目标电磁散射的混合算法研究
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摘要
本文研究了目标电磁散射的混合算法,提高电大目标电磁散射的计算效率,主要工作和结果包括:
1、介绍了计算目标电磁散射的基本方法,着重讨论了矩量法(MoM)、物理光学法(PO)和迭代物理光学法(IPO),并给出每一种方法的数值算例。
2、讨论了MoM计算一维粗糙面的方法。研究了基于电流基的二维混合算法,推导出此混合算法的计算公式,并采用此混合算法计算了一维粗糙面上目标的复合散射截面。通过不同的数值算例讨论了影响此混合方法的主要因素。
3、推导出基于三角面元的PO的基本公式,在此基础上把目标划分成物理光学法区域和矩量法区域。考虑电流连续性,结合基于RWG基的矩量法,得到了用于计算任意三维目标电磁散射的混合算法公式,并计算了组合体目标的雷达散射截面。混合法和MoM的数值算例进行了比较,结果显示混合算法具有更高的计算效率。
In this thesis, the hybrid algorithm for electromagnetic (EM) scattering of the object is studied, which improved the calculated efficiency of the electric large target. The main work and results are as follows:
1. The basic method of calculating electromagnetic scattering is discussed. The method of moment (MoM), physical optics method (PO) and iterative physical optics method (IPO) are highlighted. The numerical examples of each method are given.
2. The way to calculate the EM scattering of one dimensional rough surface by MoM is discussed. The two-dimensional hybrid current-based method is presented in detail, and the formulation of this hybrid algorithm is derived. Then the bistatic scattering of an object located on one dimensional rough surface is computed by this hybrid algorithm. The major influencing factors of this hybrid method are discussed in detail by the numerical results.
3. The formulation of PO based on triangular facets is derived, and the object is subdivided into MoM region and PO region further. The hybrid expressions for the EM scattering from the arbitrary shape three-dimensional target are obtained by using the combination of PO and MoM. For the purpose of the continuity of currents, the MoM is selected the RWG basis function. At last, the radar cross section (RCS) of the composite target is computed by the proposed hybrid method. Numerical results are compared with the MoM results and shows that the proposed scheme is more efficient.
1、介绍了计算目标电磁散射的基本方法,着重讨论了矩量法(MoM)、物理光学法(PO)和迭代物理光学法(IPO),并给出每一种方法的数值算例。
2、讨论了MoM计算一维粗糙面的方法。研究了基于电流基的二维混合算法,推导出此混合算法的计算公式,并采用此混合算法计算了一维粗糙面上目标的复合散射截面。通过不同的数值算例讨论了影响此混合方法的主要因素。
3、推导出基于三角面元的PO的基本公式,在此基础上把目标划分成物理光学法区域和矩量法区域。考虑电流连续性,结合基于RWG基的矩量法,得到了用于计算任意三维目标电磁散射的混合算法公式,并计算了组合体目标的雷达散射截面。混合法和MoM的数值算例进行了比较,结果显示混合算法具有更高的计算效率。
In this thesis, the hybrid algorithm for electromagnetic (EM) scattering of the object is studied, which improved the calculated efficiency of the electric large target. The main work and results are as follows:
1. The basic method of calculating electromagnetic scattering is discussed. The method of moment (MoM), physical optics method (PO) and iterative physical optics method (IPO) are highlighted. The numerical examples of each method are given.
2. The way to calculate the EM scattering of one dimensional rough surface by MoM is discussed. The two-dimensional hybrid current-based method is presented in detail, and the formulation of this hybrid algorithm is derived. Then the bistatic scattering of an object located on one dimensional rough surface is computed by this hybrid algorithm. The major influencing factors of this hybrid method are discussed in detail by the numerical results.
3. The formulation of PO based on triangular facets is derived, and the object is subdivided into MoM region and PO region further. The hybrid expressions for the EM scattering from the arbitrary shape three-dimensional target are obtained by using the combination of PO and MoM. For the purpose of the continuity of currents, the MoM is selected the RWG basis function. At last, the radar cross section (RCS) of the composite target is computed by the proposed hybrid method. Numerical results are compared with the MoM results and shows that the proposed scheme is more efficient.
引文
[1] D. P. Bouche, F. A. Molinet, and Mittra,“Asymptotic and hybrid techniques for electromagnetics scattering”, Proc. IEEE, 1993, 81(12): 1658-1684.
