基于TDIE的三维导体对雷达波散射模拟
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摘要
在目前的军事探测中,雷达是重要的探测手段,等离子体隐身技术作为一种新概念,正受到越来越多的关注,美俄等国家都在进行深入研究并已进入应用阶段。开展电磁场在等离子体环境下散射场的研究,探索针对性的算法是非常必要的。
目前应用于色散媒质电磁散射分析的方法主要是时域有限差分法(FDTD),它的原理简单明了,在处理复杂媒质问题时非常方便,但在遇到三维电大目标的散射问题时,计算量过大,并且FDTD方法本身也不是很精确。而时域积分方程法在求解这种问题时,对于均匀媒质只需离散散射体表面,相对于还要增加截断边界的FDTD,减少了很多未知量,同时TDIE也是一种精确的方法,不存在色散误差。若配合最近的时域平面波法(PWTD)进行加速,可望达到比较高的计算效率,是一种值得深入研究的数值方法。
鉴于此,本文研究了三维目标瞬态电磁散射的TDIE方法,以期为将来将TDIE运用于等离子体色散媒质中打下一定基础。
本文首先简要分析了课题的意义现状,与当前常见的几种数值方法作出比较后,说明了TDIE求解此类问题所具有的优势,以及存在的问题及解决方案。接着推导了时域电场、磁场、混合场的积分方程,并介绍了求解TDIE的基础:矩量法。
在第四章,系统细致地分析了如何离散散射体,处理原始数据,如何用时间空间基函数展开TDIE,并进行内积检验,求取积分值及奇异积分。还分析了TDIE的稳定性问题以及解决方法,选取了一种新的抵制振荡的平均方法。算例表明,这种方法具有很好的效果。
最后,浅谈了TDIE的快速算法PWTD的原理。这种方法能够使TDIE应用于复杂的色散媒质如等离子体,并且能把计算复杂度大大降低。这是TDIE的一个重大突破,是TDIE发展的新方向。
In the current military detecting, the radar is an important means of detection. As a new concept, the plasma stealth technology is receiving more and more attention. The United States and Russia and other countries are carrying out in-depth research and have entered the application stage. To study the scattering electromagnetic fields in the plasma environment, and to explore specific algorithm is very necessary.
The mostly used method in dispersive media for electromagnetic scattering analysis is finite-difference time-domain (FDTD). It is simple and clear, very convenient in addressing complex medium problems, but in the face of Electrically Large goals scattering problem, the calculation is excessive, besides the FDTD method itself is not very precise. On the other hand, when using the time-domain integral equation method to solve such problem, not only just the surface of scattering object is needed to be meshed for the homogeneous medium, but also a lot of unknowns will be reduced. Meanwhile, TDIE is more accurate, it does not produce dispersion error. When used with the plane-wave time-domain (PWTD) accelerating it is expected to achieve high computational efficiency and is a numerical methods worthy of in-depth study.
As such, this paper presents a three-dimensional transient electromagnetic scattering using TDIE, hoping to lay the foundation of TDIE based numerical simulation applied in plasma dispersion medium in the future.
This paper analyzes the significance of the status issue first. In comparing with the current common numerical methods, the advantages of TDIE based scheme solving such problems are shown. Then the integral equation time domain for the electric field, magnetic field, and the mixed field are derived, and the basis of the solution of TDIE : Moment Method is introduced.
In the fourth chapter, this paper detailed analysis of how to get the discrete scattering body, how to deal with raw data, how to use space-time basis function, how to apply testing procedure and how to evaluate integral values and singular integrals. The stability of the TDIE solution is also analyzed and a new averaging method is used to resist the oscillation. The numerical results of two samples show that this method is very effective.
Finally, the principle of the fast algorithm of TDIE : PWTD is briefly discussed. This approach enables TDIE to suit for complex dispersion medium such as plasma, and the computational complexity can also be reduced significantly. This is a major breakthrough for TDIE, and a new direction.
