旋转对称体时域电磁散射特性的分析
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摘要
超宽带天线、目标识别以及合成孔径雷达的发展急需一种能够对电大尺寸目标的时域宽频带电磁散射进行求解的算法。利用轴对称性可以将电大的旋转对称体电磁问题转化为求解每个具有小规模矩阵方程的问题,即原问题的傅里叶模式,从而可以大大提高计算效率,并且减少内存需求。本文在频域旋转对称矩量法的基础上,发展了时域积分方程方法分析旋转对称体时域电磁散射特性的数值方法。
本文主要研究理想金属旋转对称体在自由空间环境下的时域电磁特性问题。首先通过麦克斯韦方程、辅助位函数、等效原理和边界条件建立了电流的时域电场磁场积分方程。然后再利用旋转对称性,将等效电流空间部分展开为关于φ的傅立叶级数形式和关于t的分段函数形式。其次对时间变量使用加权拉盖尔多项式作为时间基函数进行函数展开。而对于时域入射场本文选用的是高斯平面波,高斯平面波具有有限的频谱带宽有利于数值计算的快速收敛。
基函数和测试函数确定之后,将它们代入时域磁场电场积分方程中,然后对积分方程分别进行空间测试和时间测试。接着进行离散化过程生成阻抗矩阵和激励向量,最后形成了矩阵方程。求解过程中使用时域阶数步进法求得单个傅里叶模式各个阶数的电流系数,然后将同一模式不同阶数的结果累加的得到该模式的时域模式电流。运用阶数步进法求得每个傅里叶模式的时域模式电流。因为各傅立叶模式之间存在正交性,可以分别计算单个独立模式下的时域模式电流,再对各个模式下的时域模式电流进行线性叠加就可以得到最终的电流结果,这样就大大减少了未知量个数和计算时间。
本文还进一步研究了数值计算过程中的两个主要的可变参数阶数和模式数的选取准则,以及这两个参数的变化对数值计算结果的影响。
The method to calculate time-domain wideband electromagnetic scattering of electrically large targets has been in urgent demand, since the development of ultra-wideband, target recognizing and SAR. The usage of the axisymmetric property of the body of revolution (BoR) can translate an original electrically large BoR-problem into a series problems with small size of matrix equations, namely a Fourier mode of the original one, which can greatly improve the computational efficiency and reduce the memory requirements. In this thesis, on the basis of frequency-domain method of momemt of BOR, we develope time-domai integral equations to calculate the time-domain electromagnetic scattering of BOR.
This paper mainly researches time-domain electromagnetic scattering from pefect electric conductor bodies of revolution in free space. Time-domai electric and magnetic integral equations are formulated via Maxwell's equations, potential functions, equivalent principle and the boundary conditions.With the rotational symmetry, the spatial element of unknown equivalent electric currents can be expanded in Fourier series in (?) and sectional function in t.And the temporal element of unknown equivalent electric currents can be expanded in weighted lagurre polynomials. Gaussian plane wave is used as the incident field in this paper, it has finite frequency that is propitious to get the fast convergence.
Basis functions and testing functions have been choosed, which were applied to the time-domain integral equations. Then we use the spatial and temporal testing scheme to the equations. By using the dispersive method,we get the matrix equation. A solution of each Fourier model matrix equation is solved by the marching-on-in-order procedure, then we get the time-domain equivalent electric currents of one Fourier model.Because each mode is orthogonal to the others, the problem can be solved under each mode respectively and each solution is summed up subsequently. Thus it reduces greatly the sum of unknown variable and the calculational time.
The number of the order and the Fourier component which is variable is further studied in this thesis.We discusse the method to truncate the number of the order and the Fourier component and the effect of the variable.
