基于自适应单元细分法的高效高精度近奇异域积分计算  

Efficient and High Precision Nearly Singular Domain Integrals Calculation Based on Adaptive Element Subdivision Method

作　　者：王富顺 池宝涛 贾志超 郭前建[1] 袁伟 WANG Fushun;CHI Baotao;JIA Zhichao;GUO Qianjian;YUAN Wei(School of Mechanical Engineering,Shandong University of Technology,Zibo,Shandong 255000,China;Shandong Luoxiang Automobile Manufacturing Postdoctoral Research Institute,Linyi,Shandong 276211,China)

机构地区：[1]山东理工大学机械工程学院,山东淄博255000 [2]山东锣响汽车制造有限公司博士后工作站,山东临沂276211

出　　处：《计算物理》2023年第5期548-555,共8页Chinese Journal of Computational Physics

基　　金：国家自然科学基金(12202251,51805299);中国博士后科学基金面上项目(2021M702024,2022M712393);山东省教育厅青创人才引育计划项目;山东省重点研发计划项目(2019GGX104081,2019GGX104033);淄博市校城融合发展计划项目(2018ZBXC265);山东理工大学自主科研计划(4041-420047,9101-2222431)资助。

摘　　要：本文针对边界元法在计算薄型结构力学、裂纹扩展等物理问题时存在的积分难题,提出一种基于自适应单元细分法的高效高精度近奇异域积分计算方法,该方法基于二叉树数据结构的单元细分技术对体单元进行自适应细分,消除单元几何形状所引起的近奇异性,能直接用于计算连续核函数的近奇异域积分。针对间断核函数的近奇异域积分,在细分单元的基础上采用腔面重建算法和投影算法,重新构建源点附近的积分子单元。数值算例表明:本方法可采用较少的积分点得到准确结果,是处理近奇异域积分的一种有效方法。An adaptive and efficient element subdivision method for accurate evaluation of nearly singular domain integrals is presented,which is mainly applied to address the difficulties involved with thin-structure mechanics,crack propagation,etc,in the boundary integral formulations.Based on the binary-tree data structure,the reasonable integration result of different types of volume elements can be achieved by the adaptive subdivision algorithm.Combined with the cavity construction and projection algorithms,highquality regenerated patches around the source point can be obtained for evaluation of nearly singular integrals with discontinuous kernels.Compared to other methods,the proposed element subdivision method can obtain the accurate results with fewer integration nodes.Numerical results have been given to verify the effectiveness,feasibility and robustness of the illustrated integration schemes.

关 键 词：边界元法 近奇异积分 连续或间断核函数 自适应单元细分 

分 类 号：TP391.7[自动化与计算机技术—计算机应用技术]