随机分布多目标电磁散射问题的快速分析
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摘要
电磁散射问题是电磁学中的一个重要研究领域，研究电磁波的散射机理以及计算其散射场强的大小与分布，具有十分重要的实际意义。稀疏矩阵规则网格法(SMCG)是近年来才被提出的一种数值方法。目前这种方法已被应用于随机粗糙面散射问题的分析、随机分布的二维介质柱的散射分析、微带结构的分析、密集封装的互联分析等问题中。
本文将SMCG方法应用到随机分布多目标电磁散射问题的分析中，并对SMCG方法加以改进，以达到对随机分布多目标电磁散射问题进行快速分析的目的。
论文首先运用SMCG方法对随机分布三维介质目标的电磁散射问题进行较为全面的分析和讨论，然后讨论了如何对SMCG方法进行预处理，提出了预处理SMCG方法的三种方案，接下来又讨论了将SMCG方法和广义最小余数法(GMRES)结合起来的方案，最后应用上面提出的四种方案对多个随机分布三维介质目标的电磁散射问题进行了分析。计算结果表明，本文提出的方法快速、有效。
本文的研究进一步改进了SMCG方法，使SMCG方法的计算效率得到了提高，为快速分析各种复杂的随机分布目标的电磁散射问题奠定了基础，为遥感技术的发展、电磁探矿的研究以及电路互联封装的分析提供了理论指导。
The problem of electromagnetic scattering is an important research domain in electromagnetics. It's very important to investigate mechanism of electromagnetic scattering and computation of electromagnetic field. The sparse matrix canonical grid (SMCG) method is a numerical method that was developed recently. This method has been applied to analyze electromagnetic scattering from random rough surface, two-dimensional random dielectric cylinders, microstrip structures and densely packed interconnects.
In this paper, the sparse matrix canonical grid method is applied to analyze electromagnetic scattering from three-dimensional random dielectric scatterers, and improved so that the problem of electromagnetic scattering from three-dimensional random dielectric scatterers could be quickly analyzed.
Firstly, the electromagnetic scattering from three-dimensional random dielectric scatterers is systematically analyzed and discussed by using sparse matrix canonical grid method in this paper. Then three schemes of the preconditioned sparse matrix canonical grid (P-SMCG) method are presented and discussed. The sparse matrix canonical grid method is applied to analyze electromagnetic scattering from three-dimensional random dielectric scatterers in conjunction with the generalized minimal residual (GMRES) method. In the end, these four schemes are applied to analyze electromagnetic scattering from three-dimensional random dielectric scatterers. The numerical results show that the presented methods is valid and quickly.
The investigation is very useful not only in further improving the sparse matrix canonical grid method for quickly analyzing electromagnetic scattering of complicated random scatterers, but also in improving the technology of remote sensing, investigating land mine detection and analyzing densely packed interconnects.
本文将SMCG方法应用到随机分布多目标电磁散射问题的分析中，并对SMCG方法加以改进，以达到对随机分布多目标电磁散射问题进行快速分析的目的。
论文首先运用SMCG方法对随机分布三维介质目标的电磁散射问题进行较为全面的分析和讨论，然后讨论了如何对SMCG方法进行预处理，提出了预处理SMCG方法的三种方案，接下来又讨论了将SMCG方法和广义最小余数法(GMRES)结合起来的方案，最后应用上面提出的四种方案对多个随机分布三维介质目标的电磁散射问题进行了分析。计算结果表明，本文提出的方法快速、有效。
本文的研究进一步改进了SMCG方法，使SMCG方法的计算效率得到了提高，为快速分析各种复杂的随机分布目标的电磁散射问题奠定了基础，为遥感技术的发展、电磁探矿的研究以及电路互联封装的分析提供了理论指导。
The problem of electromagnetic scattering is an important research domain in electromagnetics. It's very important to investigate mechanism of electromagnetic scattering and computation of electromagnetic field. The sparse matrix canonical grid (SMCG) method is a numerical method that was developed recently. This method has been applied to analyze electromagnetic scattering from random rough surface, two-dimensional random dielectric cylinders, microstrip structures and densely packed interconnects.
In this paper, the sparse matrix canonical grid method is applied to analyze electromagnetic scattering from three-dimensional random dielectric scatterers, and improved so that the problem of electromagnetic scattering from three-dimensional random dielectric scatterers could be quickly analyzed.
Firstly, the electromagnetic scattering from three-dimensional random dielectric scatterers is systematically analyzed and discussed by using sparse matrix canonical grid method in this paper. Then three schemes of the preconditioned sparse matrix canonical grid (P-SMCG) method are presented and discussed. The sparse matrix canonical grid method is applied to analyze electromagnetic scattering from three-dimensional random dielectric scatterers in conjunction with the generalized minimal residual (GMRES) method. In the end, these four schemes are applied to analyze electromagnetic scattering from three-dimensional random dielectric scatterers. The numerical results show that the presented methods is valid and quickly.
