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研究一种可以高效求解半空间金属目标电磁散射积分方程方法, 电场积分方程适用于任意结构电磁问题分析, 但是生成的矩阵条件数大, 迭代求解收敛性差; 而磁场积分方程生成的矩阵条件数小, 迭代收敛性好, 但是仅能分析闭合结构问题, 本文采用了混合场积分方程方法, 同时具备电场积分方程的普适性与磁场积分方程的收敛性. 由于混合场积分方程中涉及格林函数的梯度项, 为了进一步加快计算效率, 本文引入了一种针对半空间格林函数的高效四维空间插值方法, 对组成半空间格林函数的索末菲积分进行列表和Lagrange插值, 以实现高效的迭代求解, 效率在传统混合场积分方程的基础上提高12.6倍. 数值结果表明, 该方法在保证精度的同时, 可以显著降低求解问题的时间.A new acceleration method is proposed for efficiently solving the problem of electromagnetic scattering from metal targets in half-space. The analysis of electromagnetic problems in any structure can be settled by the electric field integral equation. But the generated matrix condition number is large and the iterative solution has poor convergence. The number of the matrix condition generated by the magnetic field integral equation is small and iterative convergence is good. But only the closed structure problems can be worked out. The combined field integral equation is adopted because of the universality of the electric field integral equation and the convergence of the magnetic field integral equation. The gradient term of Green's function is involved in the integral equation of the mixed field. In order to further enhance the calculation efficiency, an efficient four-dimensional spatial interpolation method is introduced for half-space Green's function. Tabulation and lagrange interpolations are performed in the Sommerfeld integrals for the half-space Green's function. The improved efficiency can be 7.5 times higher than that of the traditional combined field integral equation(CFIE). Numerical results show that the computational time can be reduced significantly by the proposed method with encouraging accuracy.
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Keywords:
- electromagnetic scattering /
- combined field integral equation /
- half-space Green's function /
- spatial interpolation /
- sommerfeld integral
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图 3 RCS计算误差和运行时间随插值间隔变化的折线图
Fig. 3. Line chart of RCS calculation error and running time for different interpolation intervals.
图 4 二维插值表示意图, 图中插值点在二维插值表
$ (\rho , z) $ 中取值Fig. 4. Schematic diagram of two-dimensional interpolation table, the interpolation points in the figure are taken in the two-dimensional interpolation table
$ (\rho , z) $ .
图 5 四维插值表示意图, 图中插值点在四维插值表
$(x-x', $ $ y-y', z-z', z+z')$ 中取值Fig. 5. Schematic diagram of the 4D interpolation table, the interpolation points in the figure are taken in the four-dimensional interpolation table
$(x-x', y-y', z-z', z+z')$ 
图 7 金属立方体双站RCS仿真结果对比图
Fig. 7. RCS comparison among the proposed method, the traditional CFIE method and the FEKO for the PEC block model.
图 9 金属slicy模型双站RCS仿真结果对比图
Fig. 9. RCS comparison between the proposed method and the traditional CFIE method for the PEC slicy model.
图 11 金属船双站RCS仿真结果对比图
Fig. 11. RCS comparison between the proposed method and the traditional CFIE method for the PEC ship model.
表 1 本文方法与FEKO、传统CFIE的计算资源比较
Table 1. Computational comparison among the proposed method, FEKO and the traditional CFIE.
模型 未知量 计算时间/s 计算内存/MB FEKO 传统CFIE 本文方法 FEKO 传统CFIE 本文方法 立方体 11682 1731 7560 1008 1229.0 1120.1 1251.9 slicy 7518 709 3204 432 533.6 545.8 557.0 船 14013 2541 18684 1476 1721.3 1613.6 1715.9 
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[1] Man L, Wei X, Xiao Z H 2017 International Applied Computational Electromagnetics Society Symposium Suzhou, China, August 1–4, 2017 p1
[2] 李冰, 马萌晨, 雷明珠 2017 物理学报 66 050301
Google Scholar
Li B, Ma M C, Lei M Z 2017 Acta Phys. Sin. 66 050301
Google Scholar
