A binary-tree element subdivision method for evaluation of singular domain integrals with continuous or discontinuous kernel

Abstract

A novel element subdivision method based on the binary tree has been proposed for evaluation of singular domain integrals in BEM. In this paper, this element subdivision technique is called the Binary-Tree Subdivision Method (BTSM), which is applicable to arbitrary shape linear and curved volume elements with arbitrary locations of the source point. Compared to the Conventional Subdivision Method (CSM), a significant advantage of the BTSM is that it can handle singular domain integrals with continuous or discontinuous kernel and improve the accuracy of integration even with distorted elements. With the distinct feature that a single binary-tree data structure can efficiently handle volume element subdivision, it is flexible and convenient for the BTSM to be implemented in the formulation of the boundary integral equation which contains volume integrals. In addition, for the volume integrals with discontinuous kernel, an improved general projection algorithm based on Newton iteration has been proposed for curved boundary matching. Experiment results have demonstrated that the volume element is always subdivided by the BTSM in a fully automated manner and high-quality patch generation can be guaranteed in any situation. Several examples are given to verify the validity, robustness and accuracy of the proposed method.