并行有限差分算法及其在新型隐身结构中的应用
|
摘要
隐身技术是现代武器生存的基础，现在战争中隐身与反隐身对抗比重增加，对战争的胜负起着越来越重要的作用。研究目标的电磁散射特性是隐身技术发展的基石，同时新兴材料不断涌现，新机理的隐身结构不断出现，都对目标电磁散射特性的研究提出了更高的要求和挑战。本文重点对频率选择表面和人工复合材料等为基础的新型隐身结构进行系统的理论和实验研究。针对这些新型隐身结构体组成复杂且多为色散介质的特点，研究了相关的快速仿真和性能预估方法，选用时域有限差分法（FDTD）作为主要的理论预估方法，完成了FDTD的高效率并行计算程序开发，并实现了适用于色散介质仿真计算的等效环路有限差分算法。
本文首先阐述了串行FDTD并行化的关键技术，并将其部署在天河1号超级计算机上。并行有限差分算法是求解电大目标的有力工具，它具有天然并行的优点，能够充分利用集群的计算资源。天河1号是世界上最快的计算机之一，它提供了强大的计算资源，充分利用其丰富计算资源能够求解电大尺寸问题。在测试中利用7200进程花费少于48小时解决的电磁问题在普通PC机上要花费几年甚至十几年的时间，而此时的并行效率高于80%。
针对传统FDTD算法计算色散介质时的缺点，实现了一种新颖的等效环路有限差分算法(EC-FDTD)。这种算法借鉴传输线算法的思想，在Yee氏网格中引入等效集总元件，包括常规介质中的等效串联电感、等效并联电容和左手材料中的等效并联电感、等效串联电容等。这样的等效方式使其可以提供适用色散介质计算的收敛性条件，更加适合仿真计算频率选择表面和超材料等色散介质。为了提高其计算效率，研究了核内加速技术，这种技术理论上可达到最高4倍的加速，实际应用中得到2倍左右的加速效果。
使用EC-FDTD算法进行了超材料吸波体结构的设计，通过单双环电阻加载技术实现超薄宽频带电磁波吸收功能，使其单环具有6GHz-14.5GHz、双环具有4.5-14.5GHz的超宽吸波频带。同时针对单双环电阻加载设计中的耗时缺点，提出了不需借助全波分析方法的等效电路解析分析方法，这种方法在设计的初期能够极大地节约人力和物力。通过电阻膜加载技术设计单层和双层的复杂吸波结构，这种结构能够实现更好的吸波效果。单层电阻膜加载结构可实现在频带4.5GHz-13.5GHz内的吸波效果，双层结构可实现3GHz-21GHz的超宽带电磁吸波。
隐身天线罩对于实现天线的带外隐身有着重要作用，利用EC-FDTD算法设计了工作频率为1GHz，隐身频带在3GHz-9GHz的电阻加载型天线罩。首次提出了利用龙膜代替电阻膜，实现工作频率2GHz，吸波频带为4.5GHz-12.5GHz的新型隐身天线罩。对上述的新型吸波结构和隐身天线罩进行了样品加工，实验结果验
证了这些新型隐身结构的性质。
The technology of stealth is foundation of survival for modern weapons. Thecounterwork between stealth and anti-stealth has a much larger proportion in today’swar and plays a more important role in deciding the final. The research on scatteringcharacteristics of the targets is the foundation to develop the technology of stealth.Furthermore the developed stealth based on new mechanisms arise as new materials arebrought forward. All of them raise the higher requirements as well as are challenges forthe relevant research. The paper places great emphasis on the novel invisible structurescomprising of frequency selective surfaces (FSS) and metamaterials. Thefinite-difference time-domain method (FDTD) was adopted as the primary predictionmethod to give a fast design and evaluation of such structures with complex anddispersive characteristics. The parallel realization of FDTD and high parallel efficencyis focused, and the equivalent circuit FDTD is realized which is suitable to cope withthe dispersive materials.
The key points for a parallel FDTD solver are reported and the solver is deployedon the Tianhe-1A supercomputer. The algorithm of parallel FDTD is a powerful tool forsolving large electrical objects for its parallel nature. The Tianhe-1A supercompuer isone of the fastest computers in the world at present, which can provide very highcomputational capability. By using parallel computations, we completed a calculationon7200processors in less than48hours, where a serial version would have taken overseveral decades. The parallel efficency is more than80%up to7200processors.
A novel FDTD algorithm named Equivalent Circuit FDTD (EC-FDTD) is realizedto overcome the shortages of the ordinary FDTD, which introduces equivalent lumpedelements from transmission line theory into Yee cell. It includes lumped elements suchas series inductance and shunt capacitance in the right-handed materials, as well asshunt inductance and series capacitance in the left-handed materials. Due to itspromising physical meaning, it can provide the condition of stabilization for thedipersive materials and can be easily generalized to arbitrary dispersive materialsincluding frequency selective surfaces and metamaterials. The technology of StreamingSingle-instruction multiple-data (SIMD) Extensions(SSE) was proposed by Intel and iscurrently utilized in personal computers. SSE is a kind of parallel speedup technology inone core. The speedup can be achieved four times in principle without changinghardware. Combined with SSE, the EC-FDTD can be apparently accelerated. Twicespeedup is achieved in the tests of this paper.
The algorithm of EC-FDTD is utilized to design the wideband metamaterialsabsorbers by employing the single square loops and double squre ones loaded with thelumped resistors. The former has an absorbent bandwidth from6GHz to14.5GHz while the later has the one from4.5GHz to14.5GHz. An equivalent circuit (EC) method forabsorbers design is proposed without using full-wave analysis, which can predict theperformance of the absorbers. The EC method can save much time. The resistivesurfaces are employed to design the absorbers by ultilizing the single construction andthe double one to achieve much better effect of absoring. The former one has theabsorbing bandwidth from4.5GHz to13.5GHz while the latter has the ultr-bandwidthfrom3GHz to21GHz.
The invisible radome has a great impact on reducing the radar cross section of theantenna out of band. Such radome loaded with the lumped resistors is designed atoperating frequency to be1GHz with the absent bandwidth from3GHz to9GHz by thealgorithm. The llumar glass is firstly used to realize such invisible radome with thetransmission properties at2GHz and absorbent bandwidth from4.5GHz to12.5GHzsimultaneously. And then these prototypes are fabricated and measured. From thecomparative results, the properties of the novel structures for stealth are verified.
本文首先阐述了串行FDTD并行化的关键技术，并将其部署在天河1号超级计算机上。并行有限差分算法是求解电大目标的有力工具，它具有天然并行的优点，能够充分利用集群的计算资源。天河1号是世界上最快的计算机之一，它提供了强大的计算资源，充分利用其丰富计算资源能够求解电大尺寸问题。在测试中利用7200进程花费少于48小时解决的电磁问题在普通PC机上要花费几年甚至十几年的时间，而此时的并行效率高于80%。
针对传统FDTD算法计算色散介质时的缺点，实现了一种新颖的等效环路有限差分算法(EC-FDTD)。这种算法借鉴传输线算法的思想，在Yee氏网格中引入等效集总元件，包括常规介质中的等效串联电感、等效并联电容和左手材料中的等效并联电感、等效串联电容等。这样的等效方式使其可以提供适用色散介质计算的收敛性条件，更加适合仿真计算频率选择表面和超材料等色散介质。为了提高其计算效率，研究了核内加速技术，这种技术理论上可达到最高4倍的加速，实际应用中得到2倍左右的加速效果。
使用EC-FDTD算法进行了超材料吸波体结构的设计，通过单双环电阻加载技术实现超薄宽频带电磁波吸收功能，使其单环具有6GHz-14.5GHz、双环具有4.5-14.5GHz的超宽吸波频带。同时针对单双环电阻加载设计中的耗时缺点，提出了不需借助全波分析方法的等效电路解析分析方法，这种方法在设计的初期能够极大地节约人力和物力。通过电阻膜加载技术设计单层和双层的复杂吸波结构，这种结构能够实现更好的吸波效果。单层电阻膜加载结构可实现在频带4.5GHz-13.5GHz内的吸波效果，双层结构可实现3GHz-21GHz的超宽带电磁吸波。
隐身天线罩对于实现天线的带外隐身有着重要作用，利用EC-FDTD算法设计了工作频率为1GHz，隐身频带在3GHz-9GHz的电阻加载型天线罩。首次提出了利用龙膜代替电阻膜，实现工作频率2GHz，吸波频带为4.5GHz-12.5GHz的新型隐身天线罩。对上述的新型吸波结构和隐身天线罩进行了样品加工，实验结果验
证了这些新型隐身结构的性质。
The technology of stealth is foundation of survival for modern weapons. Thecounterwork between stealth and anti-stealth has a much larger proportion in today’swar and plays a more important role in deciding the final. The research on scatteringcharacteristics of the targets is the foundation to develop the technology of stealth.Furthermore the developed stealth based on new mechanisms arise as new materials arebrought forward. All of them raise the higher requirements as well as are challenges forthe relevant research. The paper places great emphasis on the novel invisible structurescomprising of frequency selective surfaces (FSS) and metamaterials. Thefinite-difference time-domain method (FDTD) was adopted as the primary predictionmethod to give a fast design and evaluation of such structures with complex anddispersive characteristics. The parallel realization of FDTD and high parallel efficencyis focused, and the equivalent circuit FDTD is realized which is suitable to cope withthe dispersive materials.
