Adaptive Quadratures over Surfaces

Recently, the first author introduced a new approach for the numerical quadrature of surface integrals in the context of boundary element methods. The handling of singularities is an essential feature. It is assumed that a global parametrization P of the surface is given as a subroutine and that P is not accessible analytically. Of particular interest are parametrizations which are based on automatic triangulations of surfaces. The present paper improves and advances the method in various ways: The background is simplified and generalized, the parametrization is based on a recently developed efficient automatic triangulation of surfaces, an adaptive (recursive) quadrature method has been implemented which incorporates adaptive extrapolation steps. Several examples display the performance of the method. Codes (in C) can be obtained from the authors via e-mail.