

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.

• Research Organization: Oak Ridge National Laboratory (ORNL)
• Sponsoring Organization: SC USDOE - Office of Science (SC)
• DOE Contract Number: AC05-00OR22725
• OSTI ID: 963915
• Journal Information: Journal of Computational and Applied Mathematics, Journal Name: Journal of Computational and Applied Mathematics Journal Issue: 2 Vol. 231; ISSN JCAMDI; ISSN 0377-0427
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
99 GENERAL AND MISCELLANEOUS
Analytic integration
BOUNDARY-VALUE PROBLEMS
Galerkin approximation
INTEGRAL EQUATIONS
ITERATIVE METHODS
PERFORMANCE
THREE-DIMENSIONAL CALCULATIONS
boundary element method
hypersingular integrals
potential theory
singular integrals
triangular boundary