基于电场数值加权的跨介质元胞共形新技术

孙亚秀; 姜庆辉

doi:10.7498/aps.62.164101

摘要

针对时域有限差分法处理跨介质元胞现有共形技术中存在误差大、平行方向未被包含等问题, 提出一种利用电场数值加权法来进行跨介质元胞共形计算的新算法. 该算法不再对介电常数ε做加权平均处理, 而是根据中值定理对时域有限差分法真正的求解分量电场强度进行权值选择, 并将权值乘入积分路径中. 该方法同时考虑了跨介质安培环路元胞与跨介质法拉第环路元胞对结果带来的不连续影响, 而且对介质界面与元胞中场分量的各种位置关系均能应用, 通用性强、精度高且易于实现. 利用介质填充圆波导作为数值模型来进行理论数值计算和仿真验证, 比较不同共形方法的二维TE模式的特征根与理论值的偏差以及由共形技术所带来的各向相异性. 数值结果表明, 本文所提出算法求得的特征根最接近理论值, 而且造成的各向相异性更小, 从而验证了该算法在处理跨介质元胞时的有效性.

关键词:

Abstract

In this paper, a new method of using the electric field numerical weight to process the inhomogeneous cells is proposed, which is to resolve the problems such as high errors and parallel direction excluded in the existing finite-difference time-domain method. Instead of deriving average dielectric constant, the new method weights the electric field strength, which is the true solving variables, according to the mean value theorem, and then the length of the integral path is multiplied by the weight. In the new method both the discontinuous effects of inhomogeneous Ampere cell and the ones of inhomogeneous Faraday cell are taken into account, so it is accurate, easy to implement, versatile, and applicable to any of the various positional relationships between the dielectric interface and the electric field strength variable. A numerical model of dielectric filled circular waveguide is used for the numerical calculation and simulation, in which the deviations of the characteristic roots in two-dimensional TE mode solved by different methods from the theoretical ones are compared, and the anisotropies of different methods are also compared. The numerical result shows that the characteristic roots solved by the presented method are closer to the theoretical ones and the anisotropy caused by the proposing method is lower, which proves that this method is more efficient to process the inhomogeneous cells.

Keywords:

finite-difference time-domain /
electric field numerical weighting method /
two-dimensional TE mode /
inhomogeneous cell

作者及机构信息

1.
哈尔滨工程大学信息与通信工程学院, 哈尔滨 150001

基金项目: 国家自然科学基金(批准号: 51209055);航空科学基金(批准号: 201207P6001);中国博士后基金(批准号: 20100480966);中央高校基本科研业务费(批准号: HEUCFR1124)和飞行器控制一体化技术重点实验室资助的课题.

Authors and contacts

1.
College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51209055), the Aeronautic Science Foundation, China (Grant No. 201207P6001), the Post Doctorate Science Foundation, China (Grant No. 20100480966), the Fundamental Research Fund for the Central Universities, China (Grant No. HEUCFR1124), and the Laboratory of Science and Technology on Aircraft Control, China.

参考文献

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[2]	Liu S B, Zhu C X, Yuan N C 2005 Acta Phys. Sin. 54 2804 (in Chinese) [刘少斌, 朱传喜, 袁乃昌 2005 物理学报 54 2804]
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[4]	Wang G, Wen J H, Han X Y, Zhao H G 2003 Acta Phys. Sin. 52 1943 (in Chinese) [王刚, 温激鸿, 韩小云, 赵宏刚 2003 物理学报 52 1943]
[5]	Shibayama J, Muraki M, Takahashi R, Yamauchi J, Nakano H 2006 IEEE/OSA J. Lightw. Tech. 24 2465
[6]	Zhang X Q, Wang J H, Li Z 2011 Acta Phys. Sin. 60 051301 (in Chinese) [张雪芹, 王均宏, 李铮 2011 物理学报 60 051301]
[7]	Wei B, He Q, Li J, Ge D B, Guo L X 2011 Acta Phys. Sin. 60 104102 (in Chinese) [魏兵, 何琼, 李杰, 葛德彪, 郭立新 2011 物理学报 60 104102]
[8]	Zhuang F, Xiao S S, He J P, He S L 2002 Acta Phys. Sin. 51 2167 (in Chinese) [庄飞, 肖三水, 何江平, 何赛灵 2002 物理学报 51 2167]
[9]	Chu Q X, Ding H 2005 Preceedings of the IEEE Antennas and Propagation Society International Symposium Washington, USA, July 3-8, 2005 p205
[10]	H Ding, Chu Q X 2005 Proceedings of Asia-Pacific Microwave Conference 2005 Suzhou, China, December 4-7, 2005
[11]	H Ding, Chu Q X 2008 Proceedings of Asia-Pacific Microwave Conference 2008 Macau, China, December 16-20, 2008 p1
[12]	Taflove A, Umashankar K R, Beker B, Harfoush F, Yee K S 1988 IEEE Trans. Antenna. Propagat. 36 247
[13]	Jurgens T G, Taflove A, Umashankar K, Moore T G 1992 IEEE Trans. Antenna. Propagat. 40 357
[14]	Fan G X, Liu Q H 2000 IEEE Trans. Antenna. Propagat. 8 637
[15]	Zhang Y Q, Ge D B 2009 Acta Phys. Sin. 58 4573 (in Chinese) [张玉强, 葛德彪 2009 物理学报 58 4573]
[16]	Zhang Y Q, Ge D B 2009 Acta Phys. Sin. 58 8243 (in Chinese) [张玉强, 葛德彪 2009 物理学报 58 8243]
[17]	Ramadan O 2011 IEEE Microw. Wireless Comp. Lett. 21 513
[18]	Kaneda N, Houshmand B, Itoh T 1997 IEEE Trans. Microw. Theory Tech. 45 1645
[19]	Dey S, Mittra R 1999 IEEE Trans. Microw. Theory Tech. 47 1737
[20]	Yu W, Mittra R 2001 IEEE Microw. Guided Wave Lett. 11 25
[21]	Fujii M, Hoefer W J R 2001 IEEE Microw. Wireless Comp. Lett. 11 22
[22]	Fujii M, Hoefer W J R 2001 IEEE J. Quantum Electron. 37 1015
[23]	Fujii M, Lukashevich D, Sakagami I, Russer P 2003 IEEE Microw. Wireless Comp. Lett. 13 469
[24]	Georgakopoulos S V, Birtcher C R, Balanis C A, Renaut R A 2003 IEEE Trans. Electromagn. Compat. 45 293
[25]	Zygiridis T T, Tsiboukis T D 2004 IEEE Trans. Microw. Theory Tech. 52 1321
[26]	Wang J, Yin W Y, Liu P G, Liu Q H 2010 IEEE Trans. Antenna. Propagat. 58 2946
[27]	Liu D C, Chang H C 2012 IEEE Trans. Antenna. Propagat. 60 5259

