二维静电场问题的面片拼接等几何分析方法研究

doi:10.3969/j.issn.0372-2112.2018.02.027

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

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. 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
- 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 Feng^1,2, ZHOU Yi-hong^1,2, LIN Gao³, ZHAO Chun-ju^1,2, HE Wei-ping^1,2

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/Abstract

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

中图分类号:

TM151

王峰, 周宜红, 林皋, 赵春菊, 何卫平. 二维静电场问题的面片拼接等几何分析方法研究[J]. 电子学报, 2018, 46(2): 456-463.

WANG Feng, ZHOU Yi-hong, LIN Gao, ZHAO Chun-ju, HE Wei-ping. Isogeometric Analysis for the Two-Dimensional Electrostatic Field Problem Based on the NURBS Patch Splicing Technique[J]. Acta Electronica Sinica, 2018, 46(2): 456-463.

参考文献

[1] Taflove A. Computational Electromagnetics:The Finite-Difference Time-Domain Method[M]. London:Artech House Publishers,2000.
[2] Yee K S. Numerical solution of initial boundary value prob-lems involving Maxwell's equations in isotropic media[J]. IEEE Trans Antennas and Propagation,1966,14:302-307.
[3] 王涛. 电磁场计算中的时域有限差分法的研究[D]. 长春:吉林大学,2005. WANG Tao. Investigation of the FDTD method for electro-magnetic field[D]. Changchun:Jilin University,2005. (in Chinese)
[4] Harrington R F,Harrington J L. Field Computation by Mo-ment Methods[M]. New York:Macmilan Press,1968.
[5] Jin J M. The Finite Method in Electromagnetics[M]. New York:JohnWiley&Sons,2002.
[6] Zienkiewicz O C,Cheung Y K. Finite elements in the solu-tion of field problems[J]. The Engineer, 1965, 24:507-510.
[7] 彭玉华,董晓龙. 小波变换在电磁场数值计算中的应用[J]. 电子学报,1996,24(12):46-52. PENG Yu-hua,DONG Xiao-long. Applications of wavelet transform in electromagnetic numerical computations[J]. Acta Electronica Sinica,1996,24(12):46-52. (in Chi-nese)
[8] 张勇. 计算电磁学的无单元方法研究[D]. 武汉:华中科技大学,2006. ZHANG Yong. Meshless method for electromagnetic prob-lems[D]. Wuhan:Huazhong University of Science and Technology,2006. (in Chinese)
[9] 张淮清. 电磁场计算中的径向基函数无网格法研究[D]. 重庆:重庆大学,2008. ZHANG Huai-qing. Research on radial basis function meshless method in numerical computation of electromag-netic field[D]. Chongqing:Chongqing University, 2008. (in Chinese)
[10] 赖生建. 计算电磁学中的径向基无网格法[D]. 重庆:重庆大学,2010. LAI Sheng-jian. Research on meshless method with radial basis functions in computational electromagnetics[D]. Chongqing:Chongqing University,2010. (in Chinese)
[11] Liu J,Lin G. A scaled boundary finite element method ap-plied to electrostatic problems[J]. Engineering Analysis with Boundary Elements,2012,36(12):1721-1732.
[12] 刘俊,林皋,王复明,等. 静电场分析的比例边界有限元法[J]. 大连理工大学学报,2011,51(5):731-736. LIU Jun,LIN Gao,WANG Fu-ming,et al. Scaled bounda-ry finite element method for analysis of electrostatic field problems[J]. Journal of Dalian University of Technolo-gy,2011,51(5):731-736. (in Chinese)
[13] Li Z C. Combined Methods for Elliptic Equations with Singularities, Interfaces and Infinities[M]. Dordrecht:Kluwer Academic Publishers,1998.
[14] Givoli D,Rivkin L,Keller J B. A finite element method for domains with corners[J]. International Journal for Nu-merical Methods in Engineering, 1992, 35(6):1329-1345.
[15] Jin J,Wu X. The singular finite element method for some elliptic boundary value problem with interface[J]. Journal of Computational and Applied Mathematics, 2004, 170(1):197-216.
[16] Hughes T J R,Cottrell J A,Bazilevs Y. Isogeometric anal-ysis:CAD, finite elements, NURBS, exact geometry and mesh refinement[J]. Computer Methods in Applied Me-chanics and Engineering,2005,194:4135-4195.
[17] Cottrell J A,Hughes T J R,Bazilevs Y. Isogeometric A-nalysis:Toward Integration of CAD and FEA[M]. Chich-ester:John Wiley & Sons,2009.
[18] 张勇,林皋,刘俊,等. 静电场问题的等几何分析方法[J]. 大连理工大学学报,2012,52(6):870-877. ZHANG Yong,LIN Gao,LIU Jun,et al. Isogeometric a-nalysis method for electrostatic field problems[J]. Journal of Dalian University of Technology,2012,52(6):870-877. (in Chinese)
[19] 张勇,林皋,刘俊,等. 等几何分析法应用于偏心柱面静电场问题[J]. 电波科学学报,2012,27(1):177-183. ZHANG Yong,LIN Gao,LIU Jun,et al. Isogeometric a-nalysis and its application to eccentric parallel cylinders e-lectrostatic problem[J]. Chinese Journal of Radio Sci-ence,2012,27(1):177-183. (in Chinese)
[20] 张勇,林皋,胡志强,等. 等几何分析方法求解静电场非齐次边值问题[J]. 电波科学学报,2012,27(5):997-1004. ZHANG Yong,LIN Gao,HU Zhi-qiang,et al. Isogeomet-ric analysis for electrostatic problem with inhomogeneous boundary conditions[J]. Chinese Journal of Radio Sci-ence,2012,27(5):997-1004. (in Chinese)
[21] 张勇. 等几何分析方法和比例边界等几何分析方法的研究及其工程应用[D]. 大连:大连理工大学,2013. ZHANG Yong. Research on isogeomtric analysis and scaled boundary isogeometric analysis and their applica-tions in engineering[D]. Dalian:Dalian University of Technology,2013. (in Chinese)
[22] 张亚辉,林家浩. 结构动力学基础[M]. 大连:大连理工大学出版社,2007. ZHANG Ya-hui,LIN Jia-hao. Fundamentals of structural dynamics[M]. Dalian:Dalian University of Technology Press,2007. (in Chinese)
[23] Nguyen V P,Kerfriden P,Brino M,et al. Nitsche's method for two and three dimensional NURBS patch coupling[J]. Computational Mechanics, 2014, 53(6):1163-1182.
[24] Kapl M,Vitrih V,Jüttler B,et al. Isogeometric analysis with geometrically continuous functions on two-patch ge-ometries[J]. Computers & Mathematics with Applica-tions,2015,70(7):1518-1538.
[25] Langer U,Mantzaflaris A,Moore S E,et al. Mesh grading in isogeometric analysis[J]. Computers & Mathematics with Applications,2015,70(7):1685-1700.
[26] 王峰,林皋,刘俊,等. 基于面片拼接的等几何分析方法求解波导本征值问题[J]. 电子学报,2016,44(1):200-205. WANG Feng,LIN Gao,LIU Jun,et al. Isogeometric anal-ysis for the waveguide eigenvalue problem based on the NURBS patch splicing technique[J]. Acta Electronica Sinica,2016,44(1):200-205. (in Chinese)
[27] Dornisch W, Klinkel S. Boundary conditions and multi-patch connections in isogeometric analysis[J]. Proceed-ings in Applied Mathematics and Mechanics, 2011, 11(1):207-208.

二维静电场问题的面片拼接等几何分析方法研究

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

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