The key points for a parallel FDTD solver are reported and the solver is deployedon the Tianhe-1A supercomputer. The algorithm of parallel FDTD is a powerful tool forsolving large electrical objects for its parallel nature. The Tianhe-1A supercompuer isone of the fastest computers in the world at present, which can provide very highcomputational capability. By using parallel computations, we completed a calculationon7200processors in less than48hours, where a serial version would have taken overseveral decades. The parallel efficency is more than80%up to7200processors.
A novel FDTD algorithm named Equivalent Circuit FDTD (EC-FDTD) is realizedto overcome the shortages of the ordinary FDTD, which introduces equivalent lumpedelements from transmission line theory into Yee cell. It includes lumped elements suchas series inductance and shunt capacitance in the right-handed materials, as well asshunt inductance and series capacitance in the left-handed materials. Due to itspromising physical meaning, it can provide the condition of stabilization for thedipersive materials and can be easily generalized to arbitrary dispersive materialsincluding frequency selective surfaces and metamaterials. The technology of StreamingSingle-instruction multiple-data (SIMD) Extensions(SSE) was proposed by Intel and iscurrently utilized in personal computers. SSE is a kind of parallel speedup technology inone core. The speedup can be achieved four times in principle without changinghardware. Combined with SSE, the EC-FDTD can be apparently accelerated. Twicespeedup is achieved in the tests of this paper.
The algorithm of EC-FDTD is utilized to design the wideband metamaterialsabsorbers by employing the single square loops and double squre ones loaded with thelumped resistors. The former has an absorbent bandwidth from6GHz to14.5GHz while the later has the one from4.5GHz to14.5GHz. An equivalent circuit (EC) method forabsorbers design is proposed without using full-wave analysis, which can predict theperformance of the absorbers. The EC method can save much time. The resistivesurfaces are employed to design the absorbers by ultilizing the single construction andthe double one to achieve much better effect of absoring. The former one has theabsorbing bandwidth from4.5GHz to13.5GHz while the latter has the ultr-bandwidthfrom3GHz to21GHz.
The invisible radome has a great impact on reducing the radar cross section of theantenna out of band. Such radome loaded with the lumped resistors is designed atoperating frequency to be1GHz with the absent bandwidth from3GHz to9GHz by thealgorithm. The llumar glass is firstly used to realize such invisible radome with thetransmission properties at2GHz and absorbent bandwidth from4.5GHz to12.5GHzsimultaneously. And then these prototypes are fabricated and measured. From thecomparative results, the properties of the novel structures for stealth are verified.
引文
[1] Taflove A., Hagness S. Computational Electrodynamics: The Finite-DifferenceTime-Domain Method.2005[J]. Artech House, Norwood, MA.
[2]聂在平.目标与环境电磁散射特性建模:理论,方法与实现.基础篇[M].国防工业出版社,2009.
[3] Harrington R. F., Harrington J. L. Field computation by moment methods[M].Oxford University Press,1996.
[4] Harrington R., Field T.-H. E. McGraw-Hill Co[J]. New York,1961:292-298.
[5] Press W. H., Teukolsky S. A., Vetterling W. T., et al. Numerical recipes in C+:the art of scientific computing[M]. Cambridge University Press Cambridge,2009.
[6] Hestenes M. R., Stiefel E. Methods of conjugate gradients for solving linearsystems[Z]. NBS,1952.
[7] Rokhlin V. V Rokhlin[J]. Journal of Computational Physics,1990,86(2):414-439.
[8] Song J., Chew W. C. Multilevel fast‐multipole algorithm for solving combinedfield integral equations of electromagnetic scattering[J]. Microwave and OpticalTechnology Letters,1995,10(1):14-19.
[9] Rahman B. A., Fernandez F. A., Davies J. B. Review of finite element methodsfor microwave and optical waveguides[J]. Proceedings of the IEEE,1991,79(10):1442-1448.
[10] Jin J.-M., Jin J., Jin J.-M. The finite element method in electromagnetics[M].Wiley New York,2002.
[11]莫锦军.隐身目标低频宽带电磁散射特性研究[D].国防科学技术大学,2004.
[12]王长清,磁学,祝西里,等.电磁场计算中的时域有限差分法[M].北京大学出版社,1994.
[13]高本庆.时域有限差分法[M].国防工业出版社,1995.
[14]葛德彪,闫玉波.电磁波时域有限差分方法[M].西安电子科技大学出版社,2005.
[15] Sullivan D. M. Electromagnetic simulation using the FDTD method[M]. IEEEpress New York:,2000.
[16] Yee K. Numerical solution of initial boundary value problems involvingMaxwell's equations in isotropic media[J]. Antennas and Propagation, IEEETransactions on,1966,14(3):302-307.
[17]都志辉,李三立,陈渝,等.高性能计算之并行编程技术——MPI并行程序设计[M].北京:清华大学出版社,2001.
[18] Namiki T. A new FDTD algorithm based on alternating-direction implicitmethod[J]. Microwave Theory and Techniques, IEEE Transactions on,1999,47(10):2003-2007.
[19] Namiki T.3-D ADI-FDTD method-unconditionally stable time-domainalgorithm for solving full vector Maxwell's equations[J]. Microwave Theory andTechniques, IEEE Transactions on,2000,48(10):1743-1748.
[20] Zhen F., Chen Z., Zhang J. Toward the development of a three-dimensionalunconditionally stable finite-difference time-domain method[J]. MicrowaveTheory and Techniques, IEEE Transactions on,2000,48(9):1550-1558.
[21] Kondylis G. D., De Flaviis F., Pottie G. J., et al. A memory-efficient formulationof the finite-difference time-domain method for the solution of Maxwellequations[J]. Microwave Theory and Techniques, IEEE Transactions on,2001,49(7):1310-1320.
[22] Young J. L., Gaitonde D., Shang J. Toward the construction of a fourth-orderdifference scheme for transient EM wave simulation: staggered grid approach[J].Antennas and Propagation, IEEE Transactions on,1997,45(11):1573-1580.
[23] Georgakopoulos S. V., Renaut R. A., Balanis C. A., et al. A hybrid fourth-orderFDTD utilizing a second-order FDTD subgrid[J]. Microwave and WirelessComponents Letters, IEEE,2001,11(11):462-464.
[24] Hirono T., Lui W., Seki S., et al. A three-dimensional fourth-orderfinite-difference time-domain scheme using a symplectic integratorpropagator[J]. Microwave Theory and Techniques, IEEE Transactions on,2001,49(9):1640-1648.
[25] Holland R., Cable V. P., Wilson L. Finite-volume time-domain (FVTD)techniques for EM scattering[J]. Electromagnetic Compatibility, IEEETransactions on,1991,33(4):281-294.
[26] Mohammadian A. H., Shankar V., Hall W. F. Computation of electromagneticscattering and radiation using a time-domain finite-volume discretizationprocedure[J]. Computer Physics Communications,1991,68(1):175-196.
[27] Yee K. S., Chen J. S. The finite-difference time-domain (FDTD) and thefinite-volume time-domain (FVTD) methods in solving Maxwell's equations[J].Antennas and Propagation, IEEE Transactions on,1997,45(3):354-363.
[28] Yu W., Mittra R. A conformal FDTD software package modeling antennas andmicrostrip circuit components[J]. Antennas and Propagation Magazine, IEEE,2000,42(5):28-39.
[29] Yu W., Mittra R. A conformal FDTD algorithm for modeling perfectlyconducting objects with curve‐shaped surfaces and edges[J]. Microwave andOptical Technology Letters,2000,27(2):136-138.
[30] Waldschmidt G., Taflove A. Three-dimensional CAD-based mesh generator forthe Dey-Mittra conformal FDTD algorithm[J]. Antennas and Propagation, IEEETransactions on,2004,52(7):1658-1664.
[31] Rao S. M., Sarkar T. K. Numerical solution of time domain integral equationsfor arbitrarily shaped conductor/dielectric composite bodies[J]. Antennas andPropagation, IEEE Transactions on,2002,50(12):1831-1837.
[32] Liu Q. The pseudospectral time-domain (PSTD) method: A new algorithm forsolutions of Maxwell's equations[C]. Antennas and Propagation SocietyInternational Symposium,1997. IEEE.,1997Digest, IEEE,1997:122-125.
[33] Krumpholz M., Katehi L. P. MRTD: New time-domain schemes based onmultiresolution analysis[J]. Microwave Theory and Techniques, IEEETransactions on,1996,44(4):555-571.
