矩量法分析三维目标的电磁散射
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摘要
电磁场理论及数值计算是研究电磁散射问题的基础，在目标雷达散射截面(RCS)计算、电磁散射特性分析、电子对抗、隐身设计及目标识别等方面都有重要的应用。
本文利用矩量法计算了三维导体目标、介质目标、涂层目标的雷达散射截面。首先采用三角形面元对物体表面几何形状进行模拟，然后建立满足边界条件的电场积分方程(EFIE)和磁场积分方程(MFIE)，将物体表面的等效电磁流用RWG矢量基函数表示，最后利用伽略金法(RWG矢量基函数既作为基函数又作为检验函数)将电磁场积分方程转化为矩阵方程求解未知电磁流系数，得到了表面的等效电磁流后，可以计算散射场和目标的雷达散射截面。
本文首先研究了导体目标的电磁散射。用RWG矢量基函数表示导体表面的感应电流，建立了导体表面的电场积分方程(EFIE)，分别计算了导电球、导体平板、导电立方体的RCS，首次研究了导电平板上有多个铆钉的电磁散射，分析了多个铆钉对目标总的RCS的影响。
其次，本文研究了介质目标的电磁散射，介绍了电磁场理论的一个重要的原理——等效原理。与导体目标一样，先建立介质目标的几何模型，然后用三角形面元模拟介质表面。与导体目标不同的是，在介质表面除等效电流外，还有等效磁流，因此需建立两个方程——电场积分方程(EFIE)和磁场积分方程(MFIE)来求解未知的电磁流系数。分别计算了均匀介质球、有限长均匀介质圆柱、均匀介质立方体的雷达散射截面。
本文最后研究了涂层目标的电磁散射，分析了涂层导体目标和涂层介质目标两种情况。对于涂层导体目标，将涂层外表面和导体外表面进行三角形面元剖分，在涂层外表面有等效电磁流，导体外表面仅有等效电流(无等效磁流)。将这些等效电磁流用RWG矢量基函数表示，需建立三个积分方程来求解未知的电磁流系数；对于涂层介质目标，将涂层外表面和内层介质外表面进行三角形面元剖分，在涂层外表面有等效电磁流，内层介质外表面也有等效电磁流，这时需建立四个积分方程来求解未知的电磁流系数。
矩量法不适于分析电大尺寸的物体，这种限制不是由于方法本身，而是
⑥
硕士学位论文
凡1入STER’5 TH卜515
由于计算机速度与存储能力的限制。目前主要采用高频近似方法来研究电尺
寸较大而形状相对规则的目标。但高频近似方法对于电尺寸大而形状很复杂
的散射体各部件之间的相对祸合处理起来有些麻烦且不很精确。将高频近似
方法和数值方法(如矩量法)相结合，是以后的发展趋势和研究方向。
The electromagnetic field theory and numerical calculation are the research basis of electromagnetic scattering problem,they have important applications in many aspects such as calculation of Radar Cross Section(RCS),analysis of electromagnetic scattering characteristic of target,electronic countermeasures,stealth design and identification of target.
The Moment Method is used to calculate the RCS of three-dimensional targets in this paper.These targets include conducting targets,dielectric targets and coat targets.Triangular patches are used to model the surface of the target,then Electric Field Integral Equation(EFIE) and Magnetic Field Integral Equation(MFIE) are built which satisfy the boundary conditions.The RWG vector base functions are used to denote equivalent electric current and magnetic current on the surface of the target.Finally use the Galerkin method (RWG vector base functions are basis function and test function) to transform integral equations into matrix equation.When obtain the equivalent electric current and magnetic current, we can calculate the scattering field and the RCS of the target.
First,the conducting targets'electromagnetic scattering is researched in this paper.The RWG vector base functions are used to denote inductive current on the surface of the conducting target.EFIE is built.The RCS of conducting sphere.conducting plate,conducting cube are calculated respectively,the electromagnetic scattering of multi-rivets on the conducting plate are researched the first time,and the impaction of multi-rivets to the total RCS is analyzed.
Then,the dielectric targets'electromagnetic scattering is researched.An important principle of electromagnetic field theory--equivalent theory is introduced.As well as the conducting target,the geometrical model of the dielectric target should first be built,then triangular patches are used to model the surface of the dielectric target.Different from the conducting target,there has not only equivalent electric current but also has equivalent magnetic current on
the surface of the dielectric target.So now should built two equations-EFIE and MFIE to obtain the unknown current coefficients.The RCS of dielectric sphere,dielectric cylinder,dielectric cube are calculated respectively.
