This study presents an adaptive binary-tree element subdivision method (BTSM) to evaluate the volume integrals with continuous or discontinuous kernels to facilitate automatic and high-quality patch generation. The BTSM, an essential technique implemented in boundary integral formulations, was proposed to guarantee a successful well-shaped element subdivision under any circumstances, improve integration accuracy, and reduce the sensitivity of integration calculation to element shape. In addition, the BTSM can be adopted to evaluate singular integrals and nearly singular integrals due to its high availability and reliability for arbitrary shape volume element subdivision. If the kernel function is discontinuous, a minority of sub-elements around the source or breakpoints need to be regenerated. The geometry-adaptive projection cavity construction algorithm and several comprehensive cavity projection techniques are implemented for facilitating patch generation. The improved cavity projection algorithms can unify the element segmentation to evaluate singular integrals and nearly singular integrals simultaneously. Numerical results demonstrate the efficiency and accuracy of the proposed method.

本研究提出了一种自适应二叉树元素细分方法 (BTSM) 来评估具有连续或不连续内核的体积积分，以促进自动和高质量的补丁生成。BTSM 是边界积分公式中实施的一项基本技术，旨在保证在任何情况下都能成功地进行形状良好的单元细分，提高积分精度，并降低积分计算对单元形状的敏感性。此外，由于BTSM对任意形状体积元细分的高可用性和可靠性，可用于评估奇异积分和近似奇异积分。如果核函数不连续，则需要重新生成源或断点周围的少数子元素。实现了几何自适应投影腔构造算法和几种综合腔投影技术，以促进补丁生成。改进后的腔体投影算法可以统一单元分割，同时计算奇异积分和近似奇异积分。数值结果证明了所提出方法的有效性和准确性。