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A mapping method for numerical evaluation of two-dimensional integrals with \(1/r\) singularity. (English) Zbl 0776.73073
Summary: Singular integrals occur commonly in applications of the boundary element method (BEM). A simple mapping method is presented here for the numerical evaluation of two-dimensional integrals in which the integrands, at worst, are \(O(1/r)\) \((r\) being the distance from a source to a field point). This mapping transforms such integrals over general curved triangles into regular 2-D integrals. Over flat and curved quadratic triangles, regular line integrals are obtained, and these can be easily evaluated by standard Gaussian quadrature. Numerical tests on some typical singular integrals, encountered in BEM applications, demonstrate the accuracy and efficacy of the method.

MSC:
74S15 Boundary element methods applied to problems in solid mechanics
65D30 Numerical integration
Software:
MACSYMA
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