An adaptive binary-tree subdivision method for evaluation of nearly singular integrals in 3D BEM

Abstract

Purpose

The purpose of this paper is to present an adaptive binary-tree element subdivision method (BTSM) for the evaluation of nearly singular integrals in three-dimensional boundary element method, which can facilitate automatic and high-quality patch generation.

Design/methodology/approach

In this method, the nearly singular element is split into two sub-elements. Each sub-element is then examined to determine if it is to be subdivided based on a specific subdivision criterion. The specific subdivision ensures that those sub-elements far from the source point are sparse. And then those sub-elements in close proximity to the source point are replaced by regular triangular elements.

Findings

With the proposed method, the sub-elements obtained are automatically refined as they approach the projection point, and they are “good” in shape and size for standard Gaussian quadrature. Thus, the proposed method can be used to evaluate nearly singular integrals accurately for cases of different element shapes and various locations of the source point.

Originality/value

Numerical examples for surface elements with various relative locations of the source point are presented. The results demonstrate that the proposed method has much better accuracy and robustness than some other methods.

Citation

Ju, C., Zhang, J., Zhong, Y., Du, X., Li, J. and Chi, B. (2023), "An adaptive binary-tree subdivision method for evaluation of nearly singular integrals in 3D BEM", Engineering Computations, Vol. 40 No. 3, pp. 718-733. https://doi.org/10.1108/EC-11-2022-0670