[2] E. F. Knott,“A progression of high-frequency RCS prediction techniques”, Proc. IEEE, 1985, 73(2): 252-264.
[3] P.h. pathak,“High-frequency techniques for antenna analysis”, Proc. IEEE, 1992, 80(1): 44-65.
[4] G. A. Thiele and T. M. Newhouse,“Hybrid technique for combining moment methods with the geometrical theory of diffraction”, IEEE Trans. On Antennas and Propagat, 1975, 23(1): 551-558.
[5] W. D. Burnside, C. L. Yu, and R. J. Marhefka,“A technique to combine the geometrical theory of diffraction and the moment method”, IEEE Trans. On Antennas and Propagat, 1975, 28(11): 831-839.
[6] J. N. Sahalos and G. A. Teilee,“On the application of the GTD-MM technique and its limitations”, IEEE Trans. On Antennas and Propagat,1981, 29(5): 780-786.
[7] E. P. Ekelman, and G. A. Thiele ,“A hybrid technique for combining the moment method threatment of wire antennas with the GTD for curved surfaces”, IEEE Trans. On Antennas and Propagat., 1980,28(11): 831-839.
[8] P. H. Pathak, W. D. Burnside, and R. J. Marhefka,“A uniform GTD analysis of the diffraction of eletromagnetic waves by a smooth convex surface,”IEEE Trans. Von Antennas and Propagat., 1980,28(9): 631-642.
[9] M. Martin, and M. F. Catedra,“A study of a monopole arbitrarily located on a disk using hybrid MM/GTD thchniques”,IEEE Trans. On Antennas and Propagat., 1987, 35(3): 287-292.
[10] G. A. Thiele,“Overview of selected hybrid methods in radiating system analysis”, Proc. IEEE, 1992, 80(1): 67-78.
[11] J. Silvestro,“Scattering from slot near conducting wedge using hybrid method of moments/geometrical theory of diffraction: TE case”, Electronics Letters, 1992, 8(11): 1055-1057.
[12] L. P. Theron, D. B. Davidson, and U. Jakobus,“Extensions to the Hybrid Method of Moments/Uniform GTD Formulation for Sources Located Close to a Smooth Convex Surface,”IEEE Trans. On Antennas and Propagat., 2000, 48(6): 940-945.
[13] V. A. Fock,“Electromagnetic Diffraction and Propagation Problems”, International Series of Monographs on Electromagnetic Waves, Vol. 1, Oxford: Pergamon, 1965.
[14] P. Y. Ufimtsev,“Elementary edge waves and the physical theory of diffraction”, Electromagnetics, 1991, 11(6): 125-160
[15] L. N. Medgyesi-Mitschang and D.-S. Wand,“Hybrid methods for analysis of complex scatterers”, Proc.IEEE, 1989, 77(5):770-779.
[16] L. N. Medgyesi-Mitschang, and D.-S. Wand,“Hybrid methods in computational eletromagnetics: A review”, Computer Physics Communications, 1991, 68(4): 76-94.
[17] L. N. Medgyesi-Mitschang, D.S. Wang,“Hybrid solution for scattering from perfectly conducting bodies of revolution”IEEE Trans on Antennas and Propagat.,1983, 34(4): 570-583.
[18] L. N. Medgyesi-Mitschang, D.-S. Wand,“Hybrid solutions for large-impedance coated bodies of revolution”, IEEE Trans on Antennas and Propagat., 1986, 34(11): 1319-1329.
[19] H. J. Bilow,“Scattering by an infinite wedge with tensor impedance boundary conditions– A moment method/physical optics solution for currents”, IEEE Trans on Antennas and Propagat., 1991, 39(6): 767-773.
[20] D. S. Wang,“Current-based hybrid analysis for surface-wave effects on large scatters”, IEEE Trans. On Antennas and Propagat., 1991, 39(6): 839-850.
[21] C. S. Kim and Y. Rahmat-sammii,“Low profile antenna study using the physical optics hybrid method”, Proc. IEEE Int. Symp. Antennas Propagat., June 1991, Lodon, Ont, Canada, 1350-1353.
[22] L. N. Medgyesi-Mitschang, and J. M. Putnam,“Hybrid formulation for arbitrary 3-D bodies”, in 10th Annu. Rev. of Progress in Applied Computational Electromagnetics, ACES Conf., Monterey, CA, Mar. 1994,2: 267-274.
