Volume 17, pp. 133-150, 2004.
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.
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Key words
spherical integration, singular integrand, boundary integral, trapezoidal rule.
AMS subject classifications
65D32, 65B15.
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