目前应用于色散媒质电磁散射分析的方法主要是时域有限差分法(FDTD),它的原理简单明了,在处理复杂媒质问题时非常方便,但在遇到三维电大目标的散射问题时,计算量过大,并且FDTD方法本身也不是很精确。而时域积分方程法在求解这种问题时,对于均匀媒质只需离散散射体表面,相对于还要增加截断边界的FDTD,减少了很多未知量,同时TDIE也是一种精确的方法,不存在色散误差。若配合最近的时域平面波法(PWTD)进行加速,可望达到比较高的计算效率,是一种值得深入研究的数值方法。
鉴于此,本文研究了三维目标瞬态电磁散射的TDIE方法,以期为将来将TDIE运用于等离子体色散媒质中打下一定基础。
本文首先简要分析了课题的意义现状,与当前常见的几种数值方法作出比较后,说明了TDIE求解此类问题所具有的优势,以及存在的问题及解决方案。接着推导了时域电场、磁场、混合场的积分方程,并介绍了求解TDIE的基础:矩量法。
在第四章,系统细致地分析了如何离散散射体,处理原始数据,如何用时间空间基函数展开TDIE,并进行内积检验,求取积分值及奇异积分。还分析了TDIE的稳定性问题以及解决方法,选取了一种新的抵制振荡的平均方法。算例表明,这种方法具有很好的效果。
最后,浅谈了TDIE的快速算法PWTD的原理。这种方法能够使TDIE应用于复杂的色散媒质如等离子体,并且能把计算复杂度大大降低。这是TDIE的一个重大突破,是TDIE发展的新方向。
In the current military detecting, the radar is an important means of detection. As a new concept, the plasma stealth technology is receiving more and more attention. The United States and Russia and other countries are carrying out in-depth research and have entered the application stage. To study the scattering electromagnetic fields in the plasma environment, and to explore specific algorithm is very necessary.
The mostly used method in dispersive media for electromagnetic scattering analysis is finite-difference time-domain (FDTD). It is simple and clear, very convenient in addressing complex medium problems, but in the face of Electrically Large goals scattering problem, the calculation is excessive, besides the FDTD method itself is not very precise. On the other hand, when using the time-domain integral equation method to solve such problem, not only just the surface of scattering object is needed to be meshed for the homogeneous medium, but also a lot of unknowns will be reduced. Meanwhile, TDIE is more accurate, it does not produce dispersion error. When used with the plane-wave time-domain (PWTD) accelerating it is expected to achieve high computational efficiency and is a numerical methods worthy of in-depth study.
As such, this paper presents a three-dimensional transient electromagnetic scattering using TDIE, hoping to lay the foundation of TDIE based numerical simulation applied in plasma dispersion medium in the future.
This paper analyzes the significance of the status issue first. In comparing with the current common numerical methods, the advantages of TDIE based scheme solving such problems are shown. Then the integral equation time domain for the electric field, magnetic field, and the mixed field are derived, and the basis of the solution of TDIE : Moment Method is introduced.
In the fourth chapter, this paper detailed analysis of how to get the discrete scattering body, how to deal with raw data, how to use space-time basis function, how to apply testing procedure and how to evaluate integral values and singular integrals. The stability of the TDIE solution is also analyzed and a new averaging method is used to resist the oscillation. The numerical results of two samples show that this method is very effective.
Finally, the principle of the fast algorithm of TDIE : PWTD is briefly discussed. This approach enables TDIE to suit for complex dispersion medium such as plasma, and the computational complexity can also be reduced significantly. This is a major breakthrough for TDIE, and a new direction.
