大规模时、频域并行电磁算法研究
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摘要
近年来，并行电磁算法以其优越的加速性能受到了人们的广泛关注，越来越多地被应用于大规模电磁问题的求解和仿真中。论文以时、频域电磁算法的“并行应用”为主线，以基于ScaLAPACK和MPI数学库的并行高阶矩量法，并行物理光学方法，并行高阶矩量法、物理光学法的混合方法，以及并行时域积分方程混合自适应交叉近似法(Adaptive CrossApproximation或ACA)为研究对象，计算了金属、介质目标的时、频域电磁辐射、散射响应。论文所取得的主要研究成果为：
1.采用高阶基函数替代传统的低阶基函数（如RWG基函数）展开模型的电磁流未知量，从而解决了低阶矩量法在处理电大尺寸模型时，由于10的网格剖分尺寸所带来的未知量数目巨大，消耗计算机内存多，硬件资源不足等问题；采用Poggio-Miller-Chang-Harrington-Wu (PMCHW)积分方程分析金属、介质混合体目标；为了加快问题的求解速度，提高效率，结合MPI和ScaLAPACK数学库自身的性能特点提出了一种高效的阻抗矩阵并行填充策略，该并行策略可以保证算法具有良好的并行效率和负载均衡性；
2.利用并行高阶矩量法解决了一大批电磁问题仿真，合理的求解时间和高精度的计算结果说明该算法可用于解决实际工程问题；
3.针对金属、介质混合体目标，从阻抗边界条件出发，应用传输线理论，研究了一种基于三角形面片建模，以路德维格(Ludwig)积分方法求解积分表达式的新的物理光学方法。同时，为了加速计算，结合MPI数学库研究了算法的高效率并行方案。该算法可处理阻抗表面模型，纯介质体，多层介质涂覆目标以及传统的理想导电体(Perfect Electric Conducting或PEC)模型，用于预估自由空间中、半空间中电大尺寸模型的单、双站雷达散射截面(Radar Cross Section或RCS)；研究了并行高阶矩量法、物理光学混合方法用以分析机载复杂天线的受扰辐射方向图；提出了一种崭新的“迭代矢量场”方法，该方法仅需要极少的迭代次数就可以获得稳定的解；
4.研究了基于阶数步进(Marching-on in Degree或MOD)的并行时域积分方程方法(TDIE)。通过引入拉盖尔多项式(Laguerre polynomials)来展开时域积分方程中的暂态物理量，从而解决了传统时间步进(Marching-on in Time或MOT)方法中时间轴后半段解不稳定的问题；将自适应交叉近似方法(Adaptive CrossApproximation或ACA)应用到时域积分方程的阻抗矩阵填充中，有效地降低了计算过程中的内存资源需求，且计算精度不会受到太大的影响；为了提高计算效率，基于MPI和ScaLAPACK数学库，研究了TDIE-ACA算法的阻抗矩阵并行填充和矩阵方程并行求解的高效策略。
In recent years, more and more attention has been paid to the parallelelectromagnetic (EM) numerical methods due to their good acceleration performance.As “parallel” to be the clue, this dissertation studies the parallel algorithms based onMPI and ScaLAPACK, including parallel Higher-order Method of Moments, parallelPhysical Optics, parallel hybrid method of Higher-order Method of Moments andPhysical Optics, and parallel hybrid method of Time-domain Integral Equation andAdaptive Cross Approximation, to analyze the scattering and radiation problems ofmetal and dielectric model. This dissertation’s major contributions are outlined asfollows:
1. Higher-order basis is used to expand the unknowns so as to reduce the number ofunknowns and the memory required compared to those of RWG basis; usingPoggio-Miller-Chang-Harrington-Wu (PMCHW) integral equation to solve the EMproblem of metal and dielectric model; proposing a parallel matrix filling scheme toobtain a good load balancing and parallel efficiency;
2. Using parallel Higher-order MoM to solve a lot of challenging EM problems.The high accuracy and good computational performance demonstrate that this methodcan be used to effectively solve the practical engineering problem;
3. Based on impedance boundary condition and transmission line theory, thisdissertation studies a new Physical Optics (PO) method, which employs the triangularpatch modeling technique and uses Ludwig method to calculate the integral; moreover,this dissertation studies the parallelization of PO based on MPI and ScaLAPACK, whichcan be used to analyze the monostatic and bistatic RCS of the metal, impedance anddielectric model placed in free-space or half space; in addition, this dissertation alsostudies the parallel hybrid method of Higher-order MoM and PO, which uses a newhybrid scheme named “iterating vector fields technique”. This method can obtain astable solution with only a few iterations;
4. This dissertation studies the parallel Time-domain Integral Equation (TDIE)based on Marching-on in Degree (MOD) solver. The introduction of Laguerrepolynomial can avoid the problem of obtaining an unstable solution in late-time regionwhich exists in Marching-on in Time (MOT) solver; to reduce the memory required inthe matrix filling, this dissertation combines the Adaptive Cross Approximation (ACA)with TDIE; Finally, parallel technique based on MPI and ScaLAPACK is applied in this hybrid method to improve the computational efficiency.
