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A mapping method for numerical evaluation of two-dimensional integrals with 1/r singularity

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Abstract

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.

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Authors and Affiliations

  1. Department of Theoretical and Applied Mechanics, Cornell University, Kimball Hall, 14853, Ithaca, USA

    Anantharaman Nagarajan & Subrata Mukherjee

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  1. Anantharaman Nagarajan
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  2. Subrata Mukherjee
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Communicated by S. N. Atluri, September 12, 1992

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Nagarajan, A., Mukherjee, S. A mapping method for numerical evaluation of two-dimensional integrals with 1/r singularity. Computational Mechanics 12, 19–26 (1993). https://doi.org/10.1007/BF00370482

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