Finally,the coat targets'electromagnetic scattering is researched. Two cases are analyzedxonducting target with coat and dielectric target with coat.For the conducting target with coat, triangular patches are used to model the surfaces of the coat and the conducting object.Now there have equivalent electric current and magnetic current on the surface of the coat,but only has equivalent electric current on the surface of the conducting object.The RWG vector base functions are used to denote equivalent electric currents and magnetic current.Three integral equations should be built to obtain the unknown current coefficients;for the dielectric object with coat,triangular patches are used to model the surfaces of the coat and the dielectric object.Now there have equivalent electric current and magnetic current not only on the surface of the coat but also on the surface of the dielectric object.This time four integral equations should be built to obtain the unknown current coefficients.
The Moment Method can not be used to analyze electrical-large size targets. Such limit is not due to the method itself,but is due to the limits of the speed and memory of computers.At present,we mainly use the high-frequency approximate method to analyze the electrical-large size target whose shape is relatively regular. But using the high-frequency approximate method to deal with the coupling of parts of electrical-large size target is troublesome as well as not accurate.Combining the Moment Method and the high-frequency approximate method is a development trend and study way in the future.
本文利用矩量法计算了三维导体目标、介质目标、涂层目标的雷达散射截面。首先采用三角形面元对物体表面几何形状进行模拟，然后建立满足边界条件的电场积分方程(EFIE)和磁场积分方程(MFIE)，将物体表面的等效电磁流用RWG矢量基函数表示，最后利用伽略金法(RWG矢量基函数既作为基函数又作为检验函数)将电磁场积分方程转化为矩阵方程求解未知电磁流系数，得到了表面的等效电磁流后，可以计算散射场和目标的雷达散射截面。
本文首先研究了导体目标的电磁散射。用RWG矢量基函数表示导体表面的感应电流，建立了导体表面的电场积分方程(EFIE)，分别计算了导电球、导体平板、导电立方体的RCS，首次研究了导电平板上有多个铆钉的电磁散射，分析了多个铆钉对目标总的RCS的影响。
其次，本文研究了介质目标的电磁散射，介绍了电磁场理论的一个重要的原理——等效原理。与导体目标一样，先建立介质目标的几何模型，然后用三角形面元模拟介质表面。与导体目标不同的是，在介质表面除等效电流外，还有等效磁流，因此需建立两个方程——电场积分方程(EFIE)和磁场积分方程(MFIE)来求解未知的电磁流系数。分别计算了均匀介质球、有限长均匀介质圆柱、均匀介质立方体的雷达散射截面。
本文最后研究了涂层目标的电磁散射，分析了涂层导体目标和涂层介质目标两种情况。对于涂层导体目标，将涂层外表面和导体外表面进行三角形面元剖分，在涂层外表面有等效电磁流，导体外表面仅有等效电流(无等效磁流)。将这些等效电磁流用RWG矢量基函数表示，需建立三个积分方程来求解未知的电磁流系数；对于涂层介质目标，将涂层外表面和内层介质外表面进行三角形面元剖分，在涂层外表面有等效电磁流，内层介质外表面也有等效电磁流，这时需建立四个积分方程来求解未知的电磁流系数。
矩量法不适于分析电大尺寸的物体，这种限制不是由于方法本身，而是
⑥
硕士学位论文
凡1入STER’5 TH卜515
由于计算机速度与存储能力的限制。目前主要采用高频近似方法来研究电尺
寸较大而形状相对规则的目标。但高频近似方法对于电尺寸大而形状很复杂
的散射体各部件之间的相对祸合处理起来有些麻烦且不很精确。将高频近似
方法和数值方法(如矩量法)相结合，是以后的发展趋势和研究方向。
The electromagnetic field theory and numerical calculation are the research basis of electromagnetic scattering problem,they have important applications in many aspects such as calculation of Radar Cross Section(RCS),analysis of electromagnetic scattering characteristic of target,electronic countermeasures,stealth design and identification of target.
The Moment Method is used to calculate the RCS of three-dimensional targets in this paper.These targets include conducting targets,dielectric targets and coat targets.Triangular patches are used to model the surface of the target,then Electric Field Integral Equation(EFIE) and Magnetic Field Integral Equation(MFIE) are built which satisfy the boundary conditions.The RWG vector base functions are used to denote equivalent electric current and magnetic current on the surface of the target.Finally use the Galerkin method (RWG vector base functions are basis function and test function) to transform integral equations into matrix equation.When obtain the equivalent electric current and magnetic current, we can calculate the scattering field and the RCS of the target.
