开域静电场全源积分人工边界法的GMRES迭代算法

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摘要全源积分人工边界法将媒质等效为源,通过对场源和媒质等效源的积分计算,确定人工边界条件。该方法的计算准确度高,可以将人工边界划在距媒质很近的位置,场域的计算区域小。全源积分人工边界法的方程是有限元和人工边界条件的耦合方程。直接迭代法求解该方程时收敛速度慢,并且对于复杂的区域分解问题不能收敛。本文在没有全源积分人工边界法方程的系数矩阵的情况下,基于人工边界条件与场源和媒质的物理关系,推导了全源积分人工边界法的广义极小残量（GMRES）迭代算法。通过与2D FEM对比,验证了GMRES迭代算法的正确性,并且用GMRES迭代算法计算了交流特高压绝缘子串的电场,计算结果与已有文献一致。算例表明GMRES迭代算法收敛速度快,并且能够求解复杂的区域分解问题,为解决复杂问题提供了一种新方法。

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	李世琼
	王泽忠

关键词 ：全源积分人工边界法, 区域分解, 广义极小残量法, 有限元, 边界条件

Abstract：In finite element method(FEM)-actual charge method, the media are equivalent to sources. The artificial boundary conditions can be decided by integral calculation of sources and equivalent sources. The FEM-actual charge method can put artificial boundary closed to media. The equations of FEM-actual charge method are the coupling of FEM and artificial boundary conditions. The equations could be solved by direct iteration method, but it needed more time and could not converge for complicated domain decomposition problems. The GMRES iteration method of FEM- actual charge method was proposed. The method is based the physical relationship between artificial boundary conditions and whole sources while the matrixes are unknowable. The GMRES iteration method was verified by 2D FEM problem and electric field problem of AC extra-high voltage insulator strings. The examples indicated that the GMRES iteration method could converge more quickly and could solve complicated domain decomposition problems. It is a new method for complicated electrostatic problems.

Key words： Finite element method(FEM)-actual charge method domain decomposition method generalized minimal residual FEM boundary conditions

收稿日期: 2013-12-25 出版日期: 2014-11-05

PACS:

TM151

基金资助:高等学校博士学科点专项科研基金资助项目（20100036110009）

作者简介: 李世琼女,1973年生,博士研究生,讲师,主要研究方向为电磁场数值计算。王泽忠男,1960年生,博士,教授,博士生导师,主要研究方向为电磁场数值计算、电磁兼容和电磁测量。

引用本文:

李世琼, 王泽忠. 开域静电场全源积分人工边界法的GMRES迭代算法[J]. 电工技术学报, 2014, 29(10): 206-212. Li Shiqiong, Wang Zezhong. GMRES Iteration Method of FEM-Actual Charge Method for Open Boundary Electrostatic Field Problems. Transactions of China Electrotechnical Society, 2014, 29(10): 206-212.

链接本文:

http://dgjsxb.ces-transaction.com/CN/Y2014/V29/I10/206

[1] 王泽忠, 王炳革, 卢斌先, 等. 三维开域涡流场A-V位有限元与边界元耦合分析方法[J]. 中国电机工程学报, 2000, 20(5): 1-4.[1] Wang Zezhong, Wang Bingge, Lu Binxian, et al. FE-BE coupling method of 3-D open boundary eddy current fields in potential A-V[J]. Proceedings of the CSEE, 2000, 20(5): 1-4.
[2] Aiello G, Alfonzetti S, Dilettoso E, et al. Transient thermal analysis of an eddy-current heated conductor applying FEM-DBCI[J]. IEEE Transactions on Magnetics, 2013, 49(5): 1861-1864.
[3] Aiello G, Alfonzetti S, Rizzo S, et al. A comparison between hybrid methods for open-boundary problems [C]. 2010 14th Biennial IEEE Conference on Electro- magnetic Field Computation(CEFC), 2010: 1.
[4] Li Shiqiong, Wang Zezhong, Pan Chao. FEM-actual charge method for open boundary electrostatic fields [C]. Sixth International Conference on Electro- magnetic Field Problems and Applications(ICEF), 2012: 1-4.
[5] (美)James W. Demmel. 应用数值线性代数[M]. 王国荣, 译. 北京: 清华大学出版社, 2011.
[6] Alfonzetti S, Borzi G, Salerno N. Unbounded electro- magnetic field problem solution by means of virtual GMRES[C]. 15th IEEE Mediterranean Electrotechnical Conference(MELECON), 2010: 403-408.
[7] Aiello G, Alfonzetti S, Borzi G, et al. Efficient solution of skin-effect problems by means of the GMRES-accelerated FEM-BEM method[J]. IEEE Transactions on Magnetics, 2008, 44(6): 1274-1277.
[8] Aiello G, Alfonzetti S, Borzi G, et al. GMRES solution of FEM-BEM global systems for electrostatic problems without voltaged conductors[J]. IEEE Transactions on Magnetics, 2013, 44(5): 1701-1704.
[9] Saitoh A, Kamitani A. GMRES with new precon- ditioning for solving BEM-type linear system[J]. IEEE Transactions on Magnetics, 2004, 40(2): 1084- 1087.
[10] 李亚莎. 高精度快速边界元法及其在绝缘子电场计算中应用研究[D]. 北京: 华北电力大学, 2007.
[11] Rui P L, Chen R S, Fan Z H, et al. Fast analysis of electromagnetic scattering of 3-D dielectric bodies with augmented GMRES-FFT method[J]. IEEE Transactions on Antennas and Propagation, 2005, 53(11): 3848-3852.
[12] 芮平亮. 电磁散射分析中的快速迭代求解技术[D]. 南京: 南京理工大学, 2007.
[13] 夏沛, 汪芳宗. 大规模电力系统快速潮流计算方法研究[J]. 电力系统保护与控制, 2012, 40(9): 38-42. Xia Pei, Wang Fangzong. Study on fast power flow calculation methods of large-scale power systems[J]. Power System Protection and Control, 2012, 40(9): 38-42.
[14] 胡博, 谢开贵, 曹侃. 基于Beowulf集群的大规模电力系统牛顿法潮流求解的并行GMRES方法[J]. 电工技术学报, 2011, 26(4): 145-152. Hu Bo, Xie Kaigui, Cao Kan. Parallel GMRES techniques for solving Newton power flow of large scale power systems on the Beowulf cluster[J]. Transactions on China Electrotechnical Society, 2011, 26(4): 145-152.
[15] 韩富春, 石洋, 李少华, 等. 基于GMRES的改进连续潮流算法研究[J]. 电力系统保护与控制, 2011, 39(15): 23-27. Han Fuchun, Shi Yang, Li Shaohua, et al. Research on improved continuation power flow with GMRES[J]. Power System Protection and Control, 2011, 39(15): 23-27.
[16] 温柏坚, 胡佳怡, 郭文鑫, 等. 基于辛Gauss方法及预处理GMRES方法的暂态稳定性并行计算[J]. 电力系统保护与控制, 2012, 40(22): 19-24. Wen Baijian, Hu Jiayi, Guo Wenxin, et al. Parallel computation of power systen transient stability based on symplectic Gauss algorithm and preconditioned GMRES method[J]. Power System Protection and Control, 2012, 40(22): 19-24.
[17] 黄道春, 黄正芳, 王国利, 等. 特高压交流输电线路瓷绝缘子串电位和均压环电场分布计算模型的简化[J]. 高电压技术, 2012, 38(9): 2163-2170. Huang Daochun, Huang Zhengfang, Wang Guoli, et al. Calculation model simplification for porcelain insulator string potential and grading ring surface electric field distribution of UHV AC transmission line[J]. High Voltage Engineering, 2012, 38(9): 2163-2170.