[34] Obelleiro-Basteiro F., Luis Rodriguez J., Burkholder R. J. An iterative physicaloptics approach for analyzing the electromagnetic scattering by largeopen-ended cavities[J]. Antennas and Propagation, IEEE Transactions on,1995,43(4):356-361.
[35] Ling H., Chou R.-C., Lee S.-W. Shooting and bouncing rays: calculating theRCS of an arbitrarily shaped cavity[J]. Antennas and Propagation, IEEETransactions on,1989,37(2):194-205.
[36] Bhalla R., Ling H. Three-dimensional scattering center extraction using theshooting and bouncing ray technique[J]. Antennas and Propagation, IEEETransactions on,1996,44(11):1445-1453.
[37] Saeidi C., Hodjatkashani F., Fard A. New tube-based shooting and bouncing raytracing method[C]. Advanced Technologies for Communications,2009. ATC'09.International Conference on, IEEE,2009:269-273.
[38] Gao P. C., Tao Y. B., Lin H. Fast RCS prediction using multiresolution shootingand bouncing ray method on the GPU[J]. Progress In Electromagnetics Research,2010,107:187-202.
[39] Rius J. M., Ferrando M., Jofre L. High-frequency RCS of complex radar targetsin real-time[J]. Antennas and Propagation, IEEE Transactions on,1993,41(9):1308-1319.
[40] Rius J. M., Ferrando M., Jofre L. GRECO: graphical electromagnetic computingfor RCS prediction in real time[J]. Antennas and Propagation Magazine, IEEE,1993,35(2):7-17.
[41] Margarit G., Mallorqui J. J., Rius J. M., et al. On the Usage of GRECOSAR, anOrbital Polarimetric SAR Simulator of Complex Targets, to Vessel ClassificationStudies[J]. Geoscience and Remote Sensing, IEEE Transactions on,2006,44(12):3517-3526.
[42] Liu L., Mo J., Yuan N. Bistatic radar cross section predictions with the methodof graphical electromagnetic computing[C]. Microwave and Millimeter WaveTechnology (ICMMT),2012International Conference on, IEEE,2012:1-3.
[43]刘立国,张国军,莫锦军,等.基于图形电磁学的雷达散射截面计算方法改进[J].电波科学学报,2012,27(006):1146-1151.
[44]琼斯,洪旗,魏海滨.隐身技术:黑色魔力的艺术[M].航空工业出版社,1991.
[45] Knott E. F., Shaeffer J. F., Tuley M. T. Radar cross section[M]. SciTechPublishing,2004.
[46] Richardson D. Stealth[M]. Orion Books,1989.
[47] Richardson D. Stealth warplanes[M]. Zenith Press,2001.
[48] Richardson D. Stealth-the combat'ace'[J]. Armada International,2003,27(4):34-36.
[49]黄培康,殷红成,许小剑.雷达目标特性[M].电子工业出版社,2005.
[50]赵东林,周万城.涂敷型吸波材料及其涂层结构设计[J].兵器材料科学与工程,1998,21(4):58-62.
[51] Bachman C. G. Radar targets[J]. NASA STI/Recon Technical Report A,1982,83:30131.
[52]刘少斌.等离子体覆盖目标的电磁特性及其在隐身技术中的应用[D].长沙:国防科学技术大学工学博士学位论文,2004,3.
[53] Green R. B. The general theory of antenna scattering[D]. Ohio State University,1963.
[54] Liepa V., Senior T. Modification to the scattering behavior of a sphere byreactive loading[J]. Proceedings of the IEEE,1965,53(8):1004-1011.
[55]殷红成,黄培康,肖志河.利用MOM和LIBC求解材料涂覆导体平板的后向散射[J].系统工程与电子技术,2000,22(12):1-3.
[56]黄培康,殷红成.增强飞行器角闪烁的方法──一种新的飞行器隐身技术[J].宇航学报,1994,15(2):80-87.
[57] Fante R. L., McCormack M. T. Reflection properties of the Salisbury screen[J].Antennas and Propagation, IEEE Transactions on,1988,36(10):1443-1454.
[58] Chambers B. Optimum design of a Salisbury screen radar absorber[J].Electronics Letters,1994,30(16):1353-1354.
[59] Bahr A. J., Clausing K. R. An approximate model for artificial chiral material[J].Antennas and Propagation, IEEE Transactions on,1994,42(12):1592-1599.
[60] Pendry J., Holden A., Stewart W., et al. Extremely low frequency plasmons inmetallic mesostructures[J]. Physical review letters,1996,76(25):4773-4776.
[61] Pendry J., Holden A., Robbins D., et al. Low frequency plasmons in thin-wirestructures[J]. Journal of Physics: Condensed Matter,1998,10(22):4785.
[62] Pendry J., Holden A., Robbins D., et al. Magnetism from conductors andenhanced nonlinear phenomena[J]. Microwave Theory and Techniques, IEEETransactions on,1999,47(11):2075-2084.
[63] Shelby R. A., Smith D. R., Schultz S. Experimental verification of a negativeindex of refraction[J]. science,2001,292(5514):77-79.
[64] Pacheco Jr J., Grzegorczyk T., Wu B.-I., et al. Power propagation inhomogeneous isotropic frequency-dispersive left-handed media[J]. Physicalreview letters,2002,89(25):257401.
[65] Smith D. R., Kroll N. Negative refractive index in left-handed materials[J].Physical Review Letters,2000,85(14):2933-2936.
[66] Lagarkov A., Kissel V. Near-perfect imaging in a focusing system based on aleft-handed-material plate[J]. Physical review letters,2004,92(7):077401.
[67] Pendry J. B. Negative refraction makes a perfect lens[J]. Physical review letters,2000,85(18):3966-3969.
[68] Pendry J. B., Schurig D., Smith D. R. Controlling electromagnetic fields[J].Science,2006,312(5781):1780-1782.
[69] Schurig D., Mock J., Justice B., et al. Metamaterial electromagnetic cloak atmicrowave frequencies[J]. Science,2006,314(5801):977-980.
[70] Sheng P. Applied physics. Waves on the horizon[J]. Science (New York, NY),2006,313(5792):1399.
[71] Engheta N. Thin absorbing screens using metamaterial surfaces[C]. Antennasand Propagation Society International Symposium,2002. IEEE, IEEE,2002:392-395.
[72] Simms S., Fusco V. Thin radar absorber using artificial magnetic groundplane[J]. Electronics Letters,2005,41(24):1311-1313.
[73] Landy N., Sajuyigbe S., Mock J., et al. Perfect metamaterial absorber[J].Physical review letters,2008,100(20):207402.
[74] Lagarkov A. N., Kisel V. N., Semenenko V. Wide-angle absorption by the use ofa metamaterial plate[J]. Progress In Electromagnetics Research Letters,2008,1:35-44.
[75] Wang J., Qu S., Fu Z., et al. Three-dimensional metamaterial microwaveabsorbers composed of coplanar magnetic and electric resonators[J]. Progress InElectromagnetics Research Letters,2009,7:15-24.
[76] Huang R., Li Z. W., Kong L. B., et al. Analysis and design of an ultra-thinmetamaterial absorber[J]. Progress In Electromagnetics Research B,2009,14:407-429.
[77] Li M., Yang H. L., Hou X. W., et al. Perfect metamaterial absorber with dualbands[J]. Progress In Electromagnetics Research,2010,108:37-49.
[78] Zhu B., Wang Z., Huang C., et al. Polarization insensitive metamaterial absorberwith wide incident angle[J]. Progress In Electromagnetics Research,2010,101:231-239.
[79] Cheng Q., Cui T. J., Jiang W. X., et al. An omnidirectional electromagneticabsorber made of metamaterials[J]. New Journal of Physics,2010,12(6):063006.
[80] Gu C., Qu S., Pei Z., et al. A wide-band, polarization-insensitive and wide-angleterahertz metamaterial absorber[J]. Progress In Electromagnetics ResearchLetters,2010,17:171-179.
[81] Huang L., Chen H. Multi-band and polarization insensitive metamaterialabsorber[J]. Progress In Electromagnetics Research,2011,113:103-110.
[82] He X. J., Wang Y., Wang J., et al. Dual-band terahertz metamaterial absorberwith polarization insensitivity and wide incident angle[J]. Progress InElectromagnetics Research,2011,115:381-397.
[83] Zhou H., Ding F., Jin Y., et al. Terahertz metamaterial modulators based onabsorption[J]. Progress In Electromagnetics Research,2011,119:449-460.
[84] Shen X., Cui T. J., Zhao J., et al. Polarization-independent wide-angletriple-band metamaterial absorber[J]. Optics Express,2011,19(10):9401-9407.
[85] Li H., Yuan L. H., Zhou B., et al. Ultrathin multiband gigahertz metamaterialabsorbers[J]. Journal of Applied Physics,2011,110(1):014909-014909-8.
