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Article
Publication date: 30 May 2023

Chuanming Ju, J. Zhang, Yudong Zhong, Xianfeng Du, Jun Li and Baotao Chi

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…

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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.

Details

Engineering Computations, vol. 40 no. 3
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 8 January 2020

Jianming Zhang, Chuanming Ju and Baotao Chi

The purpose of this paper is to present a fast algorithm for the adaptive discretization of three-dimensional parametric curves.

87

Abstract

Purpose

The purpose of this paper is to present a fast algorithm for the adaptive discretization of three-dimensional parametric curves.

Design/methodology/approach

The proposed algorithm computes the parametric increments of all segments to obtain the parametric coordinates of all discrete nodes. This process is recursively applied until the optimal discretization of curves is obtained. The parametric increment of a segment is inversely proportional to the number of sub-segments, which can be subdivided, and the sum of parametric increments of all segments is constant. Thus, a new expression for parametric increment of a segment can be obtained. In addition, the number of sub-segments, which a segment can be subdivided is calculated approximately, thus avoiding Gaussian integration.

Findings

The proposed method can use less CPU time to perform the optimal discretization of three-dimensional curves. The results of curves discretization can also meet requirements for mesh generation used in the preprocessing of numerical simulation.

Originality/value

Several numerical examples presented have verified the robustness and efficiency of the proposed algorithm. Compared with the conventional algorithm, the more complex the model, the more time the algorithm saves in the process of curve discretization.

Details

Engineering Computations, vol. 37 no. 5
Type: Research Article
ISSN: 0264-4401

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