电子学报 ›› 2018, Vol. 46 ›› Issue (2): 456-463.DOI: 10.3969/j.issn.0372-2112.2018.02.027

• 学术论文 • 上一篇    下一篇

二维静电场问题的面片拼接等几何分析方法研究

王峰1,2, 周宜红1,2, 林皋3, 赵春菊1,2, 何卫平1,2   

  1. 1. 三峡大学水利与环境学院, 湖北宜昌 443002;
    2. 三峡大学湖北省水电工程施工与管理重点实验室, 湖北宜昌 443002;
    3. 大连理工大学水利工程学院, 辽宁大连 116024
  • 收稿日期:2016-08-14 修回日期:2017-02-12 出版日期:2018-02-25 发布日期:2018-02-25
  • 作者简介:王峰,男,1987年5月出生,山东莱阳人,博士、讲师.主要从事水工结构和电磁学数值仿真研究.E-mail:wangfeng@mail.dlut.edu.cn;周宜红,男,1966年9月出生,湖北枝江人,博士、教授、博士生导师.主要从事水利工程施工与组织管理方面研究.E-mail:zyhwhu2003@163.com
  • 基金资助:
    国家自然科学基金(No.51479103);国家自然科学基金青年科学基金(No.51109134);中国博士后科学基金(No.2013T60283);湖北省水电工程施工与管理重点实验室开放基金(No.2016KSD12)

Isogeometric Analysis for the Two-Dimensional Electrostatic Field Problem Based on the NURBS Patch Splicing Technique

WANG Feng1,2, ZHOU Yi-hong1,2, LIN Gao3, ZHAO Chun-ju1,2, HE Wei-ping1,2   

  1. 1. College of Hydraulic & Environmental Engineering, China Three Gorges University, Yichang, Hubei 443002, China;
    2. Hubei Key Laboratory of Construction and Management in Hydropower Engineering, China Three Gorges University, Yichang, Hubei 443002, China;
    3. School of Hydraulic Engineering, Dalian University of Technology, Dalian, Liaoning 116024, China
  • Received:2016-08-14 Revised:2017-02-12 Online:2018-02-25 Published:2018-02-25

摘要: 等几何分析方法在求解静电场问题时,实现了几何模型和计算模型的统一以及自适应网格划分过程,然而受制于单个NURBS曲面片拓扑的局限性,单片等几何分析方法难以处理含角点非凸几何域静电场及多媒质静电场问题.本文基于面片拼接技术,将单片等几何分析方法扩展到多片,并用来求解二维含角点非凸几何域静电场及多媒质静电场问题,NURBS曲面片拼接处的控制点和网格细分前后要求必须匹配.由于NURBS基函数不满足插值性,在非齐次Dirichlet边界条件的处理上本文采用Lagrange乘子法进行处理.数值算例表明:修正后的多面片等几何分析方法可以很好地处理二维含角点非凸几何域静电场及多媒质静电场问题,且相比传统的有限元法,该方法具有自由度消耗小、精度高、收敛速度快等优点.

关键词: 静电场, 等几何分析, NURBS, 面片拼接

Abstract: Isogeometric analysis (IGA) based on the non-uniform rational B-splines (NURBS) realizes the unification of the geometric model,the computational model and adaptive mesh generation process in solving electrostatic problems.However,IGA based on one single NURBS patch is difficult to deal with the non-convex electrostatic field with corners and inhomogeneous electrostatic field because of limitation of the NURBS patch topology.In this paper,IGA based on the patch splicing is used to solve two-dimensional electrostatic problems of this kind while IGA extends from one single NURBS patch to multipatches.The control points and meshes of different patches must coincide on the interface,even after refinement.Due to lack of interpolation properties for the NURBS basis functions,Lagrange multiplier method is adopted to deal with non-homogeneous Dirichlet boundary conditions.Numerical examples are presented to show that modified multi-patch IGA can solve two-dimensional electrostatic problems of this kind well and possess the advantages of better convergence on a per-degree-of-freedom and high accuracy.

Key words: electrostatic field, isogeometric analysis, NURBS, patch splicing

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