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

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 twodimensional 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.

Automated summary

This paper introduces a new technique based on the boundary element method for evaluating weak singular integrals in the solution of the three-dimensional Laplace's equation. The method utilizes the formulation of the boundary element method and a two-dimensional interpolation method for direct numerical integration of arbitrary shape surfaces. It also uses Green's second identity to transform two-dimensional integration into one-dimensional integration. Numerical examples are provided to demonstrate the efficiency of the proposed method.