引文
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[3]莫锦军 刘少斌 袁乃昌.等离子体隐身机理研究,现代雷达,2002年5月
[4]刘明海,胡希伟,江中和,刘克富,辜承林,潘垣.电磁波在大气层人造等离子体中的衰减特性.物理学报,2002,51(6):1317-1320
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[7] Balasubramaniam Shanker, A. Arif Ergin, Kemal Aygun, Eric Michielssen. Analysis of Transient Electromagnetic Scattering Phenomena Using a Two-Level PlaneWave Time-Domain Algorithm. IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL.48, NO.4, APRIL 2000
[8] Balasubramaniam Shanker, A. Arif Ergin, MingyuLu, and Eric Michielssen. Fast Analysis of Transient Electromagnetic Scattering Phenomena Using the Multilevel Plane Wave Time Domain Algorithm. IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL.51, NO.3, MARCH 2003
[9] DanielS.Weile, Greeshma Pisharody, Nan-Wei Chen Balasubramaniam Shanker, and Eric Michielssen. A Novel Scheme for the Solution of the Time-Domain Integral Equations of Electromagnetics. IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL.52, NO.1, JANUARY 2004
[10] Gregory Kobidze, Balasubramaniam Shanker. Integral Equation Based Analysisof Scattering From 3-D Inhomogeneous Anisotropic Bodies. IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 52, NO. 10, OCTOBER 2004
[11] Gregory Kobidze, Jun Gao, Balasubramaniam Shanker, Eric Michielssen. A Fast Time Domain Integral Equation Based Scheme for Analyzing Scattering From Dispersive Objects. IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL.53, NO.3, MARCH 2005
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[24] Baek Ho Jung and Tapan Kumar Sarkar. Time-Domain Electric-Field Integral Equation With Central Finite Difference. Microwave and Optical Technology Letters / Vol.31, No.6, December 20 2001.
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[2]赵青,李宏福,任同,鄢阳,罗勇.等离子体隐身技术的研究.电子科技大学学报,2004,33(2):142-145
[3]莫锦军 刘少斌 袁乃昌.等离子体隐身机理研究,现代雷达,2002年5月
[4]刘明海,胡希伟,江中和,刘克富,辜承林,潘垣.电磁波在大气层人造等离子体中的衰减特性.物理学报,2002,51(6):1317-1320
[5] A. Arif Ergin, Balasubramaniam Shanker, et a . Fast evaluation of three dimensional transient wave fields using diagonal translations operator [J].Journal of Computational Physics, 1998, 146(1): 157-180
[6] A. Arif Ergin, Balasubramaniam Shanker, Eric Michielssen. The Plane-Wave Time-Domain Algorithm for the of Transient Wave Phenomena Fast Analysis. IEEE Antennas and Propagation Magazine, Vol. 41, No. 4, August 1999
[7] Balasubramaniam Shanker, A. Arif Ergin, Kemal Aygun, Eric Michielssen. Analysis of Transient Electromagnetic Scattering Phenomena Using a Two-Level PlaneWave Time-Domain Algorithm. IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL.48, NO.4, APRIL 2000
[8] Balasubramaniam Shanker, A. Arif Ergin, MingyuLu, and Eric Michielssen. Fast Analysis of Transient Electromagnetic Scattering Phenomena Using the Multilevel Plane Wave Time Domain Algorithm. IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL.51, NO.3, MARCH 2003
[9] DanielS.Weile, Greeshma Pisharody, Nan-Wei Chen Balasubramaniam Shanker, and Eric Michielssen. A Novel Scheme for the Solution of the Time-Domain Integral Equations of Electromagnetics. IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL.52, NO.1, JANUARY 2004
[10] Gregory Kobidze, Balasubramaniam Shanker. Integral Equation Based Analysisof Scattering From 3-D Inhomogeneous Anisotropic Bodies. IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 52, NO. 10, OCTOBER 2004
[11] Gregory Kobidze, Jun Gao, Balasubramaniam Shanker, Eric Michielssen. A Fast Time Domain Integral Equation Based Scheme for Analyzing Scattering From Dispersive Objects. IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL.53, NO.3, MARCH 2005
[12] S.M.Rao and D.R.Wilton, Transient scattering by conducting surfaces of arbitrary shape, IEEE Trans on Antennas and Propagat 39(1991), 56-61.
