棱边元分区的区域分解算法及其在电磁问题中的应用

吕志清; 安翔; 洪伟

doi:10.3724/SP.J.1146.2005.01122

棱边元分区的区域分解算法及其在电磁问题中的应用

doi: 10.3724/SP.J.1146.2005.01122

吕志清^①;安翔,
安翔,
洪伟

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出版历程
- 收稿日期: 2005-09-05
- 修回日期: 2006-03-13
- 刊出日期: 2007-05-19

Edge-Element Partitioning Domain Decomposition Method for Electromagnetic Problems

摘要

摘要: 针对三维电磁问题，该文提出了采用非结构化网格剖分计算区域，并按单元进行区域划分的区域分解算法。将原求解区域划分为若干个不重叠的子区域，先通过求解容量矩阵获得子区域之间连接边界上的场值，再利用矢量有限元快速计算出每个子区域内部的场值，显著地降低了计算复杂度和存储量。通过引入预条件的Krylov子空间法求解容量矩阵方程，加速了收敛，进一步提高了效率。数值算例验证了该方法的准确性和有效性。
- 区域分解算法;容量矩阵;矢量有限元
Abstract: A fast domain decomposition method is presented for the solution of electromagnetic problems arising in three-dimensions. The original computation domain is meshed and decomposed into several nonoverlapping subdomains by edge-element partitioning technique, which yields a capacitance matrix. Once the unknowns on the interfaces between subdomains have been obtained through the capacitance matrix, the interior unknown fields in each subdomain can be computed with vector finite element method in parallel. Compared with the conventional numerical methods, such as finite element method, method of moments, the present method can greatly reduce the computational complexity and the storage requirement. A preconditioned Krylov subspace method is also developed to accelerate the convergence of the capacitance matrix, and improve the efficiency further. The validity and computational efficiency have been verified by numerical examples.

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Despres B. Domain decomposition method and the Helmholtz problem[A]. Proc. Int. Symp. Mathemat. Numerical Aspects Wave Propagation Phenomena[C]. Strasbourg France: SIAM, 1992: 44-52.[2]Despres B. Domain decomposition method and the Helmholtz problem (Part II)[A]. Proc. 2nd Int. Conf. Mathemat. Numerical Aspects Wave propagation[C]. Dover, DE: SIAM, 1993: 197-206.[3]Strupfel Bruno. A fast-domain decomposition method for the solution of electromagnetic scattering by large objects[J].IEEE Trans. on Antennas and Propagat.1996, 44(10):1375-1385[4]Strupfel Bruno and Martine Mognot. A domain decomposition method for the vector wave equation[J].IEEE Trans. on Antennas and Propagat.2000, 48(5):653-660[5]吕涛, 石济民, 林振宝. 区域分裂算法偏微分方程数值解新技术[M]. 北京: 科学出版社, 1997，第5章.[6]洪伟, 孙连友, 许锋, 尹雷等. 电磁场边值问题的区域分解算法[M]. 北京: 科学出版社, 2005: 36-78.[7]Yin Lei, Wang Jie, and Hong Wei. A novel and rigorous method based on the domain decomposition method for the full-wave analysis of 3-D structures[J].IEEE Trans. on Microwave Theory and Techniques.2002, 50(8):2011-2017[8]Hong Wei.[J].Yin Xiao Xing, An Xiang, L Zhi Qing, and Cui Tie Jun. A mixed algorithm of domain decomposition method and the measured equation of invariance for the electromagnetic problems[A]. IEEE Antennas and Propagation Society International Symposium[C]. Monterey, CA: IEEE PRESS.2004,:-[9]An Xiang, L Zhi Qing, Hong wei, Cui Tie Jun, and Yin Xiao Xing. The application of PBSV-DDM in EM scattering analysis of electrically large 2-D objects[J]. Journal of Applied Sciences, 2005, 23(2): 122-125.[10]Lu Y J and Shen C Y. A domain decomposition finite difference method for parallel numerical implementation of time dependent Maxwells equations[J].IEEE Trans. on Antennas and Propagat.1997, 45(3):556-562[11]An Xiang and L Zhi Qing. Application of DDM based on special ordered nodes in 2-D electromagnetic scattering[J]. Journal of Microwaves, 2005, 21(3): 12-15.[12]安翔. 计算电磁学中的网格生成与区域分解算法[D]. 南京: 东南大学博士后研究报告, 2004，第3章.[13]尹雷. 区域分裂算法及其在电磁问题中的应用[D]. [博士学位论文]，南京: 东南大学, 2001，第5章.[14]Saad Yousef. Iterative Methods for Sparse Linear Systems[M]. New York: PWS Publishing Company, 1996, chapter 9.[15]Chan T F. The interface probing technique in domain decomposition method[J].SIAM Journal on Matrix Analysis and Applications.1992, 13(1):212-238[16]金建铭. 电磁场有限元方法[M]. 西安: 西安电子科技大学出版社, 1997，第8章.[17]Harrington R F. Time Harmonic Electromagnetic Fields[M]. New York: McGraw-Hill, 1961, chapter 6.[18]葛德彪. 电磁波时域有限差分方法[M]. 西安: 西安电子科技大学出版社, 2002，第4章.

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