本文主要研究理想金属旋转对称体在自由空间环境下的时域电磁特性问题。首先通过麦克斯韦方程、辅助位函数、等效原理和边界条件建立了电流的时域电场磁场积分方程。然后再利用旋转对称性,将等效电流空间部分展开为关于φ的傅立叶级数形式和关于t的分段函数形式。其次对时间变量使用加权拉盖尔多项式作为时间基函数进行函数展开。而对于时域入射场本文选用的是高斯平面波,高斯平面波具有有限的频谱带宽有利于数值计算的快速收敛。
基函数和测试函数确定之后,将它们代入时域磁场电场积分方程中,然后对积分方程分别进行空间测试和时间测试。接着进行离散化过程生成阻抗矩阵和激励向量,最后形成了矩阵方程。求解过程中使用时域阶数步进法求得单个傅里叶模式各个阶数的电流系数,然后将同一模式不同阶数的结果累加的得到该模式的时域模式电流。运用阶数步进法求得每个傅里叶模式的时域模式电流。因为各傅立叶模式之间存在正交性,可以分别计算单个独立模式下的时域模式电流,再对各个模式下的时域模式电流进行线性叠加就可以得到最终的电流结果,这样就大大减少了未知量个数和计算时间。
本文还进一步研究了数值计算过程中的两个主要的可变参数阶数和模式数的选取准则,以及这两个参数的变化对数值计算结果的影响。
The method to calculate time-domain wideband electromagnetic scattering of electrically large targets has been in urgent demand, since the development of ultra-wideband, target recognizing and SAR. The usage of the axisymmetric property of the body of revolution (BoR) can translate an original electrically large BoR-problem into a series problems with small size of matrix equations, namely a Fourier mode of the original one, which can greatly improve the computational efficiency and reduce the memory requirements. In this thesis, on the basis of frequency-domain method of momemt of BOR, we develope time-domai integral equations to calculate the time-domain electromagnetic scattering of BOR.
This paper mainly researches time-domain electromagnetic scattering from pefect electric conductor bodies of revolution in free space. Time-domai electric and magnetic integral equations are formulated via Maxwell's equations, potential functions, equivalent principle and the boundary conditions.With the rotational symmetry, the spatial element of unknown equivalent electric currents can be expanded in Fourier series in (?) and sectional function in t.And the temporal element of unknown equivalent electric currents can be expanded in weighted lagurre polynomials. Gaussian plane wave is used as the incident field in this paper, it has finite frequency that is propitious to get the fast convergence.
Basis functions and testing functions have been choosed, which were applied to the time-domain integral equations. Then we use the spatial and temporal testing scheme to the equations. By using the dispersive method,we get the matrix equation. A solution of each Fourier model matrix equation is solved by the marching-on-in-order procedure, then we get the time-domain equivalent electric currents of one Fourier model.Because each mode is orthogonal to the others, the problem can be solved under each mode respectively and each solution is summed up subsequently. Thus it reduces greatly the sum of unknown variable and the calculational time.
The number of the order and the Fourier component which is variable is further studied in this thesis.We discusse the method to truncate the number of the order and the Fourier component and the effect of the variable.
引文
[1]赵延文,聂在平,徐建华,等.时域电场积分方程的稳定求解[J].电波科学学报,2004.
[2]田立松.电磁场时域计算技术研究与目标冲击响应特性分析[D].长沙：国防科技大学研究生院,2001.
[3]Bennett C L. A technique for computing approximate impulse response for conducting bodies [D].Doctor. Lafayette, Indianna:Purdue Univ,1968.
[4]S.M. Rao.Electromagnetic scattering and radiztion of arbitrarily shaped surfaces by triangular patch modeling [D].Mississippi:University of Mississippi,1980.
[5]N. J. Damaskos.Transient Scattering by Resistive Cylinders [J].IEEE Trans.On Antennas and Propagation, July 1985,vol 33.
[6]Rynne.B.P, Smith. P. D.Stability of time marching algorithms for the electric field integral equation [J].J. Electromagn. Wave Appl.,1990,4:1181-1205.
[7]Rynne.B.P, Stability and convergence from arbitrary surfaces using the electic field integral equation [J].IMAJ.Appl.Math.,1985,35:297-310.
[8]王映明.时域递推算法研究[M].长沙：国防科技大学研究生院,1990.
[9]K. Umashankar. A Taflove,S.M. Rao.Electromagnetic Scattering by Arbitrary Shaped Three-Dimensional Homogeneous Lossy Dielectric Objects [J].IEEE Trans. AP. vol.1986.AP-34,NO.6,758-766.
