基于等几何分析的边界元法求解二维Laplace方程  

Isogeometric boundary element analysis for 2D Laplace equations

作　　者：韩少燕 姜人伟 高汝鑫 王攀 HAN Shao-yan;JIANG Ren-wei;GAO Ru-xin;WANG Pan(Department of Mechanical Engineering,Xi’an Jiaotong University City College,Xi’an 710018,China;Beijing Institute of Astronautical Systems Engineering,Beijing 100076,China;Institute of Advanced Structure Technology,Beijing Institute of Technology,Beijing 100081,China)

机构地区：[1]西安交通大学城市学院机械工程系,西安710018 [2]北京宇航系统工程研究所,北京100076 [3]北京理工大学先进结构技术研究院,北京100081

出　　处：《计算力学学报》2023年第1期105-110,共6页Chinese Journal of Computational Mechanics

基　　金：中国博士后科学基金(面上项目)(2021M690403)。

摘　　要：针对二维Laplace问题,提出了基于非均匀有理B样条的等几何边界单元法(IGABEM),并利用径向积分法来处理奇异积分。该方法实现了几何与求解域的无缝融合,不仅实现了求解域与几何的完美匹配,而且节约了前处理时间。该方法可以很容易地实现模型的细分,并且在仅增加少量自由度的情况下获得更高的精度。数值算例表明,该方法能够有效地求解二维Laplace方程,且具有非常好的计算精度。In this article, an isometric boundary element method(IGABEM) based on nonuniform rational B-splines was proposed for two-dimensional Laplace problems, and the radial integral method was used to deal with singular integrals.This method not only realizes the seamless fusion of geometry and solution domain, but also saves the pre-processing time.This method can easily subdivide the model and obtain higher accuracy with only a few degrees of freedom added.Numerical examples show that this method can effectively solve the two-dimensional Laplace equation and has a very good computational accuracy.

关 键 词：等几何分析 边界单元法 径向积分法 LAPLACE方程 

分 类 号：O302[理学—力学]