二维目标电磁散射特性时域有限元方法分析
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摘要
本文将总场—散射场划分技术中的体激励法(VETSFD)应用到时域有限元方法(TDFEM)中,分析了二维目标的电磁散射特性。首先介绍了求解边值问题的TDFEM基本原理及其求解电磁问题的基本步骤。在电磁散射分析中,采用连接边界(CB)将整个计算区域划分为总场区和散射场区,并在总场区强加入射平面波,既可以减小入射波产生的误差,又可以同时得到总场和散射场的场值。采用Mur吸收边界条件(ABC)对整个计算区域进行截断。为了验证算法的有效性,首先对无目标时的计算区域进行分析,发现入射波泄露到散射场区的值只有-110dB,相对于惠更斯面元激励法-20dB的入射波泄露,VETSFD-TDFEM计算精度大为提高。进一步,利用等效原理,由输出边界(OB)上的电磁场各切向场分量外推得到远区场,从而求出了二维(2-D)目标的雷达散射截面(RCS)。
本文在TE波激励下计算了金属目标、介质目标、介质涂覆目标和机翼模型等典型目标的双站雷达散射截面。并将所得数据结果与时域有限差分方法(FDTD)计算结果以及参考文献数据进行对比,数据曲线吻合很好,从而验证了该算法的有效性和精确性。在此基础上,分析了VETSFD-TDFEM算法的计算时间、内存消耗、算法稳定性以及计算精度等要素,为将时域有限元方法从二维模拟推广到三维分析奠定了基础。
最后,应用VETSFD-TDFEM对一种特殊光子晶体—蓝蝴蝶翅膀有限周期性微结构的电磁散射特性进行了研究,主要对Morpho蝴蝶微结构所具有的光学散射带阻和角偏特性进行了深入地探讨。
In this thesis, The Volumetric Excitation (VE) method in Total- and Scattered-Field Decomposition (VETSFD) techniques is applied to Time Domain Finite Element Method (TDFEM) for electromagnetic scattering analysis of some representative 2-D objects. Firstly, TDFEM is introduced, and the theory and the steps of electromagnetism analysis are given. Secondly, to mitigate dispersion error on the incident wave, while preserving a total-field region local to the objects of interest, the whole computational area is split into Total Field (TF) and Scattered Field (SF) with connecting boundary (CB), and the incident wave is impressed on the TF. The Mur absorbing boundary condition (ABC) is used to truncate the computational area. To validate the accuracy of the VETSFD-TDFEM, the leakage in the computational area in absence of objects is investigated firstly. The maximum leakage of backward scattering into the scattered-field region is about -110 dB, which is much more accurate than the traditional Huygens’surface excitation method (the associated wave leakage is as high as -20dB). Then the far filed can be obtained from the electromagnetic field distribution on output boundary (OB) lies between CB and AB according to the equivalent theory. Radar Cross Section (RCS) of some representative 2-D objects can be obtained.
And then, the scattering of transverse electric (TE) field mode is investigated in this paper, The bistatic RCS of some metal objects, medium objects, dielectric coated metal and metal airfoil are computed and presented. The numerical results generated with VETSFD-TDFEM are compared with the results simulated with FDTD or reference results, which demonstrates that VETSFD-TDFEM is an effective method for electromagnetic scattering analysis of complex objects. Besides, computational time, memory consumption, stability of iteration and computational precision are also investigated in this paper.
Finally, the electromagnetic scattering of a special photonic crystal-the finite periodicity micro-structure of Morpho butterfly’s wing is analyzed with VETSFD-TDFEM. The bandstop and angle-dependent characteristics of the micro-structure are investigated in detail in this paper.