1.采用高阶基函数替代传统的低阶基函数（如RWG基函数）展开模型的电磁流未知量，从而解决了低阶矩量法在处理电大尺寸模型时，由于10的网格剖分尺寸所带来的未知量数目巨大，消耗计算机内存多，硬件资源不足等问题；采用Poggio-Miller-Chang-Harrington-Wu (PMCHW)积分方程分析金属、介质混合体目标；为了加快问题的求解速度，提高效率，结合MPI和ScaLAPACK数学库自身的性能特点提出了一种高效的阻抗矩阵并行填充策略，该并行策略可以保证算法具有良好的并行效率和负载均衡性；
2.利用并行高阶矩量法解决了一大批电磁问题仿真，合理的求解时间和高精度的计算结果说明该算法可用于解决实际工程问题；
3.针对金属、介质混合体目标，从阻抗边界条件出发，应用传输线理论，研究了一种基于三角形面片建模，以路德维格(Ludwig)积分方法求解积分表达式的新的物理光学方法。同时，为了加速计算，结合MPI数学库研究了算法的高效率并行方案。该算法可处理阻抗表面模型，纯介质体，多层介质涂覆目标以及传统的理想导电体(Perfect Electric Conducting或PEC)模型，用于预估自由空间中、半空间中电大尺寸模型的单、双站雷达散射截面(Radar Cross Section或RCS)；研究了并行高阶矩量法、物理光学混合方法用以分析机载复杂天线的受扰辐射方向图；提出了一种崭新的“迭代矢量场”方法，该方法仅需要极少的迭代次数就可以获得稳定的解；
4.研究了基于阶数步进(Marching-on in Degree或MOD)的并行时域积分方程方法(TDIE)。通过引入拉盖尔多项式(Laguerre polynomials)来展开时域积分方程中的暂态物理量，从而解决了传统时间步进(Marching-on in Time或MOT)方法中时间轴后半段解不稳定的问题；将自适应交叉近似方法(Adaptive CrossApproximation或ACA)应用到时域积分方程的阻抗矩阵填充中，有效地降低了计算过程中的内存资源需求，且计算精度不会受到太大的影响；为了提高计算效率，基于MPI和ScaLAPACK数学库，研究了TDIE-ACA算法的阻抗矩阵并行填充和矩阵方程并行求解的高效策略。
In recent years, more and more attention has been paid to the parallelelectromagnetic (EM) numerical methods due to their good acceleration performance.As “parallel” to be the clue, this dissertation studies the parallel algorithms based onMPI and ScaLAPACK, including parallel Higher-order Method of Moments, parallelPhysical Optics, parallel hybrid method of Higher-order Method of Moments andPhysical Optics, and parallel hybrid method of Time-domain Integral Equation andAdaptive Cross Approximation, to analyze the scattering and radiation problems ofmetal and dielectric model. This dissertation’s major contributions are outlined asfollows:
1. Higher-order basis is used to expand the unknowns so as to reduce the number ofunknowns and the memory required compared to those of RWG basis; usingPoggio-Miller-Chang-Harrington-Wu (PMCHW) integral equation to solve the EMproblem of metal and dielectric model; proposing a parallel matrix filling scheme toobtain a good load balancing and parallel efficiency;
2. Using parallel Higher-order MoM to solve a lot of challenging EM problems.The high accuracy and good computational performance demonstrate that this methodcan be used to effectively solve the practical engineering problem;
3. Based on impedance boundary condition and transmission line theory, thisdissertation studies a new Physical Optics (PO) method, which employs the triangularpatch modeling technique and uses Ludwig method to calculate the integral; moreover,this dissertation studies the parallelization of PO based on MPI and ScaLAPACK, whichcan be used to analyze the monostatic and bistatic RCS of the metal, impedance anddielectric model placed in free-space or half space; in addition, this dissertation alsostudies the parallel hybrid method of Higher-order MoM and PO, which uses a newhybrid scheme named “iterating vector fields technique”. This method can obtain astable solution with only a few iterations;
4. This dissertation studies the parallel Time-domain Integral Equation (TDIE)based on Marching-on in Degree (MOD) solver. The introduction of Laguerrepolynomial can avoid the problem of obtaining an unstable solution in late-time regionwhich exists in Marching-on in Time (MOT) solver; to reduce the memory required inthe matrix filling, this dissertation combines the Adaptive Cross Approximation (ACA)with TDIE; Finally, parallel technique based on MPI and ScaLAPACK is applied in this hybrid method to improve the computational efficiency.
引文
[I]R. F. Harrington. Field Computation by Method of Moment. New York:John Wiley&Sons,1992.
[2]R.F.Harrington. Time——Harmonic Electromagnetic Fields. New York:John Wiley&Sons,2001.
[3]J.A.Stratton,方能航译.电磁理论,北京：科学出版社,1992.
[4]R. Mitra, L. B. Felsen. Transient Electromagnetic Field, NewYork:Springer,1976.
[5]吕英华.计算电磁学的数值方法.北京：清华大学出版社,2006.
[6]王长清.现代计算电磁学基础.北京：北京大学出版社,2005.
[7]盛新庆.计算电磁学要论.合肥：中国科学技术大学出版社,2008.
[8]汪茂光.几何绕射理论,第二版.西安：西安电子科技大学出版社,1994.
[9]R. G. Kouyoumjian,"Asymptotic High-Frequency Methods", Proc. IEEE,1965,53(8):864-876.
[10]P. H. Pathak,"High-frquency techniques for antenna analysis", Proc. IEEE,1992,80(1):44-65.
[11]Cornbleet S.."Geometrical optics reviewed:A new light on an old subject" Proc. IEEE,1983,71(4):471-502.
[12]Inada H., Plonus M.A.,"The geometric optics contribution to the scattering from a large dense dielectric sphere", IEEE Transactions on Antennas and Propagation,1970,18(1):89-99.
[13]Pathak P H, Burnside W D, Marhefka R J."A uniform GTD analysis of the diffraction of electromagnetic waves by a smooth convex surface," IEEE Transactions on Antennas and Propagation,1980,28(5):631-642.
[14]Pathak P H, Wang N N, Bureside W D."A uniform GTD solution forthe radiation from sources on a convex surface," IEEE Transactions on Antennas and Propagation,1981,29(4):609-622.
[15]宗卫华,梁昌洪,曹祥玉,项铁铭.“圆锥体与圆柱体的几何绕射理论绕射线寻迹”,西安电子科技大学学报(自然科学版),2002,29(4)：482-485.
