A general algorithm for evaluating nearly singular integrals in anisotropic three-dimensional boundary element analysis

Abstract

This paper presents a new general method for the evaluation of nearly singular boundary element integrals arising in anisotropic three-dimensional (3D) boundary element analysis. It is shown that the original nearly singular integrals can be transformed into, using a sinh function, an element-by-element sum of regular integrals, each one expressed in terms of intrinsic (local) coordinates. As a consequence, the actual computation can be performed by using standard n×n Gaussian quadrature and the procedure can be easily included in any existing computer code. This new method has full generality and, therefore, can be applied to a wide class of integrals. The numerical results demonstrate the accuracy and efficiency of the method, along with its insensitivity to the location of the nearly singular points. It is shown that several orders of magnitude improvement in relative errors can be obtained using this transformation when compared to a straightforward implementation of Gaussian quadrature.