[23] U. Jakobus, J. Christ, and F. M. Lanstorfer,“PO-MoM analysis of cavity-backed antennas”, in IEE 8th Int. Conf. Antennas Propgat. Edinburgh, Conf. Publication Number 370, Apr. 1993: 111-114.
[24] U. Jakobus, and F. M. Landstorfer,“Improved PO-MM hybrid formulation for scattering from three dimensional perfectly conducting bodies of arbitrary shape”, IEEE Trans. On Antennas and Propagat, 1995, 43(1): 162-169.
[25] U. Jakobus, and F. M. Landstorfer,“Improvement of the PO-MoM hybrid method by accounting for effects of perfectly conducting wedges”, IEEE Trans. On Antennas and Propagat., 1995, 43(6):1123-1129.
[26] U. Jakobus, and F. M. Landstorfer,“Application of fock-currents for curved convex surfaces within the framework of a current-based hybrid method”, Third international Conference.On Computation in Electromagnetics, 1996:415-420
[27] R. E. Hodges, and Y. Rahmat-Samii,“An iterative current-based hybrid method for complex structures”, IEEE Trans. On Antennas and Propagat., 1997, 43(2): 265-276.
[28] F. Obelleiro, J. M. Taboada, J. L. Rodrnguez, J. O. Rubinos, and A.M. Arias,“Hybrid moment-method physical-optics formulation for modeling the electronmagnetic behavior of on-board antennas”, Microwave Opt. Tech. Lett., 2000, 27(1): 88-93.
[29] J. M. Taboada, and F. Obelleiro,“Including multibounce effects in the moment-method physical-optics method,”Microwave Opt. Tech. Lett., 2002, 32(4): 435-439.
[30] T. J. Cui, W. B. W. Hong, Z. C. Hao and X. X. Yin,“A two-region model for the fast implementation of the method of moments”, Proceeding of IEEE AP-S, Columbus, Ohio, June 2003,2(6):330-333.
[31] U. Jakobus and F. M. Landstorfer,“A combination of current and ray-based techniques for the efficient anlysis of electrically large scattering problem”, in Conference Proceedings of the 13th Annual Review of Progress in Applied Computational Electromagnetics, Mar. 1997: 748-755.
[32] Johan Edlund,“A Parallel, Iterative Method of Moments and Physical Optics Hybrid Solver for Arbitrary Surfaces”, Dissertation for the degree of Licentiate of Technology in Numerical Analysis at Uppsala University,2001.
[33] J M. Taboada, P. Obelleiro, and J. L. Rodrguez,“Improvement of the hybrid moment-method-physical-optics method through a novel evaluation of the physical optics operator”, Microwave Opt. Tech. Lett, 2001, 30(3): 357-363.
[34]华夷和,徐金平,牛臻戈,“FAFFA加速的PO-MM研究复杂金属载体上的线天线的电磁特性”,电子学报增刊,2003,31(12A):2045-2049。
[35] Jorgensen E., Meincke P., and Breinbjerg O.,“A hybrid PO-higher-order hierarchical MoM formulation using curvilinear geometry modeling”, Antennas and Propagation Society International Symposium, 2003. IEEE, June 2003,4:98-101.
[36] X. C. Wei, and E. P. Li,“Wide-Band EMC Analysis of On-platform Antennas UsingImpedance-Matrix Interpolation With the Moment Method-Physical Method”, IEEE Transactions on Electromagnetic Compatibility, 2003, 45(3):552-556.
[37] J.H.Richmond,“A wire-grid model for scattering by conducting bodies”, IEEETrans. On Antennas Propagat., 1966, 14(6): 786.
[38] E.H.Newman, and D.M.Pozar,“Electromagnetic modeling of composite wire/surface geometries”, IEEE Trans. On Antennas Propagat., 1978, 26(6): 746-754.
[39] A.W.Glisson, and D.R.Wilton.,“Simple and efficient numerical methods for problems of electro- magnetic radiation and scattering from surfaces”, IEEE Trans. On Antennas Propagat., 1980, 28(5): 593- 603.
[40] S.M.Rao, D.R.Wilton, and A.W.Glisson.,“Electromagnetic scattering by surfaces of arbitrary shape”, IEEE Trans. Antennas Propagat., 1982, 30(3): 409-418.
[41] J.M.Song, and W.C.Chew.,“Moment method solutions using parametric geometry”, Journal of Electromagnetic Waves and Appl., 1995, 9(1/2): 71-83.