The investigation is very useful not only in further improving the sparse matrix canonical grid method for quickly analyzing electromagnetic scattering of complicated random scatterers, but also in improving the technology of remote sensing, investigating land mine detection and analyzing densely packed interconnects.
引文
[1] Enizinger P D,Raz S,Shapira M.Gabor Expansion and Aperture Theory.J Opt Soc AmA, 1986,3 (4):508-522.
[2] Enizinger P D,Haramaty Y, Felsen L B.Complex Rays for Radiation from Discreted Aperture Distribution.IEEE Trans, 1987,AP-35(9): 1037-1044.
[3] Maciel J J,Felsen L B.On Gaussian Discretization of Radiation from Distributed Aperture Fields.IEEE AP-S'87,Blasckburg,USA, 1987,404-407.
[4] 射线理论基础，成都电讯工程学院出版社，成都，1989。
[5] 阮颖铮，复射线理论及其应用，电子工业出版社，北京，1991。
[6] A Taflove. Computational Electrodynamics The Finite-Difference Time-Domain Method. Artech Hourse,Boston.London,1995:51-79.
[7] M Krumpholz, L P B Katechi. MRTD:new time-domain schemes based on
multiresolution analysis. IEEE Trans. On MTT,1996,44 (4):555-571.
[8] M Fujii,W J R Hoefer. Dispersion of time domain wavelet galerkin method based on daubechies'compactly supported scaling functions with three and four vanishing moments. IEEE Microwave and Guided Wave Lett.,2000,10(4):125-127.
[9] Guangwen Pan,M V Toupikov,B K Gilbert. On the use of Coifman intervallic wavelets in the method of moments for fast construction of wavelets sparsified matrices. IEEE Trans. On AP, 1999,47(7):1189-1200.
[10] 高本庆．时域有限差分法．北京：国防工业出版社，1995：108—134．
[11] J.S.Zhao, W.C.Chew, C.C.Lu, et al. Thin-stratified medium fast-multipole algorithm for solving microstrip structures. IEEE Trans. Microwave Theory Tech.1998, 46:395-403.
[12] E.Bleszynski, M. Bleszynski, and T.Jaroszewics. A fast integral-equation solver for electromagnetic scattering problems. IEEE AP-S, Seattle,WA, 1994, Vol. I:416-419.
[13] L.Tsang, C.H.Chan, and H.Sangani, Application of a Banded Matrix Iterative Approach to Monte Carlo Simulations of Scattering of Waves by Random Rough surface:TM Case. Microwave Opt. Technol. Lett., 1993, 6(2): 148-151.
[14] L.Tsang, C.H.Chan,and K.Pak,Monto Carlo Simulation of a Two-Dimentional Random Rough Surface Using the Sparse-Matrix Flat-surface Iterative Approach,Electron. Lett., 1993, 29(13):1153-1154.
[15] L.Tsang, C.H.Chan, K.Pak, H. Sangani, A.Ishimaru, and P.Phu, Monto Carlo Simulation of Large-Scale Composite Random Rough Surface Scattering Based on the Banded Matrix Iterative Approach, J. Opt. Soc. Am. Ser. A, 1994, 11(2):691-696.
[16] L.Tsang, C.H.Chan, and K.Pak, Backscattering Enhancement of a Tow-Dimentional Random Rough Surface (Three-Dimentional scattering) Based on Monte Carlo Simulations, J. Opt. Soc. Am. Ser. A, 1994, 11(2): 711-715.
[17] L.li, C.H.Chan, and L.Tsang, Numerical Simulation of Conical Diffraction of Tapered Electromagnetic Waves from Random Rough Surfaces and Applications
to Passive Remote Sensing, Radio Sci., 1994, 29: 587-598.
[18] L.Tsang and C.H.Chan, and H. Sangani, Monte-Carlo simulations of large-scale problems of random rough surface scattering and applications to grazing incidence with the BMIA/canonical grid method. IEEE Trans. Antennas Propagation,1995,43:851-859.
[19] C.H.Chan and L.Tsang. A Sparse-Matrix canonical-grid method for scattering by many scatterers. Microwave and Optical technology Letters, 1995:114-118.
[20] C.H.Chan,C.M.Lin, L.Tsang, et al. A Sparse-Matrix/canonical-grid method for analyzing microstrip structures. IEICE Trans. Electron.,1997, E80-C(11): 1354-1359.
[21] S.Q.Li, Y.Yu, C.H.Chan, et al. A sparse-matrix/canonical grid method for analyzing densely packed interconnects. IEEE Trans., Microwave Theory Tech.2001, 49:1221-1228.