First,the conducting targets'electromagnetic scattering is researched in this paper.The RWG vector base functions are used to denote inductive current on the surface of the conducting target.EFIE is built.The RCS of conducting sphere.conducting plate,conducting cube are calculated respectively,the electromagnetic scattering of multi-rivets on the conducting plate are researched the first time,and the impaction of multi-rivets to the total RCS is analyzed.
Then,the dielectric targets'electromagnetic scattering is researched.An important principle of electromagnetic field theory--equivalent theory is introduced.As well as the conducting target,the geometrical model of the dielectric target should first be built,then triangular patches are used to model the surface of the dielectric target.Different from the conducting target,there has not only equivalent electric current but also has equivalent magnetic current on
the surface of the dielectric target.So now should built two equations-EFIE and MFIE to obtain the unknown current coefficients.The RCS of dielectric sphere,dielectric cylinder,dielectric cube are calculated respectively.
Finally,the coat targets'electromagnetic scattering is researched. Two cases are analyzedxonducting target with coat and dielectric target with coat.For the conducting target with coat, triangular patches are used to model the surfaces of the coat and the conducting object.Now there have equivalent electric current and magnetic current on the surface of the coat,but only has equivalent electric current on the surface of the conducting object.The RWG vector base functions are used to denote equivalent electric currents and magnetic current.Three integral equations should be built to obtain the unknown current coefficients;for the dielectric object with coat,triangular patches are used to model the surfaces of the coat and the dielectric object.Now there have equivalent electric current and magnetic current not only on the surface of the coat but also on the surface of the dielectric object.This time four integral equations should be built to obtain the unknown current coefficients.
The Moment Method can not be used to analyze electrical-large size targets. Such limit is not due to the method itself,but is due to the limits of the speed and memory of computers.At present,we mainly use the high-frequency approximate method to analyze the electrical-large size target whose shape is relatively regular. But using the high-frequency approximate method to deal with the coupling of parts of electrical-large size target is troublesome as well as not accurate.Combining the Moment Method and the high-frequency approximate method is a development trend and study way in the future.
引文
[1]J.A.Stratton,Electromagnetic Theory. McGraw-Hill Book co.,1941
[2]R.F.Harrington,Field Computation by Moment Methods.New York,McMillan,1968
[3]波波维奇等著，金属天线与散射体分析。哈尔滨工业大学出版社，1999
[4]薛明华，何国瑜，矩量法计算三维金属体的散射截面。航空电子技术，No．2，pp．25-28，1996
[5]Robert C.Hansen,Geometric Theory of Diffraction.IEEE Press,1970
[6]G.L.James,Geometric Theory of Diffraction for Electromagnetic Waves.Peter peregrinus Ltd,England,1981
[7]S.W.Lee,Comparison of uniform asymptotic theory and Ufimtesv's EM edge diffraction. IEEE Trans, Antennas Propagat.,Ap-25,No.2,pp:162-170,March 1977
[8]F.A.Sikta,W.D.Burnside,T.T.Chu,and L.Peters,Jr.,First-order equivalent current and corner-diffraction scattering from flat plate structures. IEEE Trans, Antennas Propagat., Vol.31, No.4, pp:584-589,July 1983
[9]R.G.Kouyoumjian Lad P.H.Pathak,A uniform geometrical theory of deffraction for an edge in a perfectly conducting surface.Proc.IEEE,Vol.62,pp:1448-1461,Nov.1974
[10]S.W.Lee and G.A.Deschamps,A uniform asymptotic theory of EM diffraction by a curved wedge. IEEE Trans.Antennas propagat.,Vol.Ap-24,pp:25-34,January 1976
[11]刘圣民，电磁场的数值方法。华中理工大学出版社，1991
[12]工程电磁场数值分析，盛剑霓著。西安交通大学出版社，1991
[13]葛德彪，闫玉波，电磁波时域有限差分方法。西安电子科技大学出版社，2002
[14]SADASIVA M.RAO,DONALD R.WILTON, Electromagnetic scattering by surfaces of arbitrary shape. IEEE Trans.Antennas Propagat.,vol.AP-
30,No.3,pp.409-418,May.1982
[15]A.W.Glisson, On the development of numerical techniques for treating arbitrary surfaces.Ph. D. dissertation, Univ. Mississippi, 1978
[16]薛明华，何国瑜，低散射目标谐振区散射特性分析。北京航空航天大学学报，Vol．23，No．4，pp：507-510,August 1997
[17]M. Domingo, F. Pdvas, J. Perez, R. P. Torres, M. F. Catedra, Computation of the RCS of complex bodies modeled using NURBS surfaces.IEEE Antennas and Propagation Magazine, 1995, Vol. 37, No. 6, pp:36-47.