[86] Kuznetsov S. A., Paulish A. G., Gelfand A. V., et al. Matrix structure ofmetamaterial absorbers for multispectral terahertz imaging[J]. Progress InElectromagnetics Research,2012,122:93-103.
[87] Costa F., Genovesi S., Monorchio A., et al. A circuit-based model for theinterpretation of perfect metamaterial absorbers[J].2012.
[88] Yang J., Shen Z. A thin and broadband absorber using double-square loops[J].Antennas and Wireless Propagation Letters, IEEE,2007,6:388-391.
[89] Costa F., Monorchio A., Manara G. Analysis and design of ultra thinelectromagnetic absorbers comprising resistively loaded high impedancesurfaces[J]. Antennas and Propagation, IEEE Transactions on,2010,58(5):1551-1558.
[90] Munk B. A. Frequency selective surfaces[M]. New York,2000.
[91] Kozakoff D. J. Analysis of radome-enclosed antennas[M]. Artech HousePublishers,2009.
[92] Costa F., Monorchio A. A Frequency Selective Radome With WidebandAbsorbing Properties[J]. Antennas and Propagation, IEEE Transactions on,2012,60(6):2740-2747.
[93]余文华.并行时域有限差分[M].中国传媒大学出版社,2005.
[94] Yu W., Mittra R. Advanced Fdtd Method: Parallelization, Acceleration, andEngineering Applications[M]. Artech House Publishers,2011.
[95] Mur G. Absorbing boundary conditions for the finite-difference approximationof the time-domain electromagnetic-field equations[J]. ElectromagneticCompatibility, IEEE Transactions on,1981,(4):377-382.
[96] Berenger J.-P. A perfectly matched layer for the absorption of electromagneticwaves[J]. Journal of computational physics,1994,114(2):185-200.
[97] Berenger J.-P. Perfectly matched layer for the FDTD solution of wave-structureinteraction problems[J]. Antennas and Propagation, IEEE Transactions on,1996,44(1):110-117.
[98] Berenger J.-P. Three-dimensional perfectly matched layer for the absorption ofelectromagnetic waves[J]. Journal of computational physics,1996,127(2):363-379.
[99] Gedney S. D. An anisotropic PML absorbing media for the FDTD simulation offields in lossy and dispersive media[J]. Electromagnetics,1996,16(4):399-415.
[100] Gedney S. D. An anisotropic perfectly matched layer-absorbing medium for thetruncation of FDTD lattices[J]. Antennas and Propagation, IEEE Transactions on,1996,44(12):1630-1639.
[101] Chew W. C., Weedon W. H. A3D perfectly matched medium from modifiedMaxwell's equations with stretched coordinates[J]. Microwave and opticaltechnology letters,1994,7(13):599-604.
[102] Chew W. C., Weedon W. H., Sezginer A. A3-D perfectly matched medium bycoordinate stretching and its absorption of static fields[C]. AppliedComputational Electromagnetics Symposium Digist, Citeseer,1995:482-489.
[103] Chew W., Jin J., Michielssen E. Complex coordinate stretching as a generalizedabsorbing boundary condition[J]. Microwave and Optical Technology Letters,1997,15(6):363-369.
[104] Roden J. A., Gedney S. D. Convolutional PML (CPML): An efficient FDTDimplementation of the CFS-PML for arbitrary media[J]. Microwave and opticaltechnology letters,2000,27(5):334-338.
[105]尹家贤.时域有限差分法在天线计算中的理论和应用研究[D].中国人民解放军国防科学技术大学,2003.
[106]刘克成,宋学诚.天线原理[M].国防科技大学出版社,1989.
[107] Yu Z. A bandpass source technique for the FDTD analysis of waveguidediscontinuity[J]. Microwave and Optical Technology Letters,1998,17(2):132-135.
[108] Yee K. S., Ingham D., Shlager K. Time-domain extrapolation to the far fieldbased on FDTD calculations[J]. Antennas and Propagation, IEEE Transactionson,1991,39(3):410-413.
[109] Luebbers R. J., Kunz K. S., Schneider M., et al. A finite-differencetime-domain near zone to far zone transformation [electromagnetic scattering][J].Antennas and Propagation, IEEE Transactions on,1991,39(4):429-433.
[110] Shlager K., Smith G. Near-field to near-field transformation for use with FDTDmethod and its application to pulsed antenna problems[J]. Electronics Letters,1994,30(16):1262-1264.
[111] Shlager K., Smith G. Comparison of two FDTD near-field to near-fieldtransformations applied to pulsed antenna problems[J]. Electronics Letters,1995,31(12):936-938.
[112] Shlager K. L., Schneider J. B. A selective survey of the finite-differencetime-domain literature[J]. Antennas and Propagation Magazine, IEEE,1995,37(4):39-57.
[113] Ramahi O. M. Near-and far-field calculations in FDTD simulations usingKirchhoff surface integral representation[J]. Antennas and Propagation, IEEETransactions on,1997,45(5):753-759.
[114] Martin T. An improved near-to far-zone transformation for the finite-differencetime-domain method[J]. Antennas and Propagation, IEEE Transactions on,1998,46(9):1263-1271.
[115]张光甫,刘培国.基于基尔霍夫积分的近远场变换的改进[J].电波科学学报,2000,15(3):339-342.
[116] Schneider J. B., Wagner C. L. FDTD dispersion revisited: Faster-than-lightpropagation[J]. Microwave and Guided Wave Letters, IEEE,1999,9(2):54-56.
[117] Hoffman J. D., Frankel S. Numerical methods for engineers and scientists[M].CRC press,2001.
[118] Sun W., Balanis C., Purchine M., et al. Three-dimensional automatic FDTDmesh generation on a PC[C]. Antennas and Propagation Society InternationalSymposium,1993. AP-S. Digest, IEEE,1994:30-33.
[119] Lee J.-F., Dyczij-Edlinger R. Automatic mesh generation using a modifiedDelaunay tessellation[J]. Antennas and Propagation Magazine, IEEE,1997,39(1):34-45.
[120] Srisukh Y., Nehrbass J., Teixeira F., et al. An approach for automatic gridgeneration in three-dimensional FDTD simulations of complex geometries[J].Antennas and Propagation Magazine, IEEE,2002,44(4):75-80.
[121]张明,林海,鲍虎军. FDTD方法中目标的快速剖分[J].现代机械,(4):1-2.
[122] Navarro E. A., Sangary N. T., Litva J. Some considerations on the accuracy ofthe nonuniform FDTD method and its application to waveguide analysis whencombined with the perfectly matched layer technique[J]. Microwave Theory andTechniques, IEEE Transactions on,1996,44(7):1115-1124.
[123] Yang M., Chen Y. AutoMesh: an automatically adjustable, nonuniform,orthogonal FDTD mesh generator[J]. Antennas and Propagation Magazine,IEEE,1999,41(2):13-19.
[124]张云泉,孙家昶,袁国兴,等.2011年中国高性能计算机发展现状分析与展望[J].高性能计算机发展与应用,2012,38(1):28-28.
[125] Gropp W. MPICH2: A new start for MPI implementations[M]. MPICH2: Anew start for MPI implementations, ed: Springer,2002,7-7.
[126] Gropp W., Lusk E., Ashton D., et al. MPICH2user’s guide[J]. Mathematics andComputer Science Division-Argonne National Laboratory, Version0.4,2005.
[127]李毅.雷达隐身目标电磁散射计算与实验研究[D].长沙:国防科学技术大学,2007.
[128] Liu L., Mo J., Zhang G., et al. A parallel FDTD simulator based on theTianhe-1A supercomputer[C]. Microwave Technology&ComputationalElectromagnetics (ICMTCE),2011IEEE International Conference on,IEEE,2011:406-409.
[129] Dominek A. K., Gilreath M. C., Wood R. M. Almond test body[Z]. GooglePatents,1989.
[130] Woo A. C., Wang H. T., Schuh M. J., et al. EM programmer'snotebook-benchmark radar targets for the validation of computationalelectromagnetics programs[J]. Antennas and Propagation Magazine, IEEE,1993,35(1):84-89.
[131] Rennings A., Otto S., Mosig J., et al. Extended composite right/left-handed(E-CRLH) metamaterial and its application as quadband quarter-wavelengthtransmission line[C]. Microwave Conference,2006. APMC2006. Asia-Pacific,IEEE,2006:1405-1408.
[132] Rennings A., Otto S., Lauer A., et al. An extended equivalent circuit basedFDTD scheme for the efficient simulation of composite right/left-handedmetamaterials[C]. Proc. of the European Microwave Association,2006:71-82.
[133] Studio C. M. ver.2011[J]. CST AG, Bad Nauheimer Str,2011,19.
[134] van Tonder J. J., Jakobus U. Fast multipole solution of metallic and dielectricscattering problems in FEKO[C]. Wireless Communications and AppliedComputational Electromagnetics,2005. IEEE/ACES International Conferenceon, IEEE,2005:511-514.
[135]刘少斌,莫锦军,袁乃昌.各向异性磁化等离子体JEC-FDTD算法[J].物理学报,2004,53(3):783-787.
