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矩量法作为数值方法中积分方程方法的代表, 具有计算精度高、所用格林函数自动满足辐射条件、无须额外设置边界条件等优点. 但是在舰船目标与海面复合后向电磁散射仿真中, 传统矩量法需针对每个入射角反复求解矩阵方程组, 导致其在处理后向散射问题时计算量大, 耗时长, 仿真效率低下. 为解决上述问题, 本文提出了一种基于压缩感知技术的矩量法的改进算法. 该算法在求解复合后向散射问题时, 首先利用观测矩阵与传统矩量法中的电压矩阵相乘, 得到一组新的低维度的电压矩阵; 其次通过求解新电压矩阵下的矩阵方程组, 获得电流矩阵的观测值; 最后利用恢复算法(本文采用正交匹配追踪算法)重构出所需的原始入射源照射下的电流系数. 通过与传统矩量法的计算结果对比, 表明本文所提算法能够在保证计算精度的前提下, 明显减少计算时间, 提高计算效率.As one of the most popular numerical methods, the method of moments (MoM) is known for its high accuracy. Besides, MoM has other advantages. For example, the integral equations satisfy the Sommerfeld radiation condition automatically, the additional boundary conditions are not needed., etc. But if the wide angle problem, especially the composite electromagnetic back scattering from a ship place on sea surface, is considered, the MoM needs to solve the integral equation at every incident angle, which needs a large calculating quantity, and is time consuming. To solve this problem, a new efficient method based on the compressive sensing and the MoM is proposed and validated in this paper. A new incident source derived through multiplying the transform matrix by the voltage matrix is first introduced. And then the measurements of the induced currents can be obtained by solving the integral equation under the new incident source. Finally the original electromagnetic currents can be recovered by using the recovery algorithms (the orthogonal matching pursuit is used in this paper). The validity and the efficiency of the new method are demonstrated by comparing with the traditional MoM.
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Keywords:
- compressive sensing /
- method of moments /
- ship /
- composite back scattering
[1] Wang X D, Gan Y B, Li L W 2003 IEEE Antennas Wirel. Propag. Lett. 2 319
[2] Wang X D, Li L W 2009 Prog. Electromagn. Res. 91 35
[3] Wang R, Guo L X, Wang A Q 2010 Acta Phys. Sin. 59 3179 (in Chinese) [王蕊, 郭立新, 王安琪 2010 59 3179]
[4] Hestenes M R, Stiefel E 1952 J. Res. Nat. Bur. Stand. 49 409
[5] Rokhlin V 1990 Antennas and Propagation Symposium Digest Dallas, USA, May 7-11, 1990 p80
[6] Lu C C, Chew W C 1994 Microw. Opt. Technol. Lett. 7 466
[7] Song J M, Chew W C 1995 Microw. Opt. Technol. Lett. 10 14
[8] Wang A Q, Guo L X, Chai C 2011 Chin. Phys. B 20 050201
[9] Wang A Q, Guo L X, Wei Y W, Ma J 2012 Prog. Electromagn. Res. 130 85
[10] Pino M, Obelleiro F, Landesa L, Burkholder R 2000 Microw. Opt. Technol. Lett. 26 78
[11] Dehmollaian M, Biglary H 2012 IEEE International Symposium on Antennas and Propagation and USNC-URSI National Radio Science Meeting Chicago, United States, July 8-14, 2012 p1
[12] Sheng X Q, Yung E K N 2002 IEEE Trans. Antennas Propag. 50 163
[13] Ma J, Guo L X, Wang A Q 2009 Chin. Phys. B 18 3431
[14] Lezar E, Davidson D B 2011 International Conference on Electromagnetics in Advanced Applications Torino, Italy, September 12-16, 2011 p452
[15] Fang M, Song K H, Huang Z X, Wu X L 2013 International Symposium on Antennas & Propagation Nanjing, China, October 23-25, 2013 p1268
[16] Candés E J 2006 Proceedings of the International Congress of Mathematicians Madrid, Spain, August 22-30, 2006 p1433
[17] Donoho D L 2006 IEEE Trans. Inf. Theory 52 1289
[18] Wang Z, Wang B Z 2014 Acta Phys. Sin. 63 120202 (in Chinese) [王哲, 王秉中 2014 63 120202]
[19] Thorsos E I 1988 J. Acoust. Soc. Am. 83 78
[20] Tropp J A, Gilbert A C 2007 IEEE Trans. Inf. Theory 53 4655
[21] Chen M S, Liu F L, Du H M, Wu X L 2011 IEEE Antennas Wirel. Propag. Lett. 10 1243
[22] Chen M S, Wang S W, Ma T, Wu X L 2014 Acta Phys. Sin. 63 170301 (in Chinese) [陈明生, 王时文, 马韬, 吴先良 2014 63 170301]
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[1] Wang X D, Gan Y B, Li L W 2003 IEEE Antennas Wirel. Propag. Lett. 2 319
[2] Wang X D, Li L W 2009 Prog. Electromagn. Res. 91 35
[3] Wang R, Guo L X, Wang A Q 2010 Acta Phys. Sin. 59 3179 (in Chinese) [王蕊, 郭立新, 王安琪 2010 59 3179]
[4] Hestenes M R, Stiefel E 1952 J. Res. Nat. Bur. Stand. 49 409
[5] Rokhlin V 1990 Antennas and Propagation Symposium Digest Dallas, USA, May 7-11, 1990 p80
[6] Lu C C, Chew W C 1994 Microw. Opt. Technol. Lett. 7 466
[7] Song J M, Chew W C 1995 Microw. Opt. Technol. Lett. 10 14
[8] Wang A Q, Guo L X, Chai C 2011 Chin. Phys. B 20 050201
[9] Wang A Q, Guo L X, Wei Y W, Ma J 2012 Prog. Electromagn. Res. 130 85
[10] Pino M, Obelleiro F, Landesa L, Burkholder R 2000 Microw. Opt. Technol. Lett. 26 78
[11] Dehmollaian M, Biglary H 2012 IEEE International Symposium on Antennas and Propagation and USNC-URSI National Radio Science Meeting Chicago, United States, July 8-14, 2012 p1
[12] Sheng X Q, Yung E K N 2002 IEEE Trans. Antennas Propag. 50 163
[13] Ma J, Guo L X, Wang A Q 2009 Chin. Phys. B 18 3431
[14] Lezar E, Davidson D B 2011 International Conference on Electromagnetics in Advanced Applications Torino, Italy, September 12-16, 2011 p452
[15] Fang M, Song K H, Huang Z X, Wu X L 2013 International Symposium on Antennas & Propagation Nanjing, China, October 23-25, 2013 p1268
[16] Candés E J 2006 Proceedings of the International Congress of Mathematicians Madrid, Spain, August 22-30, 2006 p1433
[17] Donoho D L 2006 IEEE Trans. Inf. Theory 52 1289
[18] Wang Z, Wang B Z 2014 Acta Phys. Sin. 63 120202 (in Chinese) [王哲, 王秉中 2014 63 120202]
[19] Thorsos E I 1988 J. Acoust. Soc. Am. 83 78
[20] Tropp J A, Gilbert A C 2007 IEEE Trans. Inf. Theory 53 4655
[21] Chen M S, Liu F L, Du H M, Wu X L 2011 IEEE Antennas Wirel. Propag. Lett. 10 1243
[22] Chen M S, Wang S W, Ma T, Wu X L 2014 Acta Phys. Sin. 63 170301 (in Chinese) [陈明生, 王时文, 马韬, 吴先良 2014 63 170301]
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