[22] 孙玉发．分析三维随机介质目标散射问题的SMCG方法．中国科学技术大学学报(自然科学版)，2003，33(3)：345-350．
[23] L.Tsang, J.A.Kong, K.H,Ding, et al. Scattering of Electromagnetic Waves:Numerical Simulations. New York: John Wiley &Sons, Inc., 2001.
[2] Enizinger P D,Haramaty Y, Felsen L B.Complex Rays for Radiation from Discreted Aperture Distribution.IEEE Trans, 1987,AP-35(9): 1037-1044.
[3] Maciel J J,Felsen L B.On Gaussian Discretization of Radiation from Distributed Aperture Fields.IEEE AP-S'87,Blasckburg,USA, 1987,404-407.
[4] 射线理论基础，成都电讯工程学院出版社，成都，1989。
[5] 阮颖铮，复射线理论及其应用，电子工业出版社，北京，1991。
[6] A Taflove. Computational Electrodynamics The Finite-Difference Time-Domain Method. Artech Hourse,Boston.London,1995:51-79.
[7] M Krumpholz, L P B Katechi. MRTD:new time-domain schemes based on
multiresolution analysis. IEEE Trans. On MTT,1996,44 (4):555-571.
[8] M Fujii,W J R Hoefer. Dispersion of time domain wavelet galerkin method based on daubechies'compactly supported scaling functions with three and four vanishing moments. IEEE Microwave and Guided Wave Lett.,2000,10(4):125-127.
[9] Guangwen Pan,M V Toupikov,B K Gilbert. On the use of Coifman intervallic wavelets in the method of moments for fast construction of wavelets sparsified matrices. IEEE Trans. On AP, 1999,47(7):1189-1200.
[10] 高本庆．时域有限差分法．北京：国防工业出版社，1995：108—134．
[11] J.S.Zhao, W.C.Chew, C.C.Lu, et al. Thin-stratified medium fast-multipole algorithm for solving microstrip structures. IEEE Trans. Microwave Theory Tech.1998, 46:395-403.
[12] E.Bleszynski, M. Bleszynski, and T.Jaroszewics. A fast integral-equation solver for electromagnetic scattering problems. IEEE AP-S, Seattle,WA, 1994, Vol. I:416-419.
[13] L.Tsang, C.H.Chan, and H.Sangani, Application of a Banded Matrix Iterative Approach to Monte Carlo Simulations of Scattering of Waves by Random Rough surface:TM Case. Microwave Opt. Technol. Lett., 1993, 6(2): 148-151.
[14] L.Tsang, C.H.Chan,and K.Pak,Monto Carlo Simulation of a Two-Dimentional Random Rough Surface Using the Sparse-Matrix Flat-surface Iterative Approach,Electron. Lett., 1993, 29(13):1153-1154.
[15] L.Tsang, C.H.Chan, K.Pak, H. Sangani, A.Ishimaru, and P.Phu, Monto Carlo Simulation of Large-Scale Composite Random Rough Surface Scattering Based on the Banded Matrix Iterative Approach, J. Opt. Soc. Am. Ser. A, 1994, 11(2):691-696.
[16] L.Tsang, C.H.Chan, and K.Pak, Backscattering Enhancement of a Tow-Dimentional Random Rough Surface (Three-Dimentional scattering) Based on Monte Carlo Simulations, J. Opt. Soc. Am. Ser. A, 1994, 11(2): 711-715.
[17] L.li, C.H.Chan, and L.Tsang, Numerical Simulation of Conical Diffraction of Tapered Electromagnetic Waves from Random Rough Surfaces and Applications
to Passive Remote Sensing, Radio Sci., 1994, 29: 587-598.
[18] L.Tsang and C.H.Chan, and H. Sangani, Monte-Carlo simulations of large-scale problems of random rough surface scattering and applications to grazing incidence with the BMIA/canonical grid method. IEEE Trans. Antennas Propagation,1995,43:851-859.
[19] C.H.Chan and L.Tsang. A Sparse-Matrix canonical-grid method for scattering by many scatterers. Microwave and Optical technology Letters, 1995:114-118.
[20] C.H.Chan,C.M.Lin, L.Tsang, et al. A Sparse-Matrix/canonical-grid method for analyzing microstrip structures. IEICE Trans. Electron.,1997, E80-C(11): 1354-1359.
[21] S.Q.Li, Y.Yu, C.H.Chan, et al. A sparse-matrix/canonical grid method for analyzing densely packed interconnects. IEEE Trans., Microwave Theory Tech.2001, 49:1221-1228.
[22] 孙玉发．分析三维随机介质目标散射问题的SMCG方法．中国科学技术大学学报(自然科学版)，2003，33(3)：345-350．
[23] L.Tsang, J.A.Kong, K.H,Ding, et al. Scattering of Electromagnetic Waves:Numerical Simulations. New York: John Wiley &Sons, Inc., 2001.