[16]梁昌洪,崔斌,宗卫华.“费马原理确定柱面和锥面反射点的解析表示式”,电波科学学报,2004,19(2)：153-156.
[17]梁昌洪,谭远洋,宗卫华.‘'Fermat原理求解柱2锥系统二阶反射问题”,西安电子科技大学学报,2004,31(4)：497-500.
[18]Joseph B. Keller,"Geometrical Theory of Diffraction", Journal of the Optical Society of America,1962,52(2):116-130.
[19]P. H. Pathak, W. D. Burnside, and R. J. Marhefka,"A uniform GTD analysis of the diffraction of electromagnetic waves by a smooth convex surface," IEEE Transactions on Antennas and Propagation,1980,28(9):631-642.
[20]Pathak P.H., Youngchel Kim."A uniform geometrical theory of diffraction (UTD) for curved edges illuminated by electromagnetic beams", General Assembly and Scientific Symposium,2011:1-4.
[21]Phaebua K., Lertwiriyaprapa T., Phongcharoenpanich C., Pathak PH.."A modified UTD solution for an impedance cylinder surface",8th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology,2011:208-211.
[22]Nan Wang, Hao-Bo Yuan, Xiao-Jie Dang, Chang-Hong Liang,"Edge Diffraction in NURBS-UTD Method", IEEE Transactions on Antennas and Propagation,2012,60(5):2590-2593.
[23]Rao S.M., Wilton D., Glisson A.W.,"Electromagnetic scattering by surfaces of arbitrary shape", IEEE Transactions on Antennas and Propagation,1982,30(3):409-418.
[24]Wilton D., Rao S., Glisson A..."Triangular patch modeling of arbitrary bodies-An electric field integral equation approach for both open and closed bodies", International Symposium on Antennas and Propagation Society,1979, vol.17:151-154.
[25]阮颖铮.雷达截面与隐身技术.北京：国防工业出版社,1998.
[26]Taboada J M, Obelleiro F, Rodriguez."Modeling the physical optics crrents in a hybrid Moment-Method-Physical-Optics code", IEICE transactions on Electronics,2001, E84-C(9):1207-1214.
[27]Gordon W B."High frequency approximation to the physical optics scattering integral", IEEE Transactions on Antennas and Propagation,1994,42(3):427-432.
[28]陈铭.基于NURBS建模技术的物理光学方法研究.西安：西安电子科技大学,2005.
[29]Perez J.., Catedra M.F.,"Application of physical optics to the RCS computation of bodies modeled with NURBS surfaces", IEEE Transactions on Antennas and Propagation,1994,42(10):1404-1411.
[30]Yee K S."Numerical solution of initial boundary value problems involving Maxwell's equation in isotropic media", IEEE Transactions on Antennas and Propagation,1966,14(3):302-1307.
[31]Taflove A, Hagness S C. Computational electrodynamics:the Finite-difference time-domain method,2nd ed. Boston:Artech House,2000.
[32]Taflove A."Prospects for Finite-difference time-domain (FDTD) computational electrodynamics", IEEE Transactions on Antennas and Propagation,2002.
[33]张玉.计算电磁学中的时域方法.西安：西安电子科技大学讲义,2004.
[34]葛德彪,闫玉波.电磁波时域有限差分方法.西安：西安电子科技大学出版社,2002.
[35]张玉.FDTD新技术和矩量法在波导缝隙阵中的应用.西安：西安电子科技大学,2002.
[36]袁伟良.时域有限差分法关键问题研究及其应用.西安：西安电子科技大学,1998.
[37]Baumann D., Gimersky M., Fumeaux C., Vahldieck R..."Accuracy considerations of the FVTD method for radiating structures",2005European Microwave Conference,2005, vol.2.
[38]Isleifson D., Shafai L., Barber D.G.."Numerical rough surface scattering simulations using the FVTD method",15th International Symposium on Antenna Technology and Applied Electromagnetics,2012:1-4.
[39]Cong Deng, Wenlu Yin, Shunlian Chai, Junjie Mao."A Comparative Study of the DGTD Algorithm and the FVTD Algorithm in Computational Electromagnetics", Third International Joint Conference on Computational Science and Optimization,2010, vol.1:56-59.
[40]Baumann D., Fumeaux C., Leuchtmann P., Vahldieck R..."Finite-volume time-domain (FVTD) method and its application to the analysis of hemispherical dielectric-resonator antennas", IEEE MTT-S International Microwave Symposium,2003, vol.2:985-988.
[41]Isleifson D., Shafai L., Barber D.G.."Numerical scattering from3D randomly rough surfaces using FVTD", IEEE International Symposium on Antennas and Propagation,2011:3225-3228.
[42]Bonnet P., Ferrieres X., Grando J.., Alliot J.C.."FVTD applied to dielectric or wire structures", International Symposium on Antennas and Propagation Society,1996, vol.3:2126-2129.
[43]贺之莉.基于GiD的并行FDTD及其混合方法研究.西安：西安电子科技大学,2012.
[44]Demir V., Alkan E., Elsherbeni A.Z., Arvas E.."An Algorithm for Efficient Solution of Finite-Difference Frequency-Domain (FDFD) Methods [EM Programmer's Notebook]", IEEE Antennas and Propagation Magazine,2009,51(6):143-150.
[45]Jiunn Nan Hwang."A compact2-D FDFD method for modeling microstrip structures with nonuniform grids and perfectly matched layer", IEEE Transactions on Microwave Theory and Techniques,2005,53(2):653-659.
[46]Hu Xiaojuan, Ge Debiao, Wei Bing."2-D FDFD Analysis of Electromagnetic Scattering by Complex Targets",7th International Symposium on Antennas, Propagation&EM Theory,2006:1-4.