本文在TE波激励下计算了金属目标、介质目标、介质涂覆目标和机翼模型等典型目标的双站雷达散射截面。并将所得数据结果与时域有限差分方法(FDTD)计算结果以及参考文献数据进行对比,数据曲线吻合很好,从而验证了该算法的有效性和精确性。在此基础上,分析了VETSFD-TDFEM算法的计算时间、内存消耗、算法稳定性以及计算精度等要素,为将时域有限元方法从二维模拟推广到三维分析奠定了基础。
最后,应用VETSFD-TDFEM对一种特殊光子晶体—蓝蝴蝶翅膀有限周期性微结构的电磁散射特性进行了研究,主要对Morpho蝴蝶微结构所具有的光学散射带阻和角偏特性进行了深入地探讨。
In this thesis, The Volumetric Excitation (VE) method in Total- and Scattered-Field Decomposition (VETSFD) techniques is applied to Time Domain Finite Element Method (TDFEM) for electromagnetic scattering analysis of some representative 2-D objects. Firstly, TDFEM is introduced, and the theory and the steps of electromagnetism analysis are given. Secondly, to mitigate dispersion error on the incident wave, while preserving a total-field region local to the objects of interest, the whole computational area is split into Total Field (TF) and Scattered Field (SF) with connecting boundary (CB), and the incident wave is impressed on the TF. The Mur absorbing boundary condition (ABC) is used to truncate the computational area. To validate the accuracy of the VETSFD-TDFEM, the leakage in the computational area in absence of objects is investigated firstly. The maximum leakage of backward scattering into the scattered-field region is about -110 dB, which is much more accurate than the traditional Huygens’surface excitation method (the associated wave leakage is as high as -20dB). Then the far filed can be obtained from the electromagnetic field distribution on output boundary (OB) lies between CB and AB according to the equivalent theory. Radar Cross Section (RCS) of some representative 2-D objects can be obtained.
And then, the scattering of transverse electric (TE) field mode is investigated in this paper, The bistatic RCS of some metal objects, medium objects, dielectric coated metal and metal airfoil are computed and presented. The numerical results generated with VETSFD-TDFEM are compared with the results simulated with FDTD or reference results, which demonstrates that VETSFD-TDFEM is an effective method for electromagnetic scattering analysis of complex objects. Besides, computational time, memory consumption, stability of iteration and computational precision are also investigated in this paper.
Finally, the electromagnetic scattering of a special photonic crystal-the finite periodicity micro-structure of Morpho butterfly’s wing is analyzed with VETSFD-TDFEM. The bandstop and angle-dependent characteristics of the micro-structure are investigated in detail in this paper.
引文
[1]谢德馨,唐任远,王尔智,白保东.计算电磁学的现状与发展趋势[J].电工技术学报, 2003,18(5): 1~4.
[2]孙成祥. TDFEM中吸收边界条件技术及其在二维电磁问题分析中的应用[硕士学位论文].南京:南京航空航天大学,2009.
[3]王秉中.计算电磁学[M].北京:科学出版社, 2005: 1~18.
[4]冯奎胜,卢万铮,朱章虎.电磁场数值计算方法分析[J].山西电子技术, 2005, (6): 43~46.
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[6]刘波,高本庆.电磁场时域数值方法及其混合技术概述[J].微波学报, 2006, 22(2): 1~6.
[7] R. W. Clough. The Finite Element Method of Structura Analysis. Proc.2nd Conf. Electronic Computation. ASCE, Pittsburgh, 1960, pa,9.
[8]倪光正,钱秀英.电磁场数值计算[M].高等教育出版社,1996:1~9.
[9] Silveste P.P. and R.L.Ferrari.有限元在电气工程中的应用[M](简柏敦,倪光正译).杭州:浙江大学出版社,1996:112~132.
[10] Eiber Thomas F and Volkert Hansen. 3-D FEM/BEM-Hybrid approach based on general formulation of Huyens’principle for planar layered media [J]. IEEE Trans.on Microwave Theory and Techniqes.1997,7(45):1105~1112.