[42] G.Liu and S.D.Gedney.,“High-order method of moment solution for penetrable scatterers”, IEEE AP-S Int. Symp. Dig, 2001, 4: 356-359.
[43]麻军,“矩量法及其并行计算在粗糙面和目标散射中的应用”,硕士学位论文,西安:西安电子科技大学,2003.
[44] C. C. Lu and W. C. Chew. Fast far field approximation for calculating the RCS of large objects. Microwave and Opt. Tech. Lett. , 1995, 8(5): 238-241.
[45] R.D.Graglia.,“On the numerical integration of the linear shape functions times the 3-D Green's function or its gradient on a plane triangle.”,IEEE Trans. On Antennas Propagat., 1993, 41(10): 1448-1455.
[46]谢处方,饶克谨编.电磁场与电磁波(第二版)[M].高等教育出版社.1998
[47] Timothy Griesser, and Constantine A. Balanis,“Backscattering analysis of dihereal corner relector using physical optics and the physical theory of diffraction”,IEEE Trans. On Antennas and Propogat., 1987,35(10):1137-1147
[48] Eugrne F. Knott,“Rcs reduction of dihefral corners. IEEE Trans.”, On Antennas Propagat.,1977,25(5):406-409.
[49] W.C.Anderson,“Consequences of Nonorthogonality on the Scattering Properties of Dihedral Reflectors”,1987,35(10):1154-1160.
[50] Andrade L. A , Nohara, E.L., Peixoto G. G.,and Martin I. M.,“Backscattering Analysis of Flat Plate and Dihedral Corner Reflectors using PO and Comparison with RCS Measurements in Anechoic Chamber”, IEEE MTT-S International 2003,vol(2):725-730.
[51] Timothy Griesser, and Constantine A. Balanis,“Dihedral Corner Reflector Backscatter Using Higher Order Reflections and Diffractions”,IEEE Trans, 1987,35(11):1235-1248.
[52] Hongcheng Yin, and Peikang Huang.“Po Analysis for RCS of Dihedral Corner Reflectors Coated with Chiral Material”,2002 3th Internatinal Confer on Microwave and Millimeter Wave Technology Proceedings:560-564.
[53] Michael A. Richards,and Keith D.Trott,“A Physical Optics Approximation to the Rande Profile Signature of a Dihedral Corner Reflector”, IEEE Trans 1995 37(3):478-482.
[54] Shuen-Yih Wang, and Shyh-Kang Jeng,“A Compact RCS Formula for a Dihedral Corner Reflecor at Arbitrary Aspect Angels”, IEEE Trans 1998,46(7):1112-1113.
[55] Femando Obelleiro-Basteiro,Jose Luis Rodriguez, and Robert J. Burkholder,“An iterative physical optics approach for analyzing the electromagnetic scattering by large open-ended cavities”,IEEE Trans. Antennas Propagat.,1995,43(4):356-361.
[56] Louis N. Medgyesi-Mitschang, and Y. Wang,“Hybrid solution for scattering from large bodies of revolution with material discontinuities and coatings,”IEEE Trans. On Antennas Propag., 1984,32(7):717-723.
[57]崔索民,“混合法和等效边缘电磁流法及其在电磁散射中的应用”,博士学位论文,西安:西安电子科技大学,1995.
[58]刘江涛,“电磁散射特性分析的无网格法研究”,硕士学位论文,西安:西安子科技大学,2008.
[59] J.M.Lopez-Sanchez,“An electromagnetic scattering model for multiple tree trunks above atilted rough ground plane”, IEEE Trans. On Geo-science and Remote Sensing., 1999, 37(2): 659-667
[60] J.T. Johnson,“A numerical study of scattering from an object above a rough surface”, IEEE Trans. On Antennas and Propagat., 2002,50(10): 1361-1367.
[61] T.Chiu,K. Sarabandi,“Electromagnetic scattering Interaction between a dielectric cylinder and slightly Rough surface“, IEEE Trans. On Antenna and Propagat., 1999,47(5): 902-913.
[62]李中新,金亚秋.数值模拟低掠角入射海面与船目标的双站散射.电波科学学报,2001,16(2): 231-240.
[63]陈铭,“基于NURBS曲面建模的物理光学方法及混合方法研究”,博士学位论文,西安:西安电子科技大学,2006.