[47]金建铭,王建国译.电磁场有限元方法.西安：西安电子科技大学出版社,1998.
[48]D. P. Bouche, F. A. Molinet, and Mittra."Asympotic and hybrid techniques for electromagnetic scattering", Proc. IEEE,1993,81(12):1658-1684.
[49]G. A. Thiele,"Overview of selected hybrid methods in radiating system analysis", Proc. IEEE,1992,80(1):67-78.
[50]L. N. Medgyesi-Mitschang, D.-S. Wand,"Hybrid methods in computational eletromagnetics:A review", Computer Physics Communications,1991,68(4):76-94.
[51]L. N. Medgyesi-Mitschang, D.-S. Wand,"Hybrid solution for scattering from perfectly conducting bodies of revolution", IEEE Transactions on Antennas and Propagation,1983,34(4):570-583.
[52]L. N. Medgyesi-Mitschang, D.-S. Wand,"Hybrid solutions for large impedance coated bodies of revolution", IEEE Transactions on Antennas and Propagation,1986,34(11):1319-1329.
[53]Chunzhu Dong, Fangzhi Geng, Hongcheng Yin, Chao Wang."New hybridization of PO, SBR, and MoM for scattering by large complex conducting objects", Journal of Systems Engineering and Electronics,2007,18(4):726-730.
[54]Jian-Ming Jin, Feng Ling, Carolan S.T., Song J.M., Gibson W.C., Weng Cho Chew, Cai-Cheng Lu, Kipp, R..."A hybrid SBR/MoM technique for analysis of scattering from small protrusions on a large conducting body", IEEE Transactions on Antennas and Propagation,1998,46(9):1349-1357.
[55]Ling F., Sheng X.Q., Jin J.M.,"Hybrid MoM/SBR and FEM/SBR methods for scattering by large bodies with inhomogeneous protrusions.", International Symposium on Antennas and Propagation Society,1997,2:644-647.
[56]Jin, J.M., Ling, F., Carolan S.T., Song J.M., Gibson W.C., Chew W.C., Lu C.C., Kipp R.."A hybrid SBR/MoM technique for analysis of scattering from small protrusions on a large conducting body", International Symposium on Antennas and Propagation Society,1998,2:1074-1077.
[57]R. E. Hodges, Y. Rahmat-Samii."An iterative current-based hybrid method for complex structures", IEEE Transactions on Antennas and Propagation, Feb.1997,45(2):265-276.
[58]陈晓洁,王萌,梁昌洪,史小卫.“利用PO修正MM-UTD计算机载波导缝隙天线阵的方向图”,电子与信息学报,2008,30(7)：1173-1775.
[59]D. S. Wang,"Current-based hybrid analysis for surface-wave effects on large scatters", IEEE Transactions on Antennas and Propagation,1991,39(6):839-850.
[60]U. Jakobus, J. Christ, and F. M. Lanstorfer,"PO-MOM analysis of cavity-backed antennas", in IEE8th Int. Conf. Antennas Propgat. Edinburgh, Conf. Pubication Number370, Apr.1993:111-114.
[61]U. Jakobous and F. M. Landstorfer,"Improved PO-MM hybrid formulation for scattering from three dimensional perfectly conducting bodies of arbitrary shape", IEEE Transactions on Antennas and Propagation,1995,43(1):162-169.
[62]U. Jakobus and F. M. Landstorfer,"Improvement of the PO-MM hybrid method by accounting for effects of perfectly conducting wedges", IEEE Transactions on Antennas and Propagation,1995,43(6):1123-1129.
[63]U. Jakobus and F. M. Landstorfer,"Hybrid MOM-PO-FOCK analysis of monopole antennas mounted on curved convex bodies", in Conference Proceedings of the12th Annual Review of Progress in Computational Electromagnetics, Monterey, Mar,1996:101-108.
[64]G. A. Thiele, T. M. Newhouse."Hybrid technique for combining Moment methods with the geometrical theory of diffraction", IEEE Transactions on Antennas and Propagation,1975,23(1):551-558.
[65]Gary Athiele, Thomas Hnewhouse."A hybrid technique for combining Moment methods with the geometrical theory of diffraction", IEEE Transactions on Antennas and Propagation,1975,23(l):62-69.
[66]W. D. Burnside, C. L. Yu, and R. J. Marhefka,"A technique to combine the geometrical theory of diffraction and the Moment method", IEEE Transactions on Antennas and Propagation,1975,28(11):831-839.
[67]E. P. Ekelman, G. A.Thiele,"A hybrid technique for combining the Moment method treatment of wire antennas with the GTD for curved surfaces", IEEE Transactions on Antennas and Propagation,1980,28(11):831-839.
[68]雷继兆,梁昌洪,丁伟,张玉.“并行FDTD-UTD方法分析机载相控阵天线”,电波科学报,20(3),2005.
[69]Yang He-lin, Tang Yan-mei, Lu shu."Analysis of EM Scattering by Electrically Large Coated Object", The20064th Asia-Pacific Conference on Environmental Electromagnetics,2006,869-872.
[70]Chan K.K., Wong S.."Accurate RCS prediction of electrically large jet inlets and engines", Twelfth International Conference on Antennas and Propagation,2003, vol.1,253-256.
[71]Ye Zhao, Min Zhang, Hui Chen."The EM Scattering of Electrically Large Dielectric Rough Sea Surface at240GHz Using a Scale Model", IEEE Transactions on Antennas and Propagation,2012,60(12):5890-5899.
[72]Ming Chen, Yu Zhang, Xun-Wang Zhao, Chang-Hong Liang."Analysis of Antenna Around NURBS Surface With Hybrid MoM-PO Technique.", IEEE Transactions on Antennas and Propagation,2007,55(2):407-413.