[136]刘少斌,朱传喜,袁乃昌.等离子体光子晶体的FDTD分析[J].物理学报,2005,54(6):2804-2808.
[137]刘少斌,张光甫,袁乃昌.等离子体覆盖立方散射体目标雷达散射截面的时域有限差分法分析[J].物理学报,2005,53(8):2633-2637.
[138]刘少斌,顾长青,周建江, et al.磁化等离子体光子晶体的FDTD分析[J].物理学报,2006,55(3):1283-1288.
[139] Rennings A., Otto S., Caloz C., et al. Composite right/left‐handed extendedequivalent circuit (CRLH‐EEC) FDTD: stability and dispersion analysis withexamples[J]. International Journal of Numerical Modelling: Electronic Networks,Devices and Fields,2006,19(2):141-172.
[140] Liebig T., Rennings A., Held S., et al. openEMS–a free and open sourceequivalent‐circuit (EC) FDTD simulation platform supporting cylindricalcoordinates suitable for the analysis of traveling wave MRI applications[J].International Journal of Numerical Modelling: Electronic Networks, Devicesand Fields,2012.
[141] Yu W., Yang X., Liu Y. A novel hardware acceleration technique for highperformance parallel FDTD method[C]. Electromagnetics, Applications andStudent Innovation (iWEM),2011IEEE International Workshop on, IEEE,2011:149-153.
[142] Hwang E. O. Digital Logic and Microprocessor Design[J]. La Sierra University,Riverside, CA, Thomson,2006.
[143] Raman S. K., Pentkovski V., Keshava J. Implementing streaming SIMDextensions on the Pentium III processor[J]. Micro, IEEE,2000,20(4):47-57.
[144] Diallo A., Luxey C., Le Thuc P., et al. Study and reduction of the mutualcoupling between two mobile phone PIFAs operating in the DCS1800andUMTS bands[J]. Antennas and Propagation, IEEE Transactions on,2006,54(11):3063-3074.
[145] Cui T. J., Smith D., Liu R. Metamaterials: theory, design, and applications[M].Springer,2009.
[146]崔万照.电磁超介质及其应用[M].国防工业出版社,2008.
[147] Bose J. C. On the rotation of plane of polarisation of electric waves by atwisted structure[J]. Proceedings of the Royal Society of London,1898,63(389-400):146-152.
[148] Lindman K. Om en genom ett isotropt system av spiralformiga resonatoreralstrad rotationspolarisation av de elektromagnetiska v {} gorna[J].{}fversigt af {F} inska {V} etenskaps-{S} ocietetens f {} rhandlingar,{A},1914,57(3):1-32.
[149] Lindell I. V., Sihvola A. H., Kurkijarvi J. Karl F. Lindman: The last Hertzian,and a harbinger of electromagnetic chirality[J]. Antennas and PropagationMagazine, IEEE,1992,34(3):24-30.
[150] Enoch S., Tayeb G., Sabouroux P., et al. A metamaterial for directiveemission[J]. Physical Review Letters,2002,89(21):213902.
[151] Fang N., Xi D., Xu J., et al. Ultrasonic metamaterials with negative modulus[J].Nature materials,2006,5(6):452-456.
[152]李有权.基于电磁带隙结构的隐身技术研究及其在天线阵中的应用[D].国防科学技术大学,2010.
[153] Ansoft H. ver.11[J]. Ansoft Corporation, Pittsburgh, PA,2007.
[154] Marcuvitz N. Waveguide handbook,1964[Z]. McGraw Hill.
[155] Anderson I. On the theory of self-resonant grids[J]. Bell Syst. Tech. J,1975,54(10):1725-1731.
[156] Langley R., Drinkwater A. Improved empirical model for the Jerusalemcross[J]. Microwaves, Optics and Antennas, IEE Proceedings H,1982,129(1):1-6.
[157] Langley R., Parker E. Equivalent circuit model for arrays of square loops[J].Electronics Letters,1982,18(7):294-296.
[158] Langley R., Parker E. Double-square frequency-selective surfaces and theirequivalent circuit[J]. Electronics Letters,1983,19(17):675-677.
[159] Lee C., Langley R. Equivalent-circuit models for frequency-selective surfacesat oblique angles of incidence[C]. IEE Proceedings H (Microwaves, Antennasand Propagation), IET,1985:395-399.
[160] Costa F., Monorchio A., Manara G. An equivalent circuit model of frequencyselective surfaces embedded within dielectric layers[C]. Antennas andPropagation Society International Symposium,2009. APSURSI'09. IEEE,IEEE,2009:1-4.
[161] Costa F., Monorchio A., Manara G. Efficient Analysis of Frequency-SelectiveSurfaces by a Simple Equivalent-Circuit Model[J]. Antennas and PropagationMagazine, IEEE,2012,54(4):35-48.
[162] Yilmaz A. E., Kuzuoglu M. Design of the square loop frequency selectivesurfaces with particle swarm optimization via the equivalent circuit model[J].Radioengineering,2009,18(2):95-102.
[163] Costa F., Monorchio A., Manara G. Ultra-thin absorbers by using highimpedance surfaces with resistive frequency selective surfaces[C]. Antennas andPropagation Society International Symposium,2007IEEE, IEEE,2007:861-864.
[164] Costa F., Monorchio A. Electromagnetic Absorbers based on High-ImpedanceSurfaces: From ultra-narrowband to ultra-wideband absorption[J]. AdvancedElectromagnetics,2012,1(3):7-12.
[165] Parker E., El Sheikh A. Convoluted array elements and reduced size unit cellsfor frequency-selective surfaces[C]. Microwaves, Antennas and Propagation,IEE Proceedings H, IET,1991:19-22.
[166] Chen X., Li Y., Fu Y., et al. Design and analysis of lumped resistor loadedmetamaterial absorber with transmission band[J]. Optics express,2012,20(27):28347-28352.
[167] Costa F., Monorchio A. Absorptive frequency selective radome[C]. GeneralAssembly and Scientific Symposium,2011XXXth URSI, IEEE,2011:1-4.
[2]聂在平.目标与环境电磁散射特性建模:理论,方法与实现.基础篇[M].国防工业出版社,2009.
[3] Harrington R. F., Harrington J. L. Field computation by moment methods[M].Oxford University Press,1996.
[4] Harrington R., Field T.-H. E. McGraw-Hill Co[J]. New York,1961:292-298.
[5] Press W. H., Teukolsky S. A., Vetterling W. T., et al. Numerical recipes in C+:the art of scientific computing[M]. Cambridge University Press Cambridge,2009.
[6] Hestenes M. R., Stiefel E. Methods of conjugate gradients for solving linearsystems[Z]. NBS,1952.
[7] Rokhlin V. V Rokhlin[J]. Journal of Computational Physics,1990,86(2):414-439.
[8] Song J., Chew W. C. Multilevel fast‐multipole algorithm for solving combinedfield integral equations of electromagnetic scattering[J]. Microwave and OpticalTechnology Letters,1995,10(1):14-19.
[9] Rahman B. A., Fernandez F. A., Davies J. B. Review of finite element methodsfor microwave and optical waveguides[J]. Proceedings of the IEEE,1991,79(10):1442-1448.
[10] Jin J.-M., Jin J., Jin J.-M. The finite element method in electromagnetics[M].Wiley New York,2002.
[11]莫锦军.隐身目标低频宽带电磁散射特性研究[D].国防科学技术大学,2004.
[12]王长清,磁学,祝西里,等.电磁场计算中的时域有限差分法[M].北京大学出版社,1994.
[13]高本庆.时域有限差分法[M].国防工业出版社,1995.
[14]葛德彪,闫玉波.电磁波时域有限差分方法[M].西安电子科技大学出版社,2005.
[15] Sullivan D. M. Electromagnetic simulation using the FDTD method[M]. IEEEpress New York:,2000.
[16] Yee K. Numerical solution of initial boundary value problems involvingMaxwell's equations in isotropic media[J]. Antennas and Propagation, IEEETransactions on,1966,14(3):302-307.
[17]都志辉,李三立,陈渝,等.高性能计算之并行编程技术——MPI并行程序设计[M].北京:清华大学出版社,2001.
[18] Namiki T. A new FDTD algorithm based on alternating-direction implicitmethod[J]. Microwave Theory and Techniques, IEEE Transactions on,1999,47(10):2003-2007.
[19] Namiki T.3-D ADI-FDTD method-unconditionally stable time-domainalgorithm for solving full vector Maxwell's equations[J]. Microwave Theory andTechniques, IEEE Transactions on,2000,48(10):1743-1748.
[20] Zhen F., Chen Z., Zhang J. Toward the development of a three-dimensionalunconditionally stable finite-difference time-domain method[J]. MicrowaveTheory and Techniques, IEEE Transactions on,2000,48(9):1550-1558.