施引文献

[1]	Yee K S 1966 IEEE Trans. Antenna. Propagat. 14 302
[2]	Liu S B, Zhu C X, Yuan N C 2005 Acta Phys. Sin. 54 2804 (in Chinese) [刘少斌, 朱传喜, 袁乃昌 2005 物理学报 54 2804]
[3]	Liu S B, Yuan N C, Xu L J 2005 Acta Phys. Sin. 54 4789 (in Chinese) [刘少斌, 袁乃昌, 徐利军 2005 物理学报 54 4789]
[4]	Wang G, Wen J H, Han X Y, Zhao H G 2003 Acta Phys. Sin. 52 1943 (in Chinese) [王刚, 温激鸿, 韩小云, 赵宏刚 2003 物理学报 52 1943]
[5]	Shibayama J, Muraki M, Takahashi R, Yamauchi J, Nakano H 2006 IEEE/OSA J. Lightw. Tech. 24 2465
[6]	Zhang X Q, Wang J H, Li Z 2011 Acta Phys. Sin. 60 051301 (in Chinese) [张雪芹, 王均宏, 李铮 2011 物理学报 60 051301]
[7]	Wei B, He Q, Li J, Ge D B, Guo L X 2011 Acta Phys. Sin. 60 104102 (in Chinese) [魏兵, 何琼, 李杰, 葛德彪, 郭立新 2011 物理学报 60 104102]
[8]	Zhuang F, Xiao S S, He J P, He S L 2002 Acta Phys. Sin. 51 2167 (in Chinese) [庄飞, 肖三水, 何江平, 何赛灵 2002 物理学报 51 2167]
[9]	Chu Q X, Ding H 2005 Preceedings of the IEEE Antennas and Propagation Society International Symposium Washington, USA, July 3-8, 2005 p205
[10]	H Ding, Chu Q X 2005 Proceedings of Asia-Pacific Microwave Conference 2005 Suzhou, China, December 4-7, 2005
[11]	H Ding, Chu Q X 2008 Proceedings of Asia-Pacific Microwave Conference 2008 Macau, China, December 16-20, 2008 p1
[12]	Taflove A, Umashankar K R, Beker B, Harfoush F, Yee K S 1988 IEEE Trans. Antenna. Propagat. 36 247
[13]	Jurgens T G, Taflove A, Umashankar K, Moore T G 1992 IEEE Trans. Antenna. Propagat. 40 357
[14]	Fan G X, Liu Q H 2000 IEEE Trans. Antenna. Propagat. 8 637
[15]	Zhang Y Q, Ge D B 2009 Acta Phys. Sin. 58 4573 (in Chinese) [张玉强, 葛德彪 2009 物理学报 58 4573]
[16]	Zhang Y Q, Ge D B 2009 Acta Phys. Sin. 58 8243 (in Chinese) [张玉强, 葛德彪 2009 物理学报 58 8243]
[17]	Ramadan O 2011 IEEE Microw. Wireless Comp. Lett. 21 513
[18]	Kaneda N, Houshmand B, Itoh T 1997 IEEE Trans. Microw. Theory Tech. 45 1645
[19]	Dey S, Mittra R 1999 IEEE Trans. Microw. Theory Tech. 47 1737
[20]	Yu W, Mittra R 2001 IEEE Microw. Guided Wave Lett. 11 25
[21]	Fujii M, Hoefer W J R 2001 IEEE Microw. Wireless Comp. Lett. 11 22
[22]	Fujii M, Hoefer W J R 2001 IEEE J. Quantum Electron. 37 1015
[23]	Fujii M, Lukashevich D, Sakagami I, Russer P 2003 IEEE Microw. Wireless Comp. Lett. 13 469
[24]	Georgakopoulos S V, Birtcher C R, Balanis C A, Renaut R A 2003 IEEE Trans. Electromagn. Compat. 45 293
[25]	Zygiridis T T, Tsiboukis T D 2004 IEEE Trans. Microw. Theory Tech. 52 1321
[26]	Wang J, Yin W Y, Liu P G, Liu Q H 2010 IEEE Trans. Antenna. Propagat. 58 2946
[27]	Liu D C, Chang H C 2012 IEEE Trans. Antenna. Propagat. 60 5259

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