[73]Kai Huang, Zhi-Li He, Chang-Hong Liang."Efficient Analysis of Antenna Around Electrically Large NURBS Platform With Accelerating MOM-PO Method", IEEE Antennas and Wireless Propagation Letters,2010, vol.9:134-137.
[74]Bing Hu, Xiaowen Xu, Mang He, Weihua Yu."PO-MOM analysis of an antenna with reflector enclosed in an electrically large radome", International Conference on Microwave Technology and Computational Electromagnetics,2009:115-118.
[75]H. Y. Yee."The design of large waveguide arrays of shunt slots", IEEE Transactions on Antennas and Propagation,1992,40(7):775-781.
[76]RS Elliott. Antenna theory and design. New York:Prentice-Hall, Englewood Cliffs1981.
[77]薛正辉,李伟明,任武.阵列天线分析与综合.北京：北京航空航天大学出版社,2011.
[78]卢礼芬.环境电磁兼容控制基础.北京：兵器工业出版社,1989.
[79]张玉.FDTD与矩量法的关键技术及并行电磁计算应用研究,西安电子科技大学,2004.
[80]张玉.电磁场并行计算.西安：现代电子科技大学出版社,2006.
[81]Yu Zhang, Tapan K. Sarkar, Parallel Solution of Integral Equation-based EM Problems in the Frequency Domain, Hoboken, New Jersey:John Wiley&Sons,2009.
[82]Barry Wilkinson Michael Allen,陆鑫达等译.并行程序设计.北京：机械工业出版社,2002.
[83]都志辉.高性能计算并行编挥技术——MPI并行程序.北京：清华大学出版社,2001.
[84]G. S. Almasi, A. Gottlieb. Highly Parallel Computing, Benjamin-Cummings, Redwood City, CA,1989.
[85]Lawrence Livermore National Laboratory."Introduction to Parallel Computing," High Performance Computing Training,2007.
[86]J. S. Shang."Computational Electromagnetics," ACM Computing Surveys,1996,28(1):97-99.
[87]Cheng G. A. Dataflow-based software integration model in parallel and distributed computing and applications. USA:Syraucuse University,1996.
[88]A. Rubinstein, F. Rachidi, M. Rubinstein, and B. Reusser."A Parallel Implementation of NEC for the Analysis of Large Structures," IEEE Transactions on Electromagnetic Compatibility,2003,45(2):177-188.
[89]Y. Zhang, T. K. Sarkar, P. Ghosh, M. Taylor, and A. De."Highly Efficient Parallel Schemes Using Out-of-Core Solver for MoM," IEEE Applied Electromagnetics Conference-AEMC, Kolkata, India,2007.
[90]Yu Zhang, Taylor, M., Sarkar, T., De, A., Mengtao Yuan, Hongsik Moon, and Changhong Liang."Parallel in-core and out-of-core solution of electrically large problems using the RWG basis functions," IEEE Antennas and Propagation Magazine,2008,50(5):84-94.
[91]Yu Zhang, van de Geijn, R.A., Taylor, M.C., and Sarkar, T.K.."Parallel MoM Using Higher-Order Basis Functions and PLAPACK In-Core and Out-of-Core Solvers for Challenging EM Simulations," IEEE Antennas and Propagation Magazine,2009,51(5):42-60.
[92]Jingyan Mo, Liang Shen, Bing Wei, Weidong Fang, and Ying Yan,"RCS computation of engine by parallel higher-order MoM with out-of-core technique," IET International Radar Conference,2013.
[93]Ming Chen, Meng Wang, Yu Zhang, and Chang-Hong Liang,"Parallel NURBS PO method based on the Ludwig algorithm and its application to the RCS computation", Asia-Pacific Microwave Conference,2005.
[94]Yan, Y., Zhao, H., Zhang, Y., Zhao, X.W., Liang, C.H., Garcia-Donoro, D., and Sarkar, T.K.,"Parallel computation of Radar Cross Section of target with coatings", The5th European Conference on Antennas and Propagation (EUCAP),2011.
[95]Ying Yan, Wei-Xin Zhao, Xun-Wang Zhao, Yu Zhang, and Chang-Hong Liang."Parallel Computation of RCS of Electrically Large Platform with Coatings Modeled with NURBS Surfaces", International Journal of Antennas and Propagation, vol.2012,2012.
[96]J Edlund."A parallel, iterative method of moments and physical optics hybrid solver for arbitrary surfaces", Licentiate thesis,2001.
[97]Yu Zhang, Xun-Wang Zhao, Donoro, D.G., Sio-Weng Ting, and Sarkar, T.K."Parallelized Hybrid Method With Higher-Order MoM and PO for Analysis of Phased Array Antennas on Electrically Large Platforms", IEEE Transactions on Antennas and Propagation,2010.
[98]Ying Yan, Xun-Wang Zhao, and Chang-Hong Liang."Analysis of wire antenna around dielectric or coated object using parallel MoM-PO technique", IET International Radar Conference,2013.
[99]Y. Zhang, A. De, B. H. Jung, and T. K. Sarkar."A Parallel Marching-on-in-Time Solver", IEEE AP-S&USNC/URSI Symposium,2008.
[100]Shi, Y, and Jin, JM."OpenMP parallized MOD solution of the time-domain EFIE accerlerated by the AC A algorithm", MICROWAVE AND OPTICAL TECHNOLOGY LETTERS,2012,54(5):1206-1212.
[101] T. Marshall.“Numerical Electromagnetics Code (Method of Moments),”Numerical Electromagnetics Code NEC2Unofficial Home Page,2002.
[102] R. A. van de Geijn. Using PLAPACK—Parallel Linear Algebra Package, MITPress, Cambridge, MA,1997.