[18]克拉特E．F，雷达散射截面预估、测量和减缩。阮颖铮，陈海译。北京电子工业出版社，1988
[19]徐士良，C常用算法程序集。清华大学出版社，1995
[20]鲁述，徐鹏根，电磁场边值问题解析方法。武汉大学出版社，1992
[21]杨河林，目标雷达散射截面高频预估的研究。武汉大学硕士学位论文，1996
[22]R.A.Ross,Radar Cross Section of Rectangular Flat Plates as a Function of Aspect Angle. IEEE Trans.Antennas Propagat.,vol.Ap-14,No.3, pp.329-335,May 1966
[23]C.J.Reddy, M.D.Deshpande,C.R.Cockrell,and F.B.Beck, Fast RCS computation over a frequency band using method of moments in conjunction with asymptotic waveform evaluation technique. IEEE Trans.Antennas Propagat., vol.46, No.8, pp.1229-1233,August.1998
[24]Guo Jingli,Ji Yicai,Liu Qizhong,Analysis of the scattering of rivet on aircraft. Journal of electronics,Vol. 19,No.4,pp:434-437,oct.2002
[25]J.R.Mautz and R.F.Harrington,H-field,E-field,and combined field solutions for conducting body of revolution[J].AEU,1978,32:157-164
[26]J.R.Mautz and R.F.Harrington,A combined-source solution for radiation and scattering from a perfectly conducting body[J].IEEE Trans.,1979,AP-27:445-454.
[27]A.D.Yaghjian,Augmented electric and magnetic field integral equations[J].Radio science,1981,16:987-1001
[28]T.K.Sarkar and S.M.Rao,A simple technique for solving E-field integral equations for conducting bodies at internal resonances[J].IEEE Trans.,1982,AP-30:1250-1257
[29]孙玉发，徐善驾，一种求解目标内谐振时散射截面的有效方法。电波科学学报，Vol．16，No．1，March，2001
[30]傅君眉，冯恩信，高等电磁理论。西安交通大学出版社，2000
[31]楼仁海，符果行，肖书君，工程电磁理论。国防工业出版社，1991
[32]谢处方，吴先良，电磁散射理论与计算。安徽大学出版社，2002
[33]Xin-Qing Sheng,Jian-Ming Jin,Jiming Song,Cai-Cheng Lu,and Weng Cho Chew,On the Formulation of Hybrid Finite-Element and Boundary-Integral Methods for 3-D Scattering. IEEE Trans.Antennas Propagat.,vol.46,No.3,pp.303-311,March 1998
[34]Chaowei Su and Tapan K.Sarkar,Adaptive Multiscale Moment Method(AMMM) for Analysis of Scattering From Three-Dimensional perfectly Conducting Structures.IEEE Trans.Antennas Propagat.,vol.50,No.4,pp.444-450,April 2002
[35]Multilevel Fast Multipole Algorithm for Electromagnetic Scattering by Large Complex Objects.IEEE Trans.Antennas Propagat.,vol.45,No.10,pp.1488-1493,Oct.1997
[2]R.F.Harrington,Field Computation by Moment Methods.New York,McMillan,1968
[3]波波维奇等著，金属天线与散射体分析。哈尔滨工业大学出版社，1999
[4]薛明华，何国瑜，矩量法计算三维金属体的散射截面。航空电子技术，No．2，pp．25-28，1996
[5]Robert C.Hansen,Geometric Theory of Diffraction.IEEE Press,1970
[6]G.L.James,Geometric Theory of Diffraction for Electromagnetic Waves.Peter peregrinus Ltd,England,1981
[7]S.W.Lee,Comparison of uniform asymptotic theory and Ufimtesv's EM edge diffraction. IEEE Trans, Antennas Propagat.,Ap-25,No.2,pp:162-170,March 1977
[8]F.A.Sikta,W.D.Burnside,T.T.Chu,and L.Peters,Jr.,First-order equivalent current and corner-diffraction scattering from flat plate structures. IEEE Trans, Antennas Propagat., Vol.31, No.4, pp:584-589,July 1983
[9]R.G.Kouyoumjian Lad P.H.Pathak,A uniform geometrical theory of deffraction for an edge in a perfectly conducting surface.Proc.IEEE,Vol.62,pp:1448-1461,Nov.1974