[10]G. Manara, A. Monorchio,et, al.A Space-Time Discretizetion Criterion for a Sable Time-Marching Solution of the Electric Field Integral Equation [J].IEEE Transactions on Antennas and Propagation,1997,45(3):527-532.
[11]H. Mieras, C.L.Bennett. Space-Time Integral Equation Approach to Dielectric Targets [J].IEEE Transactions on Antennas and Propagation,1982,30(1):2-9.
[12]A. G. Tijhuis.Towards a Stable Marching-on-in-Time Method for Two Dimensional Transient Electromagnetic Scattering Problems[J].Radio Science,1984,19:1311-1317.
[13]D. A. Vechinski, S.M. Rao.Transient Scattering from Two-Dimensional Dielectric Cylinders of Arbitrary Shape [J].IEEE Transient on Antennas and Propagation,1992, 40(9):1054-1060.
[14]A. A. Ergin, B.Shanker, and E. Michielssen. The plane wave time domain algorithm for fast analysis of transient wave phenomena [J],IEEE Antennas and Propagation Magazine,.1999,41(4):39-51.
[15]B.Shanker, A. A. Ergin, K. Aygun, E.Michielssen. Analysis of transient electromagnetic scattering phenomena using a two-level plane wave time domain algorithm[J],IEEE Transactions on Antennas Propagstion,2000,48(4):510-523.
[16]B.Shanker, A. A. Ergin, K. Aygun, E. Michielssen. Fast Analysis of Transient Electromagnetic Scattering Phenomena Using the Multilevel Plane Wave Time Domain Algorithm [J],IEEE Transactions on Antennas Propagstion,2003,51(3):628-641.
[17]A.E. Yilmaz, J.M. Jin, E.Michielssen. Time Domain Adaptive Integral Method for Surface Integral Equations [J],IEEE Transactions on Antennas Propagstion,2004,52(10): 2692-2708.
[18]A. E.Yilmaz, J. M. Jin, E. Michielssen. A Fast Fourier Transform Accelerated Marching-on-in-Time Algorithm for Electromagnetic Analysis [J],Electromagnetics, 2001,21:181-197.
[19]M. M. Rao, T. K. Sarkar, T. Anjali, R. S.Adve, Simultaneous extrapolation in time and frequency domain suing Hermite expansion [J],IEEE Transactions on Antennas Propagstion,1999,47(6):1108-1115.
[20]T. K. Sarkar, J. Koh. Generation of aWide-Band Electromagnetic Response through a Laguerre Expansion using Early-Time and Low-Frequecy Data [J],IEEE Transactions on Antennas Propagstion,2002,50(5):1408-1416.
[21]Allen Wang, Aluizio Prata. Jr. and W. V. T. Rush. Efficient computation of the time-domain scattering from bodies of revolution [J],Antennas and Propagstion Society International Symposium, vol.1,pp.318-321,July 1993.
[22]Baek Ho Jung, Yong-Seek Chung, and Tapan K. Sarkar. Time-domain EFIE,MFIE, and CFIE formulations using Laguerre polynomials temporal basis functions for the analysis of transient scattering from arbitrary shaped conducting tructures [J],Progress In Electromagnetics Research, PIER 39,1-45,2003.
[23]Yong-Seek Chung, Tapan K. Sarkar, Baek Ho Jung, Magdalena Salazar-Palma, Zhong Ji, Seongman Jang, and Kyungjung Kim. Solution of time domain electric field integral equation using the Laguerre Polynomials [J],IEEE Trans. Antennas Propagat.,vol.52, no.9, pp.2319-2327, Sept.2004.
[24]Baek Ho Jung, Tapan K. Sarkar, Yong-Seek Chung, Magdalena Salazar-Palma, Zhong Ji, Seongman Jang, and Kyungjung Kim. Transient electromagnetic Scsrrering from dielectric objects using the electric field integral equation with Laguerre polynomials as temporal basis functions [J],IEEE Trans. Antennas propagate.,vol.52, no.9, pp 2329-2339, Sept.2004.
