A binary-tree subdivision method for evaluation of singular integrals in 3D BEM

Abstract

A binary-tree subdivision method for evaluation of singular integrals in three-dimensional (3D) boundary element method (BEM) is presented in this paper. Element subdivision is one of the most widely used methods for evaluating singular integrals. In the traditional subdivision method, the sub-elements are obtained by simply connecting the source point with each vertex of the element and thus the integral accuracy is easily affected by the shape of the element and the location of the source point. The Spherical Element Subdivision Method can be used to evaluate singular integrals accurately and efficiently for cases of arbitrary element shape and arbitrary location of the source point. However, this method does not guarantee appropriate element subdivision. Therefore, in this paper, we present a new element subdivision method based on a binary-tree approach. This subdivision algorithm is more convenient to implement and can guarantee the convergence of the iterative subdivision based on a given terminating condition. Numerical examples for planar and curved surface elements with various relative locations of the source point are presented. The results demonstrate that the binary-tree subdivision method can provide much better accuracy and efficiency with fewer Gaussian points than the conventional subdivision method.