[11] Xing chaoYuan,Danielr. Lyneh and JohnW. Strohbehn. CouPling of finite element and moment methods for electromagnetic scattering from inhomogemeous [J]. IEEE Trans. Antennas Propagat, 1992,38(3):386~393.
[12] XingehaoYuan.Three-dimensional electromagnetic scattering from inhomogeneous objects by the hybrid moment and finite element method [J]. IEEE Trans. Microwave Theory Tech, 1990,38(8):1053~1058.
[13] Tom Cwik and Cinzia Zuffada. Modeling three dimensional Seatterers using a CouPled finite element-integral equationformulation[J]. IEEE Trans. Antennas ProPagat, 1996,44(6):453~459.
[14]金建铭.电磁场有限元方法[M](王建国,葛徳彪译).西安:西安电子科技大学出版社,1998:164~172.
[15] Sony B, Albert H and Baudrand H. Elimination of Spurious Solutions in the Caculation of Eigenmodes by Moment Method [J]. IEEE Trans M T T, 1996,44(1):154~156.
[16]谢德馨,唐任远.计算电磁学今年来的若干重要成果—第15届COMPUMAG会议概述[J].电工计算学报,2005,20(9):1~6.
[17]高本庆,刘波.电磁场时域数值技术新进展[J].北京理工大学学报, 2002, 22(4): 401~406.
[18]葛德彪,闫玉波.电磁波时域有限差分方法[M].西安:西安电子科技大学出版社, 2005:1~376.
[19] Lynch D R and Paulsen K D. Time-domain integration of the Maxwell equations on finite methods [J]. IEEE Trans. on AP, 1990, 38(12): 1933~1942.
[20] Lee J F. WETD-A finite element time-domain approach fro solving Maxwell’s equations [J]. IEEE Microwave and Guided Wave Letters, 1994, 4(1): 11~13.
[21] Komisarek K S, Wang N N, Dominek A K, et al. An investigation of new FETD/ABC methods of computation of scattering from three-dimensional material objects [J]. IEEE Trans. on AP, 1999, 47(10): 1579~1585.
[22]陈晓光,金亚秋,聂在平.轴对称有耗介质电磁问题的时域有限元方法[J].地球物理学报, 1999, 42(2): 268~276.
[23] Shao Z H and Hong W. Generalized Z-domain absorbing boundary conditions for time-domain finite-element method [C]. IEEE Antennas and Propagation Society International Symposium, 2000, 2: 765~768.
[24] Chen R S, Yung E K N, Chan C H, et al. Application of the SSOR preconditioned CG algorithm to the vector FEM for 3-D full-wave analysis of electromagnetic-field boundary-value problems [J]. IEEE Trans. on MTT, 2002, 50(4): 1165~1172.
[25]李思敏.时域有限元法与模匹配法的混合合法[硕士学位论文].成都:电子科技大学, 2003.
[26]刘鹏.完全匹配层与有限元电磁散射分析[博士学位论文].西安:西北工业大学,2001.
[27] D. J. Riley, J. M. Jin, Z. Lou and L. E. R. Petersson. Total-and scattered-field decomposition technique for the finite-element time-domain method [J]. IEEE Transaction on Antennas and Propagation, 2006, 54(1): 35-41.
[28] Z. Lou, L. E. R. Petersson, J. M. Jin and D. J. Riley. Total-and scattered-field decomposition technique for the finite-element time-domain modeling of buried scatterers [J]. IEEE Transaction on Antennas and Wireless Propagation Letters, 2005, 4:133~137.
[29] Z. Lou and J. M. Jin. A novel dual-field time-domain finite-element domain-decomposition method for computational electromagnetics [J]. IEEE Trans. Antennas Propagat. 2006,54(6):1850~1862
[30] Wong W F, Picon O and Hanna V F. A finite element method based on Whitney forms to solve Maxwell equations in the time domain [J]. IEEE Trans. on Magnetics, 1995, 31(3): 1618~1621.
