Semi-analytic treatment of nearly-singular Galerkin surface integrals

Journal Article · Fri Jan 01 04:00:00 EST 2010 · Applied Numerical Mathematics

DOI:https://doi.org/10.1016/j.apnum.2010.06.003· OSTI ID:986386

Nintcheu Fata, Sylvain ^[1]

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1. ORNL

On utilizing piecewise linear test and interpolation functions over flat triangles, three semi-analytic techniques for evaluating nearly-singular surface integrals of potential theory are developed and investigated in the context of a three-dimensional Galerkin approximation. In all procedures, the inner surface integral is calculated exactly via recursive expressions defined over the edges of the integration triangle. In addition, the proposed methods respectively employ a Duffy transformation, sinh transformations, and polynomial transformations to weaken or smooth out near singularities, followed by a standard product Gauss-Legendre quadrature rule to compute the outer boundary integral. Numerical experiments and comparisons of the proposed approaches are included to provide more insight into the performance of these techniques. Computational tests have demonstrated that the algorithm based on a Duffy transformation is the most efficient and effective method for dealing with nearly-singular as well as well-separated integrals.

• Research Organization: Oak Ridge National Laboratory (ORNL)
• Sponsoring Organization: SC USDOE - Office of Science (SC)
• DOE Contract Number: AC05-00OR22725
• OSTI ID: 986386
• Journal Information: Applied Numerical Mathematics, Journal Name: Applied Numerical Mathematics Journal Issue: 10 Vol. 60; ISSN 0168-9274
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
Boundary element method
Galerkin approximation
Hyper-singular integrals
INTERPOLATION
Nearly-singular integrals
PERFORMANCE
POLYNOMIALS
Potential theory
QUADRATURES
Singular integrals
TRANSFORMATIONS