An Exponentially Convergent Quadrature Method for Evaluating Convolutional Integrals

The Rao-Wilton-Glisson (RWG) and Schaubert-Wilton-Glisson (SWG) related convolutional integrals can be reduced to a summation of one dimensional (1D) integrals, which are prone to numerical errors when the observation points are in the vicinity of the sources. We propose that sinh transformations be used to improve the accuracy. A variety of numerical examples show that the relative errors of the proposed method drop exponentially with respect to the number of Gauss-Legendre quadrature points.