[25]Zhong Ji, Tapan K. Sarkar, Baek Ho Jung, Yong-Seek Chung, Magdalena Salazar-Palma, Mengtao Yuan. A stable solution of time domain electric field integral equation for thin-wine antennas using the Laguerre polynonials [J],IEEE Trans. Antennas Propagat. vol.52,no.10,pp.2641-2648,Oct.2004.
[26]Zhong Ji, Tapan K. Sarkar, Baek Ho Jung, Magdalena Salazar-Palma and Mengtao Yuan.A Comparison of marching-on-in-time method with marching-on-in-degree method for the TD-EFIE solver [J],IEEE AP/URSI Symposium, Washington, D.C.,July 2005
[27]包伟.旋转对称体的电磁散射研究[D].南京：南京理工大学电子信息与光电技术学院,2007年.
[28]阳晓丽.旋转对称体散射特性的高效分析[D].南京：南京理工大学电子信息与光电技术学院,2008年.
[29]李世智.电磁辐射与散射为题的矩量法.北京：电子工业出版社,1985.
[30]J.Van Bladel, Electromagnetic Fields [M].Bristol, PA:Hemisphere,1985.
[31]S.M.Rao.Time Domain Electromagnetic [M].New York:Academic Press,1999.
[32]Zhang S J, Jim J M. Computation of special function [M].New York:John Wiley & Sons, Inc,1996.
[33]Mogens G. Andreasen, Scattering from bodies of revolution [J],IEEE Trans.Antennas Propagat.vol.13,no.2,pp.303-310, Mar.1965.
[34]Mogens G. Andreasen, Scattering from bodies of revolution [J],IEEE Trans.Antennas Propagat.vol.13,no.2,pp.303-310, Mar.1965.
[35]梅志林.小F数毫米波成像折衍射透镜焦区场分析[M].东南大学,2004年6月.
[36]J. F. Shaeffer and L.N. Medgyesi-Mitschang, Radiation from wire antennas attached to bodies of revolution:The junction problem[J],IEEE Trans. Antennas Propagat,1981, AP-29:479-487.
[37]俞文明.旋转对称频域和时域积分方程方法及其软件实现和应用[M].南京：南京理工大学电子信息与光电技术学院,2007年.
[38]J.F. Shaeffer and L.N.Medgyesi-Mitschang, Radiation from wire antennas attached to bodies of revolution:The junction problem[J],IEEE Trans.Antennas Propagat,1981, AP-29:479-487。
[39]C.F. Bohren, Craig F, Light scattering by an optically active sphere[J],Chemical Physics Letters, Volume 29, Issue 3,pp.458-462,December 1974.
[40]M. Yuceer, J.R. Mautz, and E. Arvas, Method of moments solution for the radar cross section of a chiral body of revolution[J],IEEE Trans.Antennas Propagat.,Vol.53,No.3, pp.1163.1167,2005.
[41]K. A. Michalski et al, Analysis of electromagnetic scattering by conducting BOR's in layered media using the discrete complex image method[J],IEEE Antennas Propag. Symp.Dig.,Newport Beach,CA,1995.
[42]T. K. Sarkar, Odilon Pereira, Using the Matrix Pencil Method to Estimate the Parameters of a Sum of Complex Exponentials[J] IEEE Trans. Antennas Propagat.,Vol.37,No.1, pp.48-55,February 1995.
[43]方剑,任朗,时域有限面积法解手征介质涂层导体柱的电磁散射[J]，电子学报,2001,29(3)：368-372.
[44]谢处方,饶克谨,电磁场与电磁波[M],第三版,北京：高等教育出版社,1999年。
[45]T. E. Durham and C.G. Christodoulou, Integral equation analysis of dielectric and conducting bodies of revolution in the presence of arbitrary surfaces [J],IEEE Trans. Antennas Propagat,1995,43:674-680.
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[2]田立松.电磁场时域计算技术研究与目标冲击响应特性分析[D].长沙：国防科技大学研究生院,2001.
[3]Bennett C L. A technique for computing approximate impulse response for conducting bodies [D].Doctor. Lafayette, Indianna:Purdue Univ,1968.
[4]S.M. Rao.Electromagnetic scattering and radiztion of arbitrarily shaped surfaces by triangular patch modeling [D].Mississippi:University of Mississippi,1980.