[10]S.W.Lee and G.A.Deschamps,A uniform asymptotic theory of EM diffraction by a curved wedge. IEEE Trans.Antennas propagat.,Vol.Ap-24,pp:25-34,January 1976
[11]刘圣民，电磁场的数值方法。华中理工大学出版社，1991
[12]工程电磁场数值分析，盛剑霓著。西安交通大学出版社，1991
[13]葛德彪，闫玉波，电磁波时域有限差分方法。西安电子科技大学出版社，2002
[14]SADASIVA M.RAO,DONALD R.WILTON, Electromagnetic scattering by surfaces of arbitrary shape. IEEE Trans.Antennas Propagat.,vol.AP-
30,No.3,pp.409-418,May.1982
[15]A.W.Glisson, On the development of numerical techniques for treating arbitrary surfaces.Ph. D. dissertation, Univ. Mississippi, 1978
[16]薛明华，何国瑜，低散射目标谐振区散射特性分析。北京航空航天大学学报，Vol．23，No．4，pp：507-510,August 1997
[17]M. Domingo, F. Pdvas, J. Perez, R. P. Torres, M. F. Catedra, Computation of the RCS of complex bodies modeled using NURBS surfaces.IEEE Antennas and Propagation Magazine, 1995, Vol. 37, No. 6, pp:36-47.
[18]克拉特E．F，雷达散射截面预估、测量和减缩。阮颖铮，陈海译。北京电子工业出版社，1988
[19]徐士良，C常用算法程序集。清华大学出版社，1995
[20]鲁述，徐鹏根，电磁场边值问题解析方法。武汉大学出版社，1992
[21]杨河林，目标雷达散射截面高频预估的研究。武汉大学硕士学位论文，1996
[22]R.A.Ross,Radar Cross Section of Rectangular Flat Plates as a Function of Aspect Angle. IEEE Trans.Antennas Propagat.,vol.Ap-14,No.3, pp.329-335,May 1966
[23]C.J.Reddy, M.D.Deshpande,C.R.Cockrell,and F.B.Beck, Fast RCS computation over a frequency band using method of moments in conjunction with asymptotic waveform evaluation technique. IEEE Trans.Antennas Propagat., vol.46, No.8, pp.1229-1233,August.1998
[24]Guo Jingli,Ji Yicai,Liu Qizhong,Analysis of the scattering of rivet on aircraft. Journal of electronics,Vol. 19,No.4,pp:434-437,oct.2002
[25]J.R.Mautz and R.F.Harrington,H-field,E-field,and combined field solutions for conducting body of revolution[J].AEU,1978,32:157-164
[26]J.R.Mautz and R.F.Harrington,A combined-source solution for radiation and scattering from a perfectly conducting body[J].IEEE Trans.,1979,AP-27:445-454.
[27]A.D.Yaghjian,Augmented electric and magnetic field integral equations[J].Radio science,1981,16:987-1001
[28]T.K.Sarkar and S.M.Rao,A simple technique for solving E-field integral equations for conducting bodies at internal resonances[J].IEEE Trans.,1982,AP-30:1250-1257
[29]孙玉发，徐善驾，一种求解目标内谐振时散射截面的有效方法。电波科学学报，Vol．16，No．1，March，2001
[30]傅君眉，冯恩信，高等电磁理论。西安交通大学出版社，2000
[31]楼仁海，符果行，肖书君，工程电磁理论。国防工业出版社，1991
[32]谢处方，吴先良，电磁散射理论与计算。安徽大学出版社，2002
[33]Xin-Qing Sheng,Jian-Ming Jin,Jiming Song,Cai-Cheng Lu,and Weng Cho Chew,On the Formulation of Hybrid Finite-Element and Boundary-Integral Methods for 3-D Scattering. IEEE Trans.Antennas Propagat.,vol.46,No.3,pp.303-311,March 1998
[34]Chaowei Su and Tapan K.Sarkar,Adaptive Multiscale Moment Method(AMMM) for Analysis of Scattering From Three-Dimensional perfectly Conducting Structures.IEEE Trans.Antennas Propagat.,vol.50,No.4,pp.444-450,April 2002
[35]Multilevel Fast Multipole Algorithm for Electromagnetic Scattering by Large Complex Objects.IEEE Trans.Antennas Propagat.,vol.45,No.10,pp.1488-1493,Oct.1997