[21] Kondylis G. D., De Flaviis F., Pottie G. J., et al. A memory-efficient formulationof the finite-difference time-domain method for the solution of Maxwellequations[J]. Microwave Theory and Techniques, IEEE Transactions on,2001,49(7):1310-1320.
[22] Young J. L., Gaitonde D., Shang J. Toward the construction of a fourth-orderdifference scheme for transient EM wave simulation: staggered grid approach[J].Antennas and Propagation, IEEE Transactions on,1997,45(11):1573-1580.
[23] Georgakopoulos S. V., Renaut R. A., Balanis C. A., et al. A hybrid fourth-orderFDTD utilizing a second-order FDTD subgrid[J]. Microwave and WirelessComponents Letters, IEEE,2001,11(11):462-464.
[24] Hirono T., Lui W., Seki S., et al. A three-dimensional fourth-orderfinite-difference time-domain scheme using a symplectic integratorpropagator[J]. Microwave Theory and Techniques, IEEE Transactions on,2001,49(9):1640-1648.
[25] Holland R., Cable V. P., Wilson L. Finite-volume time-domain (FVTD)techniques for EM scattering[J]. Electromagnetic Compatibility, IEEETransactions on,1991,33(4):281-294.
[26] Mohammadian A. H., Shankar V., Hall W. F. Computation of electromagneticscattering and radiation using a time-domain finite-volume discretizationprocedure[J]. Computer Physics Communications,1991,68(1):175-196.
[27] Yee K. S., Chen J. S. The finite-difference time-domain (FDTD) and thefinite-volume time-domain (FVTD) methods in solving Maxwell's equations[J].Antennas and Propagation, IEEE Transactions on,1997,45(3):354-363.
[28] Yu W., Mittra R. A conformal FDTD software package modeling antennas andmicrostrip circuit components[J]. Antennas and Propagation Magazine, IEEE,2000,42(5):28-39.
[29] Yu W., Mittra R. A conformal FDTD algorithm for modeling perfectlyconducting objects with curve‐shaped surfaces and edges[J]. Microwave andOptical Technology Letters,2000,27(2):136-138.
[30] Waldschmidt G., Taflove A. Three-dimensional CAD-based mesh generator forthe Dey-Mittra conformal FDTD algorithm[J]. Antennas and Propagation, IEEETransactions on,2004,52(7):1658-1664.
[31] Rao S. M., Sarkar T. K. Numerical solution of time domain integral equationsfor arbitrarily shaped conductor/dielectric composite bodies[J]. Antennas andPropagation, IEEE Transactions on,2002,50(12):1831-1837.
[32] Liu Q. The pseudospectral time-domain (PSTD) method: A new algorithm forsolutions of Maxwell's equations[C]. Antennas and Propagation SocietyInternational Symposium,1997. IEEE.,1997Digest, IEEE,1997:122-125.
[33] Krumpholz M., Katehi L. P. MRTD: New time-domain schemes based onmultiresolution analysis[J]. Microwave Theory and Techniques, IEEETransactions on,1996,44(4):555-571.
[34] Obelleiro-Basteiro F., Luis Rodriguez J., Burkholder R. J. An iterative physicaloptics approach for analyzing the electromagnetic scattering by largeopen-ended cavities[J]. Antennas and Propagation, IEEE Transactions on,1995,43(4):356-361.
[35] Ling H., Chou R.-C., Lee S.-W. Shooting and bouncing rays: calculating theRCS of an arbitrarily shaped cavity[J]. Antennas and Propagation, IEEETransactions on,1989,37(2):194-205.
[36] Bhalla R., Ling H. Three-dimensional scattering center extraction using theshooting and bouncing ray technique[J]. Antennas and Propagation, IEEETransactions on,1996,44(11):1445-1453.
[37] Saeidi C., Hodjatkashani F., Fard A. New tube-based shooting and bouncing raytracing method[C]. Advanced Technologies for Communications,2009. ATC'09.International Conference on, IEEE,2009:269-273.
[38] Gao P. C., Tao Y. B., Lin H. Fast RCS prediction using multiresolution shootingand bouncing ray method on the GPU[J]. Progress In Electromagnetics Research,2010,107:187-202.
[39] Rius J. M., Ferrando M., Jofre L. High-frequency RCS of complex radar targetsin real-time[J]. Antennas and Propagation, IEEE Transactions on,1993,41(9):1308-1319.
[40] Rius J. M., Ferrando M., Jofre L. GRECO: graphical electromagnetic computingfor RCS prediction in real time[J]. Antennas and Propagation Magazine, IEEE,1993,35(2):7-17.
[41] Margarit G., Mallorqui J. J., Rius J. M., et al. On the Usage of GRECOSAR, anOrbital Polarimetric SAR Simulator of Complex Targets, to Vessel ClassificationStudies[J]. Geoscience and Remote Sensing, IEEE Transactions on,2006,44(12):3517-3526.
[42] Liu L., Mo J., Yuan N. Bistatic radar cross section predictions with the methodof graphical electromagnetic computing[C]. Microwave and Millimeter WaveTechnology (ICMMT),2012International Conference on, IEEE,2012:1-3.
[43]刘立国,张国军,莫锦军,等.基于图形电磁学的雷达散射截面计算方法改进[J].电波科学学报,2012,27(006):1146-1151.
[44]琼斯,洪旗,魏海滨.隐身技术:黑色魔力的艺术[M].航空工业出版社,1991.
[45] Knott E. F., Shaeffer J. F., Tuley M. T. Radar cross section[M]. SciTechPublishing,2004.
[46] Richardson D. Stealth[M]. Orion Books,1989.
[47] Richardson D. Stealth warplanes[M]. Zenith Press,2001.
[48] Richardson D. Stealth-the combat'ace'[J]. Armada International,2003,27(4):34-36.
[49]黄培康,殷红成,许小剑.雷达目标特性[M].电子工业出版社,2005.
[50]赵东林,周万城.涂敷型吸波材料及其涂层结构设计[J].兵器材料科学与工程,1998,21(4):58-62.
[51] Bachman C. G. Radar targets[J]. NASA STI/Recon Technical Report A,1982,83:30131.
[52]刘少斌.等离子体覆盖目标的电磁特性及其在隐身技术中的应用[D].长沙:国防科学技术大学工学博士学位论文,2004,3.
[53] Green R. B. The general theory of antenna scattering[D]. Ohio State University,1963.
[54] Liepa V., Senior T. Modification to the scattering behavior of a sphere byreactive loading[J]. Proceedings of the IEEE,1965,53(8):1004-1011.
[55]殷红成,黄培康,肖志河.利用MOM和LIBC求解材料涂覆导体平板的后向散射[J].系统工程与电子技术,2000,22(12):1-3.
[56]黄培康,殷红成.增强飞行器角闪烁的方法──一种新的飞行器隐身技术[J].宇航学报,1994,15(2):80-87.
[57] Fante R. L., McCormack M. T. Reflection properties of the Salisbury screen[J].Antennas and Propagation, IEEE Transactions on,1988,36(10):1443-1454.
[58] Chambers B. Optimum design of a Salisbury screen radar absorber[J].Electronics Letters,1994,30(16):1353-1354.
[59] Bahr A. J., Clausing K. R. An approximate model for artificial chiral material[J].Antennas and Propagation, IEEE Transactions on,1994,42(12):1592-1599.
[60] Pendry J., Holden A., Stewart W., et al. Extremely low frequency plasmons inmetallic mesostructures[J]. Physical review letters,1996,76(25):4773-4776.
[61] Pendry J., Holden A., Robbins D., et al. Low frequency plasmons in thin-wirestructures[J]. Journal of Physics: Condensed Matter,1998,10(22):4785.
[62] Pendry J., Holden A., Robbins D., et al. Magnetism from conductors andenhanced nonlinear phenomena[J]. Microwave Theory and Techniques, IEEETransactions on,1999,47(11):2075-2084.
[63] Shelby R. A., Smith D. R., Schultz S. Experimental verification of a negativeindex of refraction[J]. science,2001,292(5514):77-79.
[64] Pacheco Jr J., Grzegorczyk T., Wu B.-I., et al. Power propagation inhomogeneous isotropic frequency-dispersive left-handed media[J]. Physicalreview letters,2002,89(25):257401.
[65] Smith D. R., Kroll N. Negative refractive index in left-handed materials[J].Physical Review Letters,2000,85(14):2933-2936.
[66] Lagarkov A., Kissel V. Near-perfect imaging in a focusing system based on aleft-handed-material plate[J]. Physical review letters,2004,92(7):077401.
[67] Pendry J. B. Negative refraction makes a perfect lens[J]. Physical review letters,2000,85(18):3966-3969.
[68] Pendry J. B., Schurig D., Smith D. R. Controlling electromagnetic fields[J].Science,2006,312(5781):1780-1782.
[69] Schurig D., Mock J., Justice B., et al. Metamaterial electromagnetic cloak atmicrowave frequencies[J]. Science,2006,314(5801):977-980.
[70] Sheng P. Applied physics. Waves on the horizon[J]. Science (New York, NY),2006,313(5792):1399.