[31] Lee J F, Lee R, Cangellaris A. Time-domain finite-element methods[J]. IEEE Trans. on AP, 1997, 45(3): 430~442.
[32]章文勋.电磁场工程中的泛函[M].上海:上海科学技术文献出版社,1985:13~43.
[33] Gedney S D and Navsariwala U. An unconditionally stable finite element time-domain solution of the vector wave equation [J]. IEEE Microwave and Guided Wave Letters, 1995, 5(10): 332~334.
[34] Jiao D and Jin J M. A general approach for the stability analysis of the time-domain finite-element method for electromagnetic simulations [J]. IEEE Trans. on AP, 2002, 50(11): 1624~1632.
[35]杨宏伟,刘梅林,何小祥.计算电磁学中的时域有限元方法稳定性分析[J],电波科学学报,2007,22(4):712~716.
[36]梁青云.二维电磁问题TDFEM分析中基于IC的预处理技术研究与应用[硕士学位论文].南京:南京航空航天大学,2009.
[37]陈晓光,金亚秋,聂在平.轴对称有耗介质电磁问题的时域有限元法[J].地球物理学报,1999,42(2):268~276.
[38]张骅.有限元方法在二维散射问题中的应用[硕士学位论文].西安:西北工业大学,2006.
[39]赵永久.吸收边界条件的研究及其应用[博士学位论文].西安:西安电子科技大学,1998.
[40]李浩.蝴蝶翅膀微结构电磁散射特性及应用研究[硕士学位论文].南京:南京航空航天大学,2009.
[41] Vukusic P, SSambles J R, Lasernce C R, et al. Quantified interference and diffraction in single Morpho Butterfly scales [J]. Proc Roy Soc B, 1996, 26(1427): 1403~1411.
[42]邵起生.动物的体色[J].生物学通报,1995,30(10):11~13.
[43] Berthier S, Charron E and Silna A D. Determination of the cuticle index of the scales of the iridescent butterfly Morpho Menelaus [J]. Optics Express, 1999, 5:87~92.
[44] Pete Vukusic and J.Roy Sambles. Photonic structures in biology [J]. Nature, 2004, 42(4): 852~855.
[45] Saswatee Banerjee, James B.Cole and Toyohiko Yatagai. Color characterization of a Morpho butterfly wing-scale using a high accuracy nonstandard finite-difference time-domain method. Micron. 2007,38(2), 97~103.
[46] Vukusic P, Sambles J R and Ghiradella H. Optical classification of microstructure in butterfly wing scales [J]. Photonics Science News,2001, 6(1): 61~68.
[47] Luca Plattner. Optical properties of the scales of Morpho Rhetenor butterflies: theoretical and experimental investigation of the back-scattering of light in the visible spectrum [J]. J. R. Soc. Lond, 2004, 1(1):49~59.
[48] Luca Plattner. A study in biomimetics: nanometer-scale, high-efficiency, dielectric diffractive structures on the wings of butterflies and the silicon chip factory [D. Dissertation]. University of Southampton, 2003.
[49] Shiya Yoshioka and Shuichi Kinoshita. Wavelength-selective and anisotropic light-diffusing scale on the wing of the morpho butterfly [J]. Proc Biol Sci, 2004, 271(1539): 581~587.
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[51]胡连荣.蓝蝴蝶变色与梦幻纤维[J].知识就是力量,2000,(9):26~27.
[52] Hao. Li and Xiaoxiang. He. Bandstop mechanism of light scattering from morpho butterfly’s wing [J]. JEMWA, 2008, 22(13):1829~1838.
[53]何小祥,李浩.特殊光子晶体电磁散射角偏特性分析及其应用研究[J].中国光学学报,2009, 29(1):256~261.
[2]孙成祥. TDFEM中吸收边界条件技术及其在二维电磁问题分析中的应用[硕士学位论文].南京:南京航空航天大学,2009.