[5]N. J. Damaskos.Transient Scattering by Resistive Cylinders [J].IEEE Trans.On Antennas and Propagation, July 1985,vol 33.
[6]Rynne.B.P, Smith. P. D.Stability of time marching algorithms for the electric field integral equation [J].J. Electromagn. Wave Appl.,1990,4:1181-1205.
[7]Rynne.B.P, Stability and convergence from arbitrary surfaces using the electic field integral equation [J].IMAJ.Appl.Math.,1985,35:297-310.
[8]王映明.时域递推算法研究[M].长沙：国防科技大学研究生院,1990.
[9]K. Umashankar. A Taflove,S.M. Rao.Electromagnetic Scattering by Arbitrary Shaped Three-Dimensional Homogeneous Lossy Dielectric Objects [J].IEEE Trans. AP. vol.1986.AP-34,NO.6,758-766.
[10]G. Manara, A. Monorchio,et, al.A Space-Time Discretizetion Criterion for a Sable Time-Marching Solution of the Electric Field Integral Equation [J].IEEE Transactions on Antennas and Propagation,1997,45(3):527-532.
[11]H. Mieras, C.L.Bennett. Space-Time Integral Equation Approach to Dielectric Targets [J].IEEE Transactions on Antennas and Propagation,1982,30(1):2-9.
[12]A. G. Tijhuis.Towards a Stable Marching-on-in-Time Method for Two Dimensional Transient Electromagnetic Scattering Problems[J].Radio Science,1984,19:1311-1317.
[13]D. A. Vechinski, S.M. Rao.Transient Scattering from Two-Dimensional Dielectric Cylinders of Arbitrary Shape [J].IEEE Transient on Antennas and Propagation,1992, 40(9):1054-1060.
[14]A. A. Ergin, B.Shanker, and E. Michielssen. The plane wave time domain algorithm for fast analysis of transient wave phenomena [J],IEEE Antennas and Propagation Magazine,.1999,41(4):39-51.
[15]B.Shanker, A. A. Ergin, K. Aygun, E.Michielssen. Analysis of transient electromagnetic scattering phenomena using a two-level plane wave time domain algorithm[J],IEEE Transactions on Antennas Propagstion,2000,48(4):510-523.
[16]B.Shanker, A. A. Ergin, K. Aygun, E. Michielssen. Fast Analysis of Transient Electromagnetic Scattering Phenomena Using the Multilevel Plane Wave Time Domain Algorithm [J],IEEE Transactions on Antennas Propagstion,2003,51(3):628-641.
[17]A.E. Yilmaz, J.M. Jin, E.Michielssen. Time Domain Adaptive Integral Method for Surface Integral Equations [J],IEEE Transactions on Antennas Propagstion,2004,52(10): 2692-2708.
[18]A. E.Yilmaz, J. M. Jin, E. Michielssen. A Fast Fourier Transform Accelerated Marching-on-in-Time Algorithm for Electromagnetic Analysis [J],Electromagnetics, 2001,21:181-197.
[19]M. M. Rao, T. K. Sarkar, T. Anjali, R. S.Adve, Simultaneous extrapolation in time and frequency domain suing Hermite expansion [J],IEEE Transactions on Antennas Propagstion,1999,47(6):1108-1115.
[20]T. K. Sarkar, J. Koh. Generation of aWide-Band Electromagnetic Response through a Laguerre Expansion using Early-Time and Low-Frequecy Data [J],IEEE Transactions on Antennas Propagstion,2002,50(5):1408-1416.
[21]Allen Wang, Aluizio Prata. Jr. and W. V. T. Rush. Efficient computation of the time-domain scattering from bodies of revolution [J],Antennas and Propagstion Society International Symposium, vol.1,pp.318-321,July 1993.
[22]Baek Ho Jung, Yong-Seek Chung, and Tapan K. Sarkar. Time-domain EFIE,MFIE, and CFIE formulations using Laguerre polynomials temporal basis functions for the analysis of transient scattering from arbitrary shaped conducting tructures [J],Progress In Electromagnetics Research, PIER 39,1-45,2003.
