 
Summary: Electronic Transactions on Numerical Analysis.
Volume 17, pp. 133150, 2004.
Copyright © 2004, Kent State University.
ISSN 10689613.
ETNA
Kent State University
etna@mcs.kent.edu
QUADRATURE OF SINGULAR INTEGRANDS OVER SURFACES
KENDALL ATKINSON
¡
Abstract. Consider integration over a simple closed smooth surface in ¢¤£ , one that is homeomorphic to the
unit sphere, and suppose the integrand has a point singularity. We propose a numerical integration method based
on using transformations that lead to an integration problem over the unit sphere with an integrand that is much
smoother. At this point, the trapezoidal rule is applied to the spherical coordinate representation of the problem.
The method is simple to apply and it results in rapid convergence. The intended application is to the evaluation of
boundary integrals arising in boundary integral equation methods in potential theory and the radiosity equation.
Key words. spherical integration, singular integrand, boundary integral, trapezoidal rule.
AMS subject classifications. 65D32, 65B15.
1. Introduction. Consider the approximation of a surface integral
