Fast computation of Sommerfeld integral tails via direct integration based on double exponential type quadrature formulas

A direct integration algorithm, based on double exponential-type quadrature rules, is presented for the efficient computation of the Sommerfeld integral tails, arising in the evaluation of multilayered Green's functions. The proposed scheme maintains the error controllable nature of the so-called partition-extrapolation methods, often used to tackle this problem, whereas it requires substantially reduced computational time. Moreover, the proposed method is very easy to implement, since the associated weights and abscissas can be precomputed. The overall behavior of the proposed method both in terms of accuracy and efficiency is demonstrated through a series of representative numerical experiments, where compared with one of the most proven methods available in the literature

On the evaluation of hyper-singular double normal derivative kernels in surface integral equation methods

A stable and efficient numerical scheme for the evaluation of surface integrals with 1/R-3-type singularities is presented. The method is based on the combination of the direct evaluation method and the singularity subtraction technique. The proposed method allows robust numerical evaluation of integral operators containing hyper-singular double normal derivative kernels in the cases where the integral equations are discretized with Galerkin's type techniques. (C) 2012 Elsevier Ltd. All rights reserved