[13] S.M. Rao, D.R. Wilton and A.W. Glisson, Electromagnetic Scatterng by Surfaces of Arbitrary Shape, IEEE Trans. On Antennas and Propagat., Vol 30,pp.409-418, May 1982
[14] D.A. Vechinski and S.M. Rao , A stable procedure to calculate the transient scattering by conducting surfaces of arbitrary shape, IEEE Trans on Antennas and Propagat 40(1992), 661-665
[15] B.P. Rynne,“Time domain scattering from arbitrary surfaces using the electric field integral equation”[J], Electromagnetic waves Appl., jan. 1991,vol.5, pp.93-112.
[16] S. M. Rao and T. K. Sarkar,“Time domain modeling of two dimensional conduc-ting cylinders utilizing an implicit scheme—TM incident”[J], Microwave Opt. Technol. Lett., vol. 15, no. 6, pp. 342–347, Aug. 1997.
[17] M. D. Pocock, M. J. Bluck, and S. P. Walker,“Electromagnetic scattering from 3-D curved dielectric bodies using time-domain integral equations”[J], IEEE Trans. Antennas Propagat., vol. 46, pp. 1212–1219, Aug. 1998.
[18] S. J. Dodson, S. P. Walker, and M. J. Bluck,“Implicitness and stability of time domain integral equation scattering analysis”[J], ACES J., vol. 13, no. 3, pp. 291–301, Nov. 1998.
[19] S.M.Rao,D.A.Vechinski, and T.K.Sarkar, Transient scattering by conducting cylinders-Implicit solution for the transverse electric case, Microwave Opt Technol Lett 21(1999),129-134.
[20] S.M.Rao and T.K.Sarkar, An alternative version of the time-domain electric field integral equation for arbitrarily shaped conductors, IEEE Trans Antennas Propagat 41(1993), 831-834.
[21] T.K.Sarkar. and Odilon Pereira. Using the Matrix Pencil Method to Estimate the Parameters of a Sum of Complex Exponentials. IEEE.Antennas and Propagation Magazine, Vol.37,No.1,February 1995.
[22] S.M.Rao and T.K.Sarkar, An efficient method to evaluate the time-domain scattering from arbitrarily shaped conducting bodies, Microwave Opt Technol Lett 17(1998),321-325.
[23] T.K.Sarkar, W.Lee, and S.M.Rao, Analysis of transient scattering from composite arbitrarily shaped complex structures, IEEE Trans Antennas Propagat 48(2000), 1625-1634.
[24] Baek Ho Jung and Tapan Kumar Sarkar. Time-Domain Electric-Field Integral Equation With Central Finite Difference. Microwave and Optical Technology Letters / Vol.31, No.6, December 20 2001.
[25] Baek Ho Jung and T.K. Sarkar, Time-Domain CFIE For The Analysis of Transient Scattering form Arbtrarily Shaped 3D Conducting Objects, Microwave and Optical Technology Letters Vol.34, No.4,pp. 289-296, Aug. 20 2002.
[26] P.J.Davies, On the stability of time-marching schemes for the general surface electric-field integral equation, IEEE Trans Antennas Propagat 44(1996), 1467-1473.
[27] G. Manara, A. Monorchio and R. Reginanini, A Space-Time Discretization Criterion for Stable Time Marching Solution of Electric Field Integral Equation, IEEE Trans. Antennas and Propagat., Vol. 45, pp. 527-531, March 1997
[28] Murli Mohan Rao, Tapan K.Sarka. Extrapolation of Electromagnetic Responses from Conducting Objects in Time and Frequency Domains. IEEE. Transactions On Transactions On Microwave Theory and Techniques. Vol.47.No.10.Octorber 1999.
[29] S.P. Walker,M.J. Bluck and I. Chatzis, The Stability of Integral Equation Time-Domain Computaions for Three-Dimentional Scattering; Similarities and Differences beteween Electrodynamic and Elastodynamic Comutations, Int. J. Numer. Model.,2002 ,pp.459-473
[30] J. L.Hu and C.H.Chan.“A new temporal basis function for the time-domain integral equation method.”IEEE.Trans.Microwave and Wireless Components letters.Vol.11, No,11,November 2001.
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