[23]Yong-Seek Chung, Tapan K. Sarkar, Baek Ho Jung, Magdalena Salazar-Palma, Zhong Ji, Seongman Jang, and Kyungjung Kim. Solution of time domain electric field integral equation using the Laguerre Polynomials [J],IEEE Trans. Antennas Propagat.,vol.52, no.9, pp.2319-2327, Sept.2004.
[24]Baek Ho Jung, Tapan K. Sarkar, Yong-Seek Chung, Magdalena Salazar-Palma, Zhong Ji, Seongman Jang, and Kyungjung Kim. Transient electromagnetic Scsrrering from dielectric objects using the electric field integral equation with Laguerre polynomials as temporal basis functions [J],IEEE Trans. Antennas propagate.,vol.52, no.9, pp 2329-2339, Sept.2004.
[25]Zhong Ji, Tapan K. Sarkar, Baek Ho Jung, Yong-Seek Chung, Magdalena Salazar-Palma, Mengtao Yuan. A stable solution of time domain electric field integral equation for thin-wine antennas using the Laguerre polynonials [J],IEEE Trans. Antennas Propagat. vol.52,no.10,pp.2641-2648,Oct.2004.
[26]Zhong Ji, Tapan K. Sarkar, Baek Ho Jung, Magdalena Salazar-Palma and Mengtao Yuan.A Comparison of marching-on-in-time method with marching-on-in-degree method for the TD-EFIE solver [J],IEEE AP/URSI Symposium, Washington, D.C.,July 2005
[27]包伟.旋转对称体的电磁散射研究[D].南京：南京理工大学电子信息与光电技术学院,2007年.
[28]阳晓丽.旋转对称体散射特性的高效分析[D].南京：南京理工大学电子信息与光电技术学院,2008年.
[29]李世智.电磁辐射与散射为题的矩量法.北京：电子工业出版社,1985.
[30]J.Van Bladel, Electromagnetic Fields [M].Bristol, PA:Hemisphere,1985.
[31]S.M.Rao.Time Domain Electromagnetic [M].New York:Academic Press,1999.
[32]Zhang S J, Jim J M. Computation of special function [M].New York:John Wiley & Sons, Inc,1996.
[33]Mogens G. Andreasen, Scattering from bodies of revolution [J],IEEE Trans.Antennas Propagat.vol.13,no.2,pp.303-310, Mar.1965.
[34]Mogens G. Andreasen, Scattering from bodies of revolution [J],IEEE Trans.Antennas Propagat.vol.13,no.2,pp.303-310, Mar.1965.
[35]梅志林.小F数毫米波成像折衍射透镜焦区场分析[M].东南大学,2004年6月.
[36]J. F. Shaeffer and L.N. Medgyesi-Mitschang, Radiation from wire antennas attached to bodies of revolution:The junction problem[J],IEEE Trans. Antennas Propagat,1981, AP-29:479-487.
[37]俞文明.旋转对称频域和时域积分方程方法及其软件实现和应用[M].南京：南京理工大学电子信息与光电技术学院,2007年.
[38]J.F. Shaeffer and L.N.Medgyesi-Mitschang, Radiation from wire antennas attached to bodies of revolution:The junction problem[J],IEEE Trans.Antennas Propagat,1981, AP-29:479-487。
[39]C.F. Bohren, Craig F, Light scattering by an optically active sphere[J],Chemical Physics Letters, Volume 29, Issue 3,pp.458-462,December 1974.
[40]M. Yuceer, J.R. Mautz, and E. Arvas, Method of moments solution for the radar cross section of a chiral body of revolution[J],IEEE Trans.Antennas Propagat.,Vol.53,No.3, pp.1163.1167,2005.
[41]K. A. Michalski et al, Analysis of electromagnetic scattering by conducting BOR's in layered media using the discrete complex image method[J],IEEE Antennas Propag. Symp.Dig.,Newport Beach,CA,1995.
[42]T. K. Sarkar, Odilon Pereira, Using the Matrix Pencil Method to Estimate the Parameters of a Sum of Complex Exponentials[J] IEEE Trans. Antennas Propagat.,Vol.37,No.1, pp.48-55,February 1995.
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