[2] E. F. Knott,“A progression of high-frequency RCS prediction techniques”, Proc. IEEE, 1985, 73(2): 252-264.
[3] P.h. pathak,“High-frequency techniques for antenna analysis”, Proc. IEEE, 1992, 80(1): 44-65.
[4] G. A. Thiele and T. M. Newhouse,“Hybrid technique for combining moment methods with the geometrical theory of diffraction”, IEEE Trans. On Antennas and Propagat, 1975, 23(1): 551-558.
[5] W. D. Burnside, C. L. Yu, and R. J. Marhefka,“A technique to combine the geometrical theory of diffraction and the moment method”, IEEE Trans. On Antennas and Propagat, 1975, 28(11): 831-839.
[6] J. N. Sahalos and G. A. Teilee,“On the application of the GTD-MM technique and its limitations”, IEEE Trans. On Antennas and Propagat,1981, 29(5): 780-786.
[7] E. P. Ekelman, and G. A. Thiele ,“A hybrid technique for combining the moment method threatment of wire antennas with the GTD for curved surfaces”, IEEE Trans. On Antennas and Propagat., 1980,28(11): 831-839.
[8] P. H. Pathak, W. D. Burnside, and R. J. Marhefka,“A uniform GTD analysis of the diffraction of eletromagnetic waves by a smooth convex surface,”IEEE Trans. Von Antennas and Propagat., 1980,28(9): 631-642.
[9] M. Martin, and M. F. Catedra,“A study of a monopole arbitrarily located on a disk using hybrid MM/GTD thchniques”,IEEE Trans. On Antennas and Propagat., 1987, 35(3): 287-292.
[10] G. A. Thiele,“Overview of selected hybrid methods in radiating system analysis”, Proc. IEEE, 1992, 80(1): 67-78.
[11] J. Silvestro,“Scattering from slot near conducting wedge using hybrid method of moments/geometrical theory of diffraction: TE case”, Electronics Letters, 1992, 8(11): 1055-1057.
[12] L. P. Theron, D. B. Davidson, and U. Jakobus,“Extensions to the Hybrid Method of Moments/Uniform GTD Formulation for Sources Located Close to a Smooth Convex Surface,”IEEE Trans. On Antennas and Propagat., 2000, 48(6): 940-945.
[13] V. A. Fock,“Electromagnetic Diffraction and Propagation Problems”, International Series of Monographs on Electromagnetic Waves, Vol. 1, Oxford: Pergamon, 1965.
[14] P. Y. Ufimtsev,“Elementary edge waves and the physical theory of diffraction”, Electromagnetics, 1991, 11(6): 125-160
[15] L. N. Medgyesi-Mitschang and D.-S. Wand,“Hybrid methods for analysis of complex scatterers”, Proc.IEEE, 1989, 77(5):770-779.
[16] L. N. Medgyesi-Mitschang, and D.-S. Wand,“Hybrid methods in computational eletromagnetics: A review”, Computer Physics Communications, 1991, 68(4): 76-94.
[17] L. N. Medgyesi-Mitschang, D.S. Wang,“Hybrid solution for scattering from perfectly conducting bodies of revolution”IEEE Trans on Antennas and Propagat.,1983, 34(4): 570-583.
[18] L. N. Medgyesi-Mitschang, D.-S. Wand,“Hybrid solutions for large-impedance coated bodies of revolution”, IEEE Trans on Antennas and Propagat., 1986, 34(11): 1319-1329.
[19] H. J. Bilow,“Scattering by an infinite wedge with tensor impedance boundary conditions– A moment method/physical optics solution for currents”, IEEE Trans on Antennas and Propagat., 1991, 39(6): 767-773.
[20] D. S. Wang,“Current-based hybrid analysis for surface-wave effects on large scatters”, IEEE Trans. On Antennas and Propagat., 1991, 39(6): 839-850.
[21] C. S. Kim and Y. Rahmat-sammii,“Low profile antenna study using the physical optics hybrid method”, Proc. IEEE Int. Symp. Antennas Propagat., June 1991, Lodon, Ont, Canada, 1350-1353.
[22] L. N. Medgyesi-Mitschang, and J. M. Putnam,“Hybrid formulation for arbitrary 3-D bodies”, in 10th Annu. Rev. of Progress in Applied Computational Electromagnetics, ACES Conf., Monterey, CA, Mar. 1994,2: 267-274.