[103] S. M. Rao, D. R. Wilton, and A. W. Glisson.“Electromagnetic Scattering bySurfaces of Arbitrary Shape,” IEEE Transactions on Antennas and Propagation,1982,30(3):409–418.
[104] T. Cwik, R. A. van de Geijn, and J. E. Patterson.“The Application of ParallelComputation to Integral Equation Models of Electromagnetic Scattering,”Journal of the Optical Society of America,1994,11(4):1538–1545.
[105] L. S. Blackford, J. Choi, A. Cleary, E. D’Azevedo, J. Demmel, I. Dhillon, J.Dongarra, S. Hammarling, G. Henry, A. Petitet, K. Stanley, D. Walker, and R. C.Whaley. ScaLAPACK User’s Guide, Society for Industrial Mathematics,Philadelphia, PA,1997.
[106] U. Jakobus.“Parallel Computation of Electromagnetic Fields Based on IntegralEquations,” Penn State Citeseer,1999.
[107] Lawrence Livermore National Laboratory.“Message Passing Interface (MPI),”High Performance Computer Training,2008.
[108] Oak Ridge National Laboratory.“PVM: Parallel Virtual Machine,” ComputerScience and Mathematics,2008.
[109] Y. Zhang, T. K. Sarkar, H. Moon, A. De, and M. C. Taylor.“Solution of LargeComplex Problems in Computational Electromagnetics Using Higher OrderBasis in MoM with Parallel Solvers”, IEEE Antennas and Propagation SocietyInternational Symposium,2007:5620–5623.
[110] Y. Zhang, T.K. Sarkar, X.W.Zhao, D. García-Do oro, W.X.Zhao, M.Salazar-Palma and S.W. Ting. Higher Order Basis Based Integral EquationSolver (HOBBIES). Hoboken, NJ: Wiley,2012.
[111] J. S. Asvestas.“The Physical Optics Method in Electromagnetic Scattering”,Journal of Mathematical Physics,1980,21(2):290–299.
[112] J. Edlund. A Parallel, Iterative Method of Moments and Physical Optics HybridSolver for Arbitrary Surfaces, Uppsala University,2001.
[113] Y. Zhang, X. W. Zhao, M. Chen, and C. H. Liang.“An Efficient MPI VirtualTopology Based Parallel, Iterative MoM-PO Hybrid Method on PC Clusters”,Journal of Electromagnetic Waves and Applications,2006,20(5):661–676.
[114] T. K. Sarkar, E. Arvas, and S. M. Rao.“Application of FFT and the ConjugateGradient Method for the Solution of Electromagnetic Radiation fromElectrically Large and Small Conducting Bodies”, IEEE Transactions onAntennas and Propagation,1986,34(5):635–640.
[115] E. Bleszynski, M. Bleszynski, and T. Jaroszewicz.“AIM: Adaptive IntegralMethod for Solving Large-Scale Electromagnetic Scattering and RadiationProblems”, Radio Science,1996,31(5):1225–1251.
[116] V. Rokhlin.“Rapid Solution of Integral Equations of Scattering Theory in TwoDimensions”, Journal of Computational Phyics,1990, Vol.86:414–439.
[117] X. C. Nie, L. W. Li, and N. Yuan.“Precorrected-FFT Algorithm for SolvingCombined Field Integral Equations in Electromagnetic Scattering”, IEEEAntennas and Propagation Society International Symposium,2002, Vol.3:574–577.
[118] J. M. Song, C. Lu, and W. Chew.“Multilevel Fast Multipole Algorithm forElectromagnetic Scattering by Large Complex Objects”, IEEE Transactions onAntennas and Propagation,1997,45(10):1488–1493.
[119] J. Song, C. Lu, W. Chew, and S. Lee.“Fast Illinois Solver Code (FISC)”, IEEEAntennas and Propagation Magazine,1998,40,(3):27–34.
[120] S. Velamparambil, J. Schutt-Aine, J. Nickel, J. Song, and W. Chew.“SolvingLarge Scale Electromagnetic Problems Using a Linux Cluster and ParallelMLFMA”, IEEE Antennas and Propagation Society International Symposium,1999, Vol.1:636–639.
[121] S. Velamparambil and W. Chew.“Analysis and Performance of a DistributedMemory Multilevel Fast Multipole Algorithm”, IEEE Transactions on Antennasand Propagation,2005,53(8):2719–2727.
[122] S. Velamparambil, J. Song, and W. C. Chew.“Parallelization of Multilevel FastMultipole Algorithm on Distributed Memory Computers in Fast and EfficientAlgorithms”, Computational Electromagnetics, Chap.4, Artech House, Boston,MA,2001.
[123] M. Nilsson. A Parallel Shared Memory Implementation of the Fast MultipoleMethod for Electromagnetics, Technical Report2003-049, Department ofInformation Technology, Scientific Computing, Uppsala University, Uppsala,Sweden, Oct.2003.
[124]Velamparambil, S.., Weng Cho Chew, Jiming Song."10million unknowns:is it that big?" IEEE Antennas and Propagation Magazine.,2003,45(2):43-58.
[125]Fang Wu, Yaojiang Zhang, Zaw Zaw Oo, Erping Li."Parallel Multilevel Fast Multipole Method for Solving Large-Scale Problems", IEEE Antennas and Propagation Magazine,2005,47(4):110-118.
[126]S. M. Rao and T. K. Sarkar."Numerical Solution of Time Domain Integral Equations for Arbitrarily Shaped Conductor/Dielectric Composite Bodies" IEEE Transactions on Antennas and Propagation,2002,50(12):1831-1837.
[127]B. H. Jung, Z. Ji, T. K. Sarkar, M. Salazar-Palma and M. Yuan."A Comparison of Marching-on-in-time Method with Marching-on-in-degree Method for the TDIE Solver", Progress in Electromagnetics Research,2007, Vol.70:281-296.