[3]王秉中.计算电磁学[M].北京:科学出版社, 2005: 1~18.
[4]冯奎胜,卢万铮,朱章虎.电磁场数值计算方法分析[J].山西电子技术, 2005, (6): 43~46.
[5]高本庆.时域有限差分法[M].北京:国防工业出版社,1995:1~22.
[6]刘波,高本庆.电磁场时域数值方法及其混合技术概述[J].微波学报, 2006, 22(2): 1~6.
[7] R. W. Clough. The Finite Element Method of Structura Analysis. Proc.2nd Conf. Electronic Computation. ASCE, Pittsburgh, 1960, pa,9.
[8]倪光正,钱秀英.电磁场数值计算[M].高等教育出版社,1996:1~9.
[9] Silveste P.P. and R.L.Ferrari.有限元在电气工程中的应用[M](简柏敦,倪光正译).杭州:浙江大学出版社,1996:112~132.
[10] Eiber Thomas F and Volkert Hansen. 3-D FEM/BEM-Hybrid approach based on general formulation of Huyens’principle for planar layered media [J]. IEEE Trans.on Microwave Theory and Techniqes.1997,7(45):1105~1112.
[11] Xing chaoYuan,Danielr. Lyneh and JohnW. Strohbehn. CouPling of finite element and moment methods for electromagnetic scattering from inhomogemeous [J]. IEEE Trans. Antennas Propagat, 1992,38(3):386~393.
[12] XingehaoYuan.Three-dimensional electromagnetic scattering from inhomogeneous objects by the hybrid moment and finite element method [J]. IEEE Trans. Microwave Theory Tech, 1990,38(8):1053~1058.
[13] Tom Cwik and Cinzia Zuffada. Modeling three dimensional Seatterers using a CouPled finite element-integral equationformulation[J]. IEEE Trans. Antennas ProPagat, 1996,44(6):453~459.
[14]金建铭.电磁场有限元方法[M](王建国,葛徳彪译).西安:西安电子科技大学出版社,1998:164~172.
[15] Sony B, Albert H and Baudrand H. Elimination of Spurious Solutions in the Caculation of Eigenmodes by Moment Method [J]. IEEE Trans M T T, 1996,44(1):154~156.
[16]谢德馨,唐任远.计算电磁学今年来的若干重要成果—第15届COMPUMAG会议概述[J].电工计算学报,2005,20(9):1~6.
[17]高本庆,刘波.电磁场时域数值技术新进展[J].北京理工大学学报, 2002, 22(4): 401~406.
[18]葛德彪,闫玉波.电磁波时域有限差分方法[M].西安:西安电子科技大学出版社, 2005:1~376.
[19] Lynch D R and Paulsen K D. Time-domain integration of the Maxwell equations on finite methods [J]. IEEE Trans. on AP, 1990, 38(12): 1933~1942.
[20] Lee J F. WETD-A finite element time-domain approach fro solving Maxwell’s equations [J]. IEEE Microwave and Guided Wave Letters, 1994, 4(1): 11~13.
[21] Komisarek K S, Wang N N, Dominek A K, et al. An investigation of new FETD/ABC methods of computation of scattering from three-dimensional material objects [J]. IEEE Trans. on AP, 1999, 47(10): 1579~1585.
[22]陈晓光,金亚秋,聂在平.轴对称有耗介质电磁问题的时域有限元方法[J].地球物理学报, 1999, 42(2): 268~276.
[23] Shao Z H and Hong W. Generalized Z-domain absorbing boundary conditions for time-domain finite-element method [C]. IEEE Antennas and Propagation Society International Symposium, 2000, 2: 765~768.
[24] Chen R S, Yung E K N, Chan C H, et al. Application of the SSOR preconditioned CG algorithm to the vector FEM for 3-D full-wave analysis of electromagnetic-field boundary-value problems [J]. IEEE Trans. on MTT, 2002, 50(4): 1165~1172.
