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.

提出了一种新的基于二叉树的元素细分方法，用于评价BEM中的奇异域积分。在本文中，这种元素细分技术称为二叉树细分方法（BTSM），它适用于具有任意源点位置的任意形状的线性和弯曲体素元素。与传统的细分方法（CSM）相比，BTSM的显着优势在于它可以处理具有连续或不连续核的奇异域积分，并且即使元素变形也可以提高积分的准确性。凭借独特的功能，即单个二叉树数据结构可以有效地处理体积元素细分，BTSM在包含体积积分的边界积分方程的制定中灵活而方便。此外，对于具有不连续核的体积积分，提出了一种基于牛顿迭代的改进的通用投影算法，用于曲面边界匹配。实验结果表明，体积元素始终由BTSM完全自动化地细分，并且在任何情况下都可以保证高质量的补丁生成。给出了几个例子来验证所提方法的有效性，鲁棒性和准确性。实验结果表明，体积元素始终由BTSM完全自动化地细分，并且在任何情况下都可以保证高质量的补丁生成。给出了几个例子来验证所提方法的有效性，鲁棒性和准确性。实验结果表明，体积元素始终由BTSM完全自动化地细分，并且在任何情况下都可以保证高质量的补丁生成。给出了几个例子来验证所提方法的有效性，鲁棒性和准确性。