[128]B. M. Kolundzija, J. S. Ognjanovic, T. K. Sarkar, and R. F. Harrington, WIPL: Electromagnetic Modeling of Composite Wire and Plate Structures, Artech House, Boston,1995.
[129]B. M. Kolundzija, J. S. Ognjanovic, and T. K. Sarkar, WIPL-D:Electromagnetic Modeling of Composite Metallic and Dielectric Structures, Software and User's Manual, Artech House, Boston,2000.
[130]B. M. Kolundzija, J. S. Ognjanovic, and T.K. Sarkar,"Analysis of Composite Metallic and Dielectric Structures-WIPL-D Code," Proceedings of17th Applied Computational Electromagnetics Conference, pp.246-253, Monterey, CA, March2001.
[131]B. M. Kolundzija,"Electromagnetic Modeling of Composite Metallic and Dielectric Structures," IEEE Transactions on Microwave Theory Techniques, Vol.47, pp.1021-1032, July1999.
[132]B. D. Popovic and B. M. Kolundzija, Analysis of Metallic Antennas and Scatterers, IEE Electromagnetic Wave Series, No.38, London,1994.
[133]B. D. Popovic and B. M. Kolundzija, Analysis of Metallic Antennas and Scatterers, IEE Electromagnetic Wave Series, No.38, London,1994.
[134]D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler,"Potential Integrals for Uniform and Linear Source Distributions on Polygonal and Polyhedral Domains," IEEE Transactions on Antennas and Propagation, Vol.32, No.3, pp.276-281, March1984.
[135]Fernandez-Recio, R., Jurado-Lucena, A., Errasti-Alcala, B., Poyatos-Martinez, D.,"RCS Measurements and Predictions of different Targets for RadarBenchmark Purpose”, Electromagnetics in Advanced Applications (ICEAA),2009.
[136]上海超级计算中心“魔方”计算机用户手册：http://www.ssc.net.cn/
[137] S.M. Rao, D.R. Wilton, and A.W. Glisson,“Electromagnetic Scattering bySurfaces of Arbitrary Shape,” IEEE Transactions on Antennas and Propagation,Vol.30, No.5, pp.409-418,1982.
[138] S. M. Rao, C. C. Cha, R. L. Cravey, and D. L. Wilkes,“ElectromagneticScattering from Arbitrary Shaped Conducting Bodies Coated with LossyMaterials of Arbitrary Thickness,” IEEE Transactions on Antennas andPropagation, Vol.39, No.5, pp.627–631, May1991.
[139] R. F. Harrington, Field Computation by Moment Methods, IEEE Series onElectromagnetic Waves. New York: IEEE,1993.
[140] Schleher, D. Curtis, Electronic Warfare in the Information Age, Artech House,Norwood, Massachusetts,1999.
[141] Jenn, David C., Radar and Laser Cross Section Engineering, AIAA EducationsSeries, Washington D.C.,1995.
[142] Skolnik, Merill I., Introduction to Radar Systems,3rd Edition, McGraw Hill,New York,2001.
[143] Garrido, Elmo Jr., Graphical User Interface for a Physical Optics Radar CrossSection Prediction Code, Master’s Thesis, Naval Postgraduate School, Monterey,California, September2000.
[144] Moreira, Fernando J. S., and Prata, Aluizio Jr.,“A Self Predictor-CorrectorAlgorithm for Efficient Evaluation of Reflector Antenna Radiation Integrals,”IEEE Transactions on Antennas and Propagation, vol.42, no.2, pp.246-254,February,1994.
[145] U.Jakobous. F.M.Landstorfer,Improved PO-MOM hybrid formulation forscattering from three dimensional perfectly conducting bodies of arbitrary shape,IEEE Trans. On AP, Feb.1995,43:162-169.
[146] U. Jakobus and F. M. Landstorfer,“Improvement of the PO-MM hybrid methodby accounting for effects of perfectly conducting wedges”, IEEE Trans. onAntennas and Propagat.,1995,43(6):1123-1129.
[147] U. Jakobus and F. M. Landstorfer,“Hybrid MOM-PO-FOCK analysis ofmonopole antennas mounted on curved convex bodies”, ConferenceProceedings of the12th Annual Review of Progress in ComputationalElectromagnetics, Monterey, Mar,1996:101-108.
[148] Lei, J.-Z., C.-H. Liang, W. Ding, and Y. Zhang,“Analysis of airbornephased-array antennas using hybrid method of parallel FDTD and UTD”,Chinese Journal of Radio Science, Vol.24, No.1,2009.
[149] Wang, M., C.-H. Liang, and Y. Zhang,“Combining UTD with MM for patternprediction of the antenna in complex environment”, Chinese Journal of RadioScience, Vol.22, No.3,508-512,2007.
[150] Z. L. He, K. Huang, and C. H. Liang,“ANALYSIS OF COMPLEX ANTENNAAROUND ELECTRICALLY LARGE PLATFORM USING ITERATIVVECTOR FIELDS AND UTD METHOD”, Progress In ElectromagneticsResearch M, Vol.10,103-117,2009.
[151] Beak Ho Jung, T.K. Sarkar,“Time-Domain Eleetric-Field Integral EquationWith Central Finite Difference”, Microwave And Optical Technology Letters,December2001,vol.31,NO.6,429一435.
[152] Beak Ho Jung, T.K. Sarkar,“Time-Domain CFIE For The Analysis Of TransientScattering From Arbitrarily Shaped3D Condueting Objects”, Microwave AndOptical Technology Letters, August2002,vol.34,NO.4,289-296.
[153] Beak Ho Jung, T.K. Sarkar, ZhongJi, Young-seek Chung.“Time-DomainAnalysis Of Condueting Wire Antanna And Scatterers”, Microwave And OpticalTechnology Letters, vol.38, September2003,NO.6,433-436.
