Calculation of singular integrals on elements of three-dimensional problems by triple-reciprocity boundary element method

Abstract

Accurate numerical evaluation of integrals arising in the boundary element method is fundamental to achieving useful results via this solution technique. In this paper, a new technique is considered to evaluate the weak singular integrals that arise in the solution of three-dimensional Laplace's equation. This new application of the triple-reciprocity boundary element method is proposed for the calculation of singular integrals. A formulation of the boundary element method is utilized, and a method for the direct numerical integration of the two-dimensional surface using a two-dimensional interpolation method is proposed. In numerical integral calculation, the numerical integration of arbitrary shape is possible, and integration in the case of two-dimensional integration is approximately changed into a one-dimensional integration by using the Green's second identity. In the introduced line integral, there is no singularity. To evaluate the efficiency of this method, several numerical examples are given.