[71] Engheta N. Thin absorbing screens using metamaterial surfaces[C]. Antennasand Propagation Society International Symposium,2002. IEEE, IEEE,2002:392-395.
[72] Simms S., Fusco V. Thin radar absorber using artificial magnetic groundplane[J]. Electronics Letters,2005,41(24):1311-1313.
[73] Landy N., Sajuyigbe S., Mock J., et al. Perfect metamaterial absorber[J].Physical review letters,2008,100(20):207402.
[74] Lagarkov A. N., Kisel V. N., Semenenko V. Wide-angle absorption by the use ofa metamaterial plate[J]. Progress In Electromagnetics Research Letters,2008,1:35-44.
[75] Wang J., Qu S., Fu Z., et al. Three-dimensional metamaterial microwaveabsorbers composed of coplanar magnetic and electric resonators[J]. Progress InElectromagnetics Research Letters,2009,7:15-24.
[76] Huang R., Li Z. W., Kong L. B., et al. Analysis and design of an ultra-thinmetamaterial absorber[J]. Progress In Electromagnetics Research B,2009,14:407-429.
[77] Li M., Yang H. L., Hou X. W., et al. Perfect metamaterial absorber with dualbands[J]. Progress In Electromagnetics Research,2010,108:37-49.
[78] Zhu B., Wang Z., Huang C., et al. Polarization insensitive metamaterial absorberwith wide incident angle[J]. Progress In Electromagnetics Research,2010,101:231-239.
[79] Cheng Q., Cui T. J., Jiang W. X., et al. An omnidirectional electromagneticabsorber made of metamaterials[J]. New Journal of Physics,2010,12(6):063006.
[80] Gu C., Qu S., Pei Z., et al. A wide-band, polarization-insensitive and wide-angleterahertz metamaterial absorber[J]. Progress In Electromagnetics ResearchLetters,2010,17:171-179.
[81] Huang L., Chen H. Multi-band and polarization insensitive metamaterialabsorber[J]. Progress In Electromagnetics Research,2011,113:103-110.
[82] He X. J., Wang Y., Wang J., et al. Dual-band terahertz metamaterial absorberwith polarization insensitivity and wide incident angle[J]. Progress InElectromagnetics Research,2011,115:381-397.
[83] Zhou H., Ding F., Jin Y., et al. Terahertz metamaterial modulators based onabsorption[J]. Progress In Electromagnetics Research,2011,119:449-460.
[84] Shen X., Cui T. J., Zhao J., et al. Polarization-independent wide-angletriple-band metamaterial absorber[J]. Optics Express,2011,19(10):9401-9407.
[85] Li H., Yuan L. H., Zhou B., et al. Ultrathin multiband gigahertz metamaterialabsorbers[J]. Journal of Applied Physics,2011,110(1):014909-014909-8.
[86] Kuznetsov S. A., Paulish A. G., Gelfand A. V., et al. Matrix structure ofmetamaterial absorbers for multispectral terahertz imaging[J]. Progress InElectromagnetics Research,2012,122:93-103.
[87] Costa F., Genovesi S., Monorchio A., et al. A circuit-based model for theinterpretation of perfect metamaterial absorbers[J].2012.
[88] Yang J., Shen Z. A thin and broadband absorber using double-square loops[J].Antennas and Wireless Propagation Letters, IEEE,2007,6:388-391.
[89] Costa F., Monorchio A., Manara G. Analysis and design of ultra thinelectromagnetic absorbers comprising resistively loaded high impedancesurfaces[J]. Antennas and Propagation, IEEE Transactions on,2010,58(5):1551-1558.
[90] Munk B. A. Frequency selective surfaces[M]. New York,2000.
[91] Kozakoff D. J. Analysis of radome-enclosed antennas[M]. Artech HousePublishers,2009.
[92] Costa F., Monorchio A. A Frequency Selective Radome With WidebandAbsorbing Properties[J]. Antennas and Propagation, IEEE Transactions on,2012,60(6):2740-2747.
[93]余文华.并行时域有限差分[M].中国传媒大学出版社,2005.
[94] Yu W., Mittra R. Advanced Fdtd Method: Parallelization, Acceleration, andEngineering Applications[M]. Artech House Publishers,2011.
[95] Mur G. Absorbing boundary conditions for the finite-difference approximationof the time-domain electromagnetic-field equations[J]. ElectromagneticCompatibility, IEEE Transactions on,1981,(4):377-382.
[96] Berenger J.-P. A perfectly matched layer for the absorption of electromagneticwaves[J]. Journal of computational physics,1994,114(2):185-200.
[97] Berenger J.-P. Perfectly matched layer for the FDTD solution of wave-structureinteraction problems[J]. Antennas and Propagation, IEEE Transactions on,1996,44(1):110-117.
[98] Berenger J.-P. Three-dimensional perfectly matched layer for the absorption ofelectromagnetic waves[J]. Journal of computational physics,1996,127(2):363-379.
[99] Gedney S. D. An anisotropic PML absorbing media for the FDTD simulation offields in lossy and dispersive media[J]. Electromagnetics,1996,16(4):399-415.
[100] Gedney S. D. An anisotropic perfectly matched layer-absorbing medium for thetruncation of FDTD lattices[J]. Antennas and Propagation, IEEE Transactions on,1996,44(12):1630-1639.
[101] Chew W. C., Weedon W. H. A3D perfectly matched medium from modifiedMaxwell's equations with stretched coordinates[J]. Microwave and opticaltechnology letters,1994,7(13):599-604.
[102] Chew W. C., Weedon W. H., Sezginer A. A3-D perfectly matched medium bycoordinate stretching and its absorption of static fields[C]. AppliedComputational Electromagnetics Symposium Digist, Citeseer,1995:482-489.
[103] Chew W., Jin J., Michielssen E. Complex coordinate stretching as a generalizedabsorbing boundary condition[J]. Microwave and Optical Technology Letters,1997,15(6):363-369.
[104] Roden J. A., Gedney S. D. Convolutional PML (CPML): An efficient FDTDimplementation of the CFS-PML for arbitrary media[J]. Microwave and opticaltechnology letters,2000,27(5):334-338.
[105]尹家贤.时域有限差分法在天线计算中的理论和应用研究[D].中国人民解放军国防科学技术大学,2003.
[106]刘克成,宋学诚.天线原理[M].国防科技大学出版社,1989.
[107] Yu Z. A bandpass source technique for the FDTD analysis of waveguidediscontinuity[J]. Microwave and Optical Technology Letters,1998,17(2):132-135.
[108] Yee K. S., Ingham D., Shlager K. Time-domain extrapolation to the far fieldbased on FDTD calculations[J]. Antennas and Propagation, IEEE Transactionson,1991,39(3):410-413.
[109] Luebbers R. J., Kunz K. S., Schneider M., et al. A finite-differencetime-domain near zone to far zone transformation [electromagnetic scattering][J].Antennas and Propagation, IEEE Transactions on,1991,39(4):429-433.
[110] Shlager K., Smith G. Near-field to near-field transformation for use with FDTDmethod and its application to pulsed antenna problems[J]. Electronics Letters,1994,30(16):1262-1264.
[111] Shlager K., Smith G. Comparison of two FDTD near-field to near-fieldtransformations applied to pulsed antenna problems[J]. Electronics Letters,1995,31(12):936-938.
[112] Shlager K. L., Schneider J. B. A selective survey of the finite-differencetime-domain literature[J]. Antennas and Propagation Magazine, IEEE,1995,37(4):39-57.
[113] Ramahi O. M. Near-and far-field calculations in FDTD simulations usingKirchhoff surface integral representation[J]. Antennas and Propagation, IEEETransactions on,1997,45(5):753-759.
[114] Martin T. An improved near-to far-zone transformation for the finite-differencetime-domain method[J]. Antennas and Propagation, IEEE Transactions on,1998,46(9):1263-1271.
[115]张光甫,刘培国.基于基尔霍夫积分的近远场变换的改进[J].电波科学学报,2000,15(3):339-342.
[116] Schneider J. B., Wagner C. L. FDTD dispersion revisited: Faster-than-lightpropagation[J]. Microwave and Guided Wave Letters, IEEE,1999,9(2):54-56.
[117] Hoffman J. D., Frankel S. Numerical methods for engineers and scientists[M].CRC press,2001.
[118] Sun W., Balanis C., Purchine M., et al. Three-dimensional automatic FDTDmesh generation on a PC[C]. Antennas and Propagation Society InternationalSymposium,1993. AP-S. Digest, IEEE,1994:30-33.
[119] Lee J.-F., Dyczij-Edlinger R. Automatic mesh generation using a modifiedDelaunay tessellation[J]. Antennas and Propagation Magazine, IEEE,1997,39(1):34-45.
[120] Srisukh Y., Nehrbass J., Teixeira F., et al. An approach for automatic gridgeneration in three-dimensional FDTD simulations of complex geometries[J].Antennas and Propagation Magazine, IEEE,2002,44(4):75-80.