[23] U. Jakobus, J. Christ, and F. M. Lanstorfer,“PO-MoM analysis of cavity-backed antennas”, in IEE 8th Int. Conf. Antennas Propgat. Edinburgh, Conf. Publication Number 370, Apr. 1993: 111-114.
[24] U. Jakobus, and F. M. Landstorfer,“Improved PO-MM hybrid formulation for scattering from three dimensional perfectly conducting bodies of arbitrary shape”, IEEE Trans. On Antennas and Propagat, 1995, 43(1): 162-169.
[25] U. Jakobus, and F. M. Landstorfer,“Improvement of the PO-MoM hybrid method by accounting for effects of perfectly conducting wedges”, IEEE Trans. On Antennas and Propagat., 1995, 43(6):1123-1129.
[26] U. Jakobus, and F. M. Landstorfer,“Application of fock-currents for curved convex surfaces within the framework of a current-based hybrid method”, Third international Conference.On Computation in Electromagnetics, 1996:415-420
[27] R. E. Hodges, and Y. Rahmat-Samii,“An iterative current-based hybrid method for complex structures”, IEEE Trans. On Antennas and Propagat., 1997, 43(2): 265-276.
[28] F. Obelleiro, J. M. Taboada, J. L. Rodrnguez, J. O. Rubinos, and A.M. Arias,“Hybrid moment-method physical-optics formulation for modeling the electronmagnetic behavior of on-board antennas”, Microwave Opt. Tech. Lett., 2000, 27(1): 88-93.
[29] J. M. Taboada, and F. Obelleiro,“Including multibounce effects in the moment-method physical-optics method,”Microwave Opt. Tech. Lett., 2002, 32(4): 435-439.
[30] T. J. Cui, W. B. W. Hong, Z. C. Hao and X. X. Yin,“A two-region model for the fast implementation of the method of moments”, Proceeding of IEEE AP-S, Columbus, Ohio, June 2003,2(6):330-333.
[31] U. Jakobus and F. M. Landstorfer,“A combination of current and ray-based techniques for the efficient anlysis of electrically large scattering problem”, in Conference Proceedings of the 13th Annual Review of Progress in Applied Computational Electromagnetics, Mar. 1997: 748-755.
[32] Johan Edlund,“A Parallel, Iterative Method of Moments and Physical Optics Hybrid Solver for Arbitrary Surfaces”, Dissertation for the degree of Licentiate of Technology in Numerical Analysis at Uppsala University,2001.
[33] J M. Taboada, P. Obelleiro, and J. L. Rodrguez,“Improvement of the hybrid moment-method-physical-optics method through a novel evaluation of the physical optics operator”, Microwave Opt. Tech. Lett, 2001, 30(3): 357-363.
[34]华夷和,徐金平,牛臻戈,“FAFFA加速的PO-MM研究复杂金属载体上的线天线的电磁特性”,电子学报增刊,2003,31(12A):2045-2049。
[35] Jorgensen E., Meincke P., and Breinbjerg O.,“A hybrid PO-higher-order hierarchical MoM formulation using curvilinear geometry modeling”, Antennas and Propagation Society International Symposium, 2003. IEEE, June 2003,4:98-101.
[36] X. C. Wei, and E. P. Li,“Wide-Band EMC Analysis of On-platform Antennas UsingImpedance-Matrix Interpolation With the Moment Method-Physical Method”, IEEE Transactions on Electromagnetic Compatibility, 2003, 45(3):552-556.
[37] J.H.Richmond,“A wire-grid model for scattering by conducting bodies”, IEEETrans. On Antennas Propagat., 1966, 14(6): 786.
[38] E.H.Newman, and D.M.Pozar,“Electromagnetic modeling of composite wire/surface geometries”, IEEE Trans. On Antennas Propagat., 1978, 26(6): 746-754.
[39] A.W.Glisson, and D.R.Wilton.,“Simple and efficient numerical methods for problems of electro- magnetic radiation and scattering from surfaces”, IEEE Trans. On Antennas Propagat., 1980, 28(5): 593- 603.
[40] S.M.Rao, D.R.Wilton, and A.W.Glisson.,“Electromagnetic scattering by surfaces of arbitrary shape”, IEEE Trans. Antennas Propagat., 1982, 30(3): 409-418.
[41] J.M.Song, and W.C.Chew.,“Moment method solutions using parametric geometry”, Journal of Electromagnetic Waves and Appl., 1995, 9(1/2): 71-83.
