基于特征分区的奇异域积分单元细分法

兰州理工大学学报 ›› 2024, Vol. 50 ›› Issue (3): 143-150.

基于特征分区的奇异域积分单元细分法

贾志超, 王富顺, 郭前建^*, 袁伟, 魏峥

山东理工大学机械工程学院, 山东淄博 255000

收稿日期:2022-09-07 出版日期:2024-06-28 发布日期:2024-07-02
通讯作者: 郭前建(1979-),男,山东济南人,教授,博导.Email:guoqj_xs@163.com
基金资助:
国家自然科学基金(12202251,12172126,11972010),中国博士后科学基金(2021M702024,2022M712393),教育部产学合作协同育人项目(220606517023742),山东省教育厅青创人才引育计划项目,山东省自然科学基金(ZR2022ME122,ZR2022QA072),山东省重点研发计划项目(2019GGX104081,2019GGX104033)

An element subdivision method for singular domain integrals based on feature partition technique

JIA Zhi-chao, WANG Fu-shun, GUO Qian-jian, YUAN Wei, WEI Zheng

School of Mechanical Engineering, Shandong University of Technology, Zibo 255000, China

Received:2022-09-07 Online:2024-06-28 Published:2024-07-02

摘要/Abstract

摘要： 针对传统方法难以解决积分方程中的奇异性问题,提出一种基于特征分区的奇异域积分单元细分法,该方法基于体二叉树数据结构对不同类型体单元自适应细分,能精确计算任意源点位置的三维奇异积分,消除积分的奇异性.在笛卡尔坐标系下,通过在源点构建包围盒对体单元特征分区,将体单元划分为腔面投影区域和单元细分区域,依照细分准则对单元细分区域递归细分,采用腔面重构算法和投影算法,重新在源点附近生成高质量的积分子单元.数值算例表明,该方法的积分计算精度、稳定性优于传统单元细分方法.

关键词: 边界元法, 奇异积分, 体二叉树, 特征分区, 单元细分

Abstract: Aiming at the difficulty of solving the singular integrals by traditional algorithms, an adaptive element subdivision method for singular domain integrals based on feature partition technique is presented. The element subdivision method is based on binary-tree data structure, which is applicable to arbitrary shape volume elements with arbitrary locations of the source point. By using the techniques of the binary-tree subdivision scheme, construction of the projection cavities and the cavity projection algorithm, well-shaped patches can be obtained for singular domain integrals. Numerical examples demonstrate that the proposed method has much better accuracy and efficiency than conventional methods.

Key words: boundary element method, singular integrals, volume binary tree, feature partition, element subdivision

中图分类号:

O241.8

贾志超, 王富顺, 郭前建, 袁伟, 魏峥. 基于特征分区的奇异域积分单元细分法[J]. 兰州理工大学学报, 2024, 50(3): 143-150.

JIA Zhi-chao, WANG Fu-shun, GUO Qian-jian, YUAN Wei, WEI Zheng. An element subdivision method for singular domain integrals based on feature partition technique[J]. Journal of Lanzhou University of Technology, 2024, 50(3): 143-150.

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