[121]张明,林海,鲍虎军. FDTD方法中目标的快速剖分[J].现代机械,(4):1-2.
[122] Navarro E. A., Sangary N. T., Litva J. Some considerations on the accuracy ofthe nonuniform FDTD method and its application to waveguide analysis whencombined with the perfectly matched layer technique[J]. Microwave Theory andTechniques, IEEE Transactions on,1996,44(7):1115-1124.
[123] Yang M., Chen Y. AutoMesh: an automatically adjustable, nonuniform,orthogonal FDTD mesh generator[J]. Antennas and Propagation Magazine,IEEE,1999,41(2):13-19.
[124]张云泉,孙家昶,袁国兴,等.2011年中国高性能计算机发展现状分析与展望[J].高性能计算机发展与应用,2012,38(1):28-28.
[125] Gropp W. MPICH2: A new start for MPI implementations[M]. MPICH2: Anew start for MPI implementations, ed: Springer,2002,7-7.
[126] Gropp W., Lusk E., Ashton D., et al. MPICH2user’s guide[J]. Mathematics andComputer Science Division-Argonne National Laboratory, Version0.4,2005.
[127]李毅.雷达隐身目标电磁散射计算与实验研究[D].长沙:国防科学技术大学,2007.
[128] Liu L., Mo J., Zhang G., et al. A parallel FDTD simulator based on theTianhe-1A supercomputer[C]. Microwave Technology&ComputationalElectromagnetics (ICMTCE),2011IEEE International Conference on,IEEE,2011:406-409.
[129] Dominek A. K., Gilreath M. C., Wood R. M. Almond test body[Z]. GooglePatents,1989.
[130] Woo A. C., Wang H. T., Schuh M. J., et al. EM programmer'snotebook-benchmark radar targets for the validation of computationalelectromagnetics programs[J]. Antennas and Propagation Magazine, IEEE,1993,35(1):84-89.
[131] Rennings A., Otto S., Mosig J., et al. Extended composite right/left-handed(E-CRLH) metamaterial and its application as quadband quarter-wavelengthtransmission line[C]. Microwave Conference,2006. APMC2006. Asia-Pacific,IEEE,2006:1405-1408.
[132] Rennings A., Otto S., Lauer A., et al. An extended equivalent circuit basedFDTD scheme for the efficient simulation of composite right/left-handedmetamaterials[C]. Proc. of the European Microwave Association,2006:71-82.
[133] Studio C. M. ver.2011[J]. CST AG, Bad Nauheimer Str,2011,19.
[134] van Tonder J. J., Jakobus U. Fast multipole solution of metallic and dielectricscattering problems in FEKO[C]. Wireless Communications and AppliedComputational Electromagnetics,2005. IEEE/ACES International Conferenceon, IEEE,2005:511-514.
[135]刘少斌,莫锦军,袁乃昌.各向异性磁化等离子体JEC-FDTD算法[J].物理学报,2004,53(3):783-787.
[136]刘少斌,朱传喜,袁乃昌.等离子体光子晶体的FDTD分析[J].物理学报,2005,54(6):2804-2808.
[137]刘少斌,张光甫,袁乃昌.等离子体覆盖立方散射体目标雷达散射截面的时域有限差分法分析[J].物理学报,2005,53(8):2633-2637.
[138]刘少斌,顾长青,周建江, et al.磁化等离子体光子晶体的FDTD分析[J].物理学报,2006,55(3):1283-1288.
[139] Rennings A., Otto S., Caloz C., et al. Composite right/left‐handed extendedequivalent circuit (CRLH‐EEC) FDTD: stability and dispersion analysis withexamples[J]. International Journal of Numerical Modelling: Electronic Networks,Devices and Fields,2006,19(2):141-172.
[140] Liebig T., Rennings A., Held S., et al. openEMS–a free and open sourceequivalent‐circuit (EC) FDTD simulation platform supporting cylindricalcoordinates suitable for the analysis of traveling wave MRI applications[J].International Journal of Numerical Modelling: Electronic Networks, Devicesand Fields,2012.
[141] Yu W., Yang X., Liu Y. A novel hardware acceleration technique for highperformance parallel FDTD method[C]. Electromagnetics, Applications andStudent Innovation (iWEM),2011IEEE International Workshop on, IEEE,2011:149-153.
[142] Hwang E. O. Digital Logic and Microprocessor Design[J]. La Sierra University,Riverside, CA, Thomson,2006.
[143] Raman S. K., Pentkovski V., Keshava J. Implementing streaming SIMDextensions on the Pentium III processor[J]. Micro, IEEE,2000,20(4):47-57.
[144] Diallo A., Luxey C., Le Thuc P., et al. Study and reduction of the mutualcoupling between two mobile phone PIFAs operating in the DCS1800andUMTS bands[J]. Antennas and Propagation, IEEE Transactions on,2006,54(11):3063-3074.
[145] Cui T. J., Smith D., Liu R. Metamaterials: theory, design, and applications[M].Springer,2009.
[146]崔万照.电磁超介质及其应用[M].国防工业出版社,2008.
[147] Bose J. C. On the rotation of plane of polarisation of electric waves by atwisted structure[J]. Proceedings of the Royal Society of London,1898,63(389-400):146-152.
[148] Lindman K. Om en genom ett isotropt system av spiralformiga resonatoreralstrad rotationspolarisation av de elektromagnetiska v {} gorna[J].{}fversigt af {F} inska {V} etenskaps-{S} ocietetens f {} rhandlingar,{A},1914,57(3):1-32.
[149] Lindell I. V., Sihvola A. H., Kurkijarvi J. Karl F. Lindman: The last Hertzian,and a harbinger of electromagnetic chirality[J]. Antennas and PropagationMagazine, IEEE,1992,34(3):24-30.
[150] Enoch S., Tayeb G., Sabouroux P., et al. A metamaterial for directiveemission[J]. Physical Review Letters,2002,89(21):213902.
[151] Fang N., Xi D., Xu J., et al. Ultrasonic metamaterials with negative modulus[J].Nature materials,2006,5(6):452-456.
[152]李有权.基于电磁带隙结构的隐身技术研究及其在天线阵中的应用[D].国防科学技术大学,2010.
[153] Ansoft H. ver.11[J]. Ansoft Corporation, Pittsburgh, PA,2007.
[154] Marcuvitz N. Waveguide handbook,1964[Z]. McGraw Hill.
[155] Anderson I. On the theory of self-resonant grids[J]. Bell Syst. Tech. J,1975,54(10):1725-1731.
[156] Langley R., Drinkwater A. Improved empirical model for the Jerusalemcross[J]. Microwaves, Optics and Antennas, IEE Proceedings H,1982,129(1):1-6.
[157] Langley R., Parker E. Equivalent circuit model for arrays of square loops[J].Electronics Letters,1982,18(7):294-296.
[158] Langley R., Parker E. Double-square frequency-selective surfaces and theirequivalent circuit[J]. Electronics Letters,1983,19(17):675-677.
[159] Lee C., Langley R. Equivalent-circuit models for frequency-selective surfacesat oblique angles of incidence[C]. IEE Proceedings H (Microwaves, Antennasand Propagation), IET,1985:395-399.
[160] Costa F., Monorchio A., Manara G. An equivalent circuit model of frequencyselective surfaces embedded within dielectric layers[C]. Antennas andPropagation Society International Symposium,2009. APSURSI'09. IEEE,IEEE,2009:1-4.
[161] Costa F., Monorchio A., Manara G. Efficient Analysis of Frequency-SelectiveSurfaces by a Simple Equivalent-Circuit Model[J]. Antennas and PropagationMagazine, IEEE,2012,54(4):35-48.
[162] Yilmaz A. E., Kuzuoglu M. Design of the square loop frequency selectivesurfaces with particle swarm optimization via the equivalent circuit model[J].Radioengineering,2009,18(2):95-102.
[163] Costa F., Monorchio A., Manara G. Ultra-thin absorbers by using highimpedance surfaces with resistive frequency selective surfaces[C]. Antennas andPropagation Society International Symposium,2007IEEE, IEEE,2007:861-864.
[164] Costa F., Monorchio A. Electromagnetic Absorbers based on High-ImpedanceSurfaces: From ultra-narrowband to ultra-wideband absorption[J]. AdvancedElectromagnetics,2012,1(3):7-12.
[165] Parker E., El Sheikh A. Convoluted array elements and reduced size unit cellsfor frequency-selective surfaces[C]. Microwaves, Antennas and Propagation,IEE Proceedings H, IET,1991:19-22.
[166] Chen X., Li Y., Fu Y., et al. Design and analysis of lumped resistor loadedmetamaterial absorber with transmission band[J]. Optics express,2012,20(27):28347-28352.
[167] Costa F., Monorchio A. Absorptive frequency selective radome[C]. GeneralAssembly and Scientific Symposium,2011XXXth URSI, IEEE,2011:1-4.