[42] G.Liu and S.D.Gedney.,“High-order method of moment solution for penetrable scatterers”, IEEE AP-S Int. Symp. Dig, 2001, 4: 356-359.
[43]麻军,“矩量法及其并行计算在粗糙面和目标散射中的应用”,硕士学位论文,西安:西安电子科技大学,2003.
[44] C. C. Lu and W. C. Chew. Fast far field approximation for calculating the RCS of large objects. Microwave and Opt. Tech. Lett. , 1995, 8(5): 238-241.
[45] R.D.Graglia.,“On the numerical integration of the linear shape functions times the 3-D Green's function or its gradient on a plane triangle.”,IEEE Trans. On Antennas Propagat., 1993, 41(10): 1448-1455.
[46]谢处方,饶克谨编.电磁场与电磁波(第二版)[M].高等教育出版社.1998
[47] Timothy Griesser, and Constantine A. Balanis,“Backscattering analysis of dihereal corner relector using physical optics and the physical theory of diffraction”,IEEE Trans. On Antennas and Propogat., 1987,35(10):1137-1147
[48] Eugrne F. Knott,“Rcs reduction of dihefral corners. IEEE Trans.”, On Antennas Propagat.,1977,25(5):406-409.
[49] W.C.Anderson,“Consequences of Nonorthogonality on the Scattering Properties of Dihedral Reflectors”,1987,35(10):1154-1160.
[50] Andrade L. A , Nohara, E.L., Peixoto G. G.,and Martin I. M.,“Backscattering Analysis of Flat Plate and Dihedral Corner Reflectors using PO and Comparison with RCS Measurements in Anechoic Chamber”, IEEE MTT-S International 2003,vol(2):725-730.
[51] Timothy Griesser, and Constantine A. Balanis,“Dihedral Corner Reflector Backscatter Using Higher Order Reflections and Diffractions”,IEEE Trans, 1987,35(11):1235-1248.
[52] Hongcheng Yin, and Peikang Huang.“Po Analysis for RCS of Dihedral Corner Reflectors Coated with Chiral Material”,2002 3th Internatinal Confer on Microwave and Millimeter Wave Technology Proceedings:560-564.
[53] Michael A. Richards,and Keith D.Trott,“A Physical Optics Approximation to the Rande Profile Signature of a Dihedral Corner Reflector”, IEEE Trans 1995 37(3):478-482.
[54] Shuen-Yih Wang, and Shyh-Kang Jeng,“A Compact RCS Formula for a Dihedral Corner Reflecor at Arbitrary Aspect Angels”, IEEE Trans 1998,46(7):1112-1113.
[55] Femando Obelleiro-Basteiro,Jose Luis Rodriguez, and Robert J. Burkholder,“An iterative physical optics approach for analyzing the electromagnetic scattering by large open-ended cavities”,IEEE Trans. Antennas Propagat.,1995,43(4):356-361.
[56] Louis N. Medgyesi-Mitschang, and Y. Wang,“Hybrid solution for scattering from large bodies of revolution with material discontinuities and coatings,”IEEE Trans. On Antennas Propag., 1984,32(7):717-723.
[57]崔索民,“混合法和等效边缘电磁流法及其在电磁散射中的应用”,博士学位论文,西安:西安电子科技大学,1995.
[58]刘江涛,“电磁散射特性分析的无网格法研究”,硕士学位论文,西安:西安子科技大学,2008.
[59] J.M.Lopez-Sanchez,“An electromagnetic scattering model for multiple tree trunks above atilted rough ground plane”, IEEE Trans. On Geo-science and Remote Sensing., 1999, 37(2): 659-667
[60] J.T. Johnson,“A numerical study of scattering from an object above a rough surface”, IEEE Trans. On Antennas and Propagat., 2002,50(10): 1361-1367.
[61] T.Chiu,K. Sarabandi,“Electromagnetic scattering Interaction between a dielectric cylinder and slightly Rough surface“, IEEE Trans. On Antenna and Propagat., 1999,47(5): 902-913.
[62]李中新,金亚秋.数值模拟低掠角入射海面与船目标的双站散射.电波科学学报,2001,16(2): 231-240.
[63]陈铭,“基于NURBS曲面建模的物理光学方法及混合方法研究”,博士学位论文,西安:西安电子科技大学,2006.