[25]李思敏.时域有限元法与模匹配法的混合合法[硕士学位论文].成都:电子科技大学, 2003.
[26]刘鹏.完全匹配层与有限元电磁散射分析[博士学位论文].西安:西北工业大学,2001.
[27] D. J. Riley, J. M. Jin, Z. Lou and L. E. R. Petersson. Total-and scattered-field decomposition technique for the finite-element time-domain method [J]. IEEE Transaction on Antennas and Propagation, 2006, 54(1): 35-41.
[28] Z. Lou, L. E. R. Petersson, J. M. Jin and D. J. Riley. Total-and scattered-field decomposition technique for the finite-element time-domain modeling of buried scatterers [J]. IEEE Transaction on Antennas and Wireless Propagation Letters, 2005, 4:133~137.
[29] Z. Lou and J. M. Jin. A novel dual-field time-domain finite-element domain-decomposition method for computational electromagnetics [J]. IEEE Trans. Antennas Propagat. 2006,54(6):1850~1862
[30] Wong W F, Picon O and Hanna V F. A finite element method based on Whitney forms to solve Maxwell equations in the time domain [J]. IEEE Trans. on Magnetics, 1995, 31(3): 1618~1621.
[31] Lee J F, Lee R, Cangellaris A. Time-domain finite-element methods[J]. IEEE Trans. on AP, 1997, 45(3): 430~442.
[32]章文勋.电磁场工程中的泛函[M].上海:上海科学技术文献出版社,1985:13~43.
[33] Gedney S D and Navsariwala U. An unconditionally stable finite element time-domain solution of the vector wave equation [J]. IEEE Microwave and Guided Wave Letters, 1995, 5(10): 332~334.
[34] Jiao D and Jin J M. A general approach for the stability analysis of the time-domain finite-element method for electromagnetic simulations [J]. IEEE Trans. on AP, 2002, 50(11): 1624~1632.
[35]杨宏伟,刘梅林,何小祥.计算电磁学中的时域有限元方法稳定性分析[J],电波科学学报,2007,22(4):712~716.
[36]梁青云.二维电磁问题TDFEM分析中基于IC的预处理技术研究与应用[硕士学位论文].南京:南京航空航天大学,2009.
[37]陈晓光,金亚秋,聂在平.轴对称有耗介质电磁问题的时域有限元法[J].地球物理学报,1999,42(2):268~276.
[38]张骅.有限元方法在二维散射问题中的应用[硕士学位论文].西安:西北工业大学,2006.
[39]赵永久.吸收边界条件的研究及其应用[博士学位论文].西安:西安电子科技大学,1998.
[40]李浩.蝴蝶翅膀微结构电磁散射特性及应用研究[硕士学位论文].南京:南京航空航天大学,2009.
[41] Vukusic P, SSambles J R, Lasernce C R, et al. Quantified interference and diffraction in single Morpho Butterfly scales [J]. Proc Roy Soc B, 1996, 26(1427): 1403~1411.
[42]邵起生.动物的体色[J].生物学通报,1995,30(10):11~13.
[43] Berthier S, Charron E and Silna A D. Determination of the cuticle index of the scales of the iridescent butterfly Morpho Menelaus [J]. Optics Express, 1999, 5:87~92.
[44] Pete Vukusic and J.Roy Sambles. Photonic structures in biology [J]. Nature, 2004, 42(4): 852~855.
[45] Saswatee Banerjee, James B.Cole and Toyohiko Yatagai. Color characterization of a Morpho butterfly wing-scale using a high accuracy nonstandard finite-difference time-domain method. Micron. 2007,38(2), 97~103.
[46] Vukusic P, Sambles J R and Ghiradella H. Optical classification of microstructure in butterfly wing scales [J]. Photonics Science News,2001, 6(1): 61~68.
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