[3] 向敏, 牛立强, 武沛羽, 谢拥军, 石宋华, 严杰 2019 电子技术应用 45 1
Xiang M, Niu L Q, Wu P Y, Xie Y J, Shi S H, Yan J 2019 Appl. Electr. Tech. 45 1
[4] 聂在平, 陈涌频 2017 中国科学: 信息科学 47 545
Nie Z P, Chen Y P 2017 Chin. Sci. (Informationis) 47 545 (in Chinese)
[5] Yuan H, Wang C, Li Y, Liu N, Cui G 2016 International Symposium on Antennas, Propagation and EM Theory Guilin, China, Oct. 18–21, 2016 p75
[6] 魏仪文 2016 博士学位论文 (西安: 西安电子科技大学)
Wei Y W 2016 Ph. D. Dissertation (Xi'an: Xidian University) (in Chinese)
[7] 邵芸, 宫华泽, 田维, 张庆君, 王国军, 卞小林, 张婷婷, 张风丽, 李坤, 刘致曲, 倪崇 2021 遥感学报 25 323
Google Scholar
Shao Y, Gong H Z, Tian W, Zhang Q J, Wang G J, Bian X L, Zhang T T, Zhang F L, Li K, Liu Z Q, Ni C 2021 J. Remote. Sens. 25 323
Google Scholar
[8] 綦鑫 2019博士学位论文(成都: 电子科技大学)
Qi X 2019 Ph. D. Dissertation (Chengdu: University of Electronic Science and Technology of China)(in Chinese)
[9] Zhang R, Jia P, Hu L 2018 IEEE International Conference on Computational Electromagnetics Chendu, China, March 26–28, 2018 p1
[10] Li B C, Zhang Q Z, Liu H L 2021 2020 15th Symposium on Piezoelectrcity, Acoustic Waves and Device Applications Zhengzhou, China, April 16–19, 2021 p54
[11] Wang Y, Wang J, Yao L 2020 IEEE J. Multiscale and Multiphys. Comput. Techn. 5 273
Google Scholar
[12] Zhang Y, Wang P, Li W, Yang S 2019 International Conference on Electromagnetics in Advanced Applications Granada, Spain, Sept 9–13, 2019 p0780
[13] 徐润汶, 郭立新, 范天奇 2013 物理学报 62 170301
Google Scholar
Xu R W, Guo L X, Fan T Q 2013 Acta Phys. Sin. 62 170301
Google Scholar
[14] 陈涌频, 聂在平, 胡俊 2008 电子学报 3 562
Google Scholar
Chen Y P, Nie Z P, Hu J 2008 Acta Electron. Sin. 3 562
Google Scholar
[15] Sommerfeld A 1909 Ann. Phys. 28 665
[16] Weyl H 1919 Ann. Phys. 365 481
Google Scholar
[17] Siegel M, King R 1971 IEEE Trans. Antennas. Propag. 19 477
Google Scholar
[18] Xu X B, Butler C 1986 IEEE Trans. Antennas. Propag. 34 880
Google Scholar
[19] Stratton I A 1941 Electromagnetic Theory (New York: Mc Graw-Hill Book Company)
[20] Michalski K A, Zheng D 1990 IEEE Trans. Antennas. Propag. 38 335
Google Scholar
[21] Vitebskiy S, Carin L 1995 IEEE Trans. Antennas. Propag. 43 1303
[22] Geng N, Sullivan A, Carin L 2000 IEEE Trans. Geosci. Remote Sens. 38 1561
Google Scholar
[23] Yang J J, Chow Y L, Fang D G 1991 IEEE Trans. Antennas. Propag. 138 319
[24] Aksun M I 1996 IEEE Trans. Microw. Theory Techn. 44 651
Google Scholar
[25] Yuan M T, Sarkar T K, Salazar-Palma M 2006 IEEE Trans. Microw. Theory Techn. 5 1025
[26] Zhuang L, Zhu G Q, Zhang Y H 2007 IEEE Microw. Wireless Compon. Lett. 49 1337
[27] 潘锦, 文希理 1996 地球物理学报 s1 400
Pan J, Wen X L 1996 Chin. J. Geophys. s1 400 (in Chinese)
[28] 胡俊, 聂在平 1998 电子学报 3 126
Google Scholar
Hu J, Nie Z P 1998 Acta Electron. Sin. 3 126
Google Scholar
[29] Song Z, Zhou H, Zheng K, Hu J, Li W, Hong W 2013 IEEE Antennas. Propag. Mag. 55 92
Google Scholar
[30] Wu B, Sheng X A 2015 IEEE Trans. Antennas. Propag. 63 3727
Google Scholar
[31] Burke G, Miller E 1984 IEEE Trans. Antennas. Propag. 32 1040
Google Scholar
[32] Eskelinen P 2002 IEEE Aerosp. Electr. Syst. Mag. 17 41
Google Scholar
[33] Chen J Y, Kishk A A, Glisson A W 2000 Electromagnetics 20 1
Google Scholar
[34] 罗万 2016 博士学位论文 (成都: 电子科技大学)
Luo W 2016 Ph. D. Dissertation (Chengdu: University of Electronic Science and Technology of China) (in Chinese)
[35] 胡云琴 2012 博士学位论文 (南京: 南京理工大学)
Hu Y Q 2012 Ph. D. Dissertation (Nanjing: Nanjing University of Science and Technology) (in Chinese)
[36] 张民, 李乐伟, 李良超, 吴振森 2008 中国科学 2 298
Zhang M, Li L W, Li L C, Wu Z S 2008 Chin. Sci. 2 298
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