[154] Young-seek Chung, T.K. Sarkar, Beak Ho Jung,“Solution Of A Time-DomainMagnetic-Field Integral Equation For Arbitrarily Closed Conducting BodiesUsing An Unconditionally Stable Methodology”, Microwave And OpticalTechnology Letters, December2002,vol.35,NO.6,493-499.
[155] Zhong Ji, T.K. Sarkar, Beak Ho Jung, Young-seek Chung,“A Stable SolutionOf Time-Domain Electric Field Integral Equation For Thin-Wire AntennasUsing the Laguerre Polynomials”, IEEE Transactions On Antennas AndPropagation, October2004,Vol.52,NO.10.
[156] B.H.Jung, Y.S.Chung, T.K.Sarkar.“Time-Domain EFIE, MFIE and CFIEFormulations Using Laguerre Polynomials As Temporal Basis Functions for TheAnalysis of Transient Scattering From Arbitrary Shaped Conducting Struetures”,PIER39,2003,1-45.
[157]蔡明娟.时域积分方程在分析介质问题中的算法研究与应用.长沙:国防科技大学研究生院，2006.
[158]周东明.时域积分方程快速算法及其应用研究.长沙:国防科技大学研究生院，2006.
[159]王映明.时域递推法研究.长沙:国防科技大学研究生院，1990.
[160] S. M. Rao, Time domain electromagnetics. Acdemic press, New York,1999.
[161] S. M. Rao, T. K. Sarkar,“An alternative version of the time-domain electricfield integral equation for arbitrarily shaped conductors”, IEEE Trans. AntennasProp., Vol.41, pp.831-834,1993.
[162] T. K. Sarkar and J. Koh,“Generation of a wide-band electromagnetic responsethrough a laguerre expansion using early–time and low-frequency data”, IEEETrans. Microwave Theory Tech., Vol.50, pp.1408-1416,2002.
[163] B. H. Jung, T. K. Sarkar, S. W. Ting, Y. Zhang, Z. Mei, Z. Ji, M. Yuan, A. De,M. Salazar-Palma, S. M. Rao, Time and Frequency Domain Solutions of EMProblems Using Integral Equations and a Hybrid Methodology. Wiley, IEEEpress,2010.
[164] K. Zhao, M. Vouvakis, and J.-F. Lee,“The adaptive cross approximationalgorithm for accelerated method of moment computations of EMC problems”,IEEE Trans. Electromagn. Compat., vol.47, no.4, Nov.2005.
[165] R. Coifman, V. Roknlin, S. Wandzura,“The fast multipole method for the waveequation: A pedestrian prescription”, IEEE Trans. Antennas Propag., vol.35, no.3, pp.7-12,1993.
[166] E. Bleszynski, M. Bleszynski, and T. Jaroszewicz,“AIM: Adaptive integralmethod for solving large-scale electromagnetic scattering and radiationproblems,” Radio Sci., vol.31, no.5, pp.1225–1251, May1996.
[167] C. F.Wang and J.M. Jin,“Adaptive integral solution of combined field integralequation,” Microw. Opt. Tech. Lett., vol.19, no.5, pp.321–328, Dec.1998.
[168] J. R. Phillips and J. K. White,“A precorrected-FFT method for electrostaticanalysis of complicated3-D structures,” IEEE Trans. Comput. Aided Des. Integr.Circuits Syst., vol.16, no.10, pp.1059–1072, Oct.1997.
[169] M. Bebendorf,“Approximation of boundary element matrices,” Numer. Math.,vol.86, no.4, pp.565-589,2000.
[170] Yousef Saad, Iterative Methods for Sparse Linear Systems. Boston: PWSPublishing Company,1996.
[2]R.F.Harrington. Time——Harmonic Electromagnetic Fields. New York:John Wiley&Sons,2001.
[3]J.A.Stratton,方能航译.电磁理论,北京：科学出版社,1992.
[4]R. Mitra, L. B. Felsen. Transient Electromagnetic Field, NewYork:Springer,1976.
[5]吕英华.计算电磁学的数值方法.北京：清华大学出版社,2006.
[6]王长清.现代计算电磁学基础.北京：北京大学出版社,2005.
[7]盛新庆.计算电磁学要论.合肥：中国科学技术大学出版社,2008.
[8]汪茂光.几何绕射理论,第二版.西安：西安电子科技大学出版社,1994.
[9]R. G. Kouyoumjian,"Asymptotic High-Frequency Methods", Proc. IEEE,1965,53(8):864-876.
[10]P. H. Pathak,"High-frquency techniques for antenna analysis", Proc. IEEE,1992,80(1):44-65.
[11]Cornbleet S.."Geometrical optics reviewed:A new light on an old subject" Proc. IEEE,1983,71(4):471-502.
[12]Inada H., Plonus M.A.,"The geometric optics contribution to the scattering from a large dense dielectric sphere", IEEE Transactions on Antennas and Propagation,1970,18(1):89-99.
[13]Pathak P H, Burnside W D, Marhefka R J."A uniform GTD analysis of the diffraction of electromagnetic waves by a smooth convex surface," IEEE Transactions on Antennas and Propagation,1980,28(5):631-642.
[14]Pathak P H, Wang N N, Bureside W D."A uniform GTD solution forthe radiation from sources on a convex surface," IEEE Transactions on Antennas and Propagation,1981,29(4):609-622.
[15]宗卫华,梁昌洪,曹祥玉,项铁铭.“圆锥体与圆柱体的几何绕射理论绕射线寻迹”,西安电子科技大学学报(自然科学版),2002,29(4)：482-485.
[16]梁昌洪,崔斌,宗卫华.“费马原理确定柱面和锥面反射点的解析表示式”,电波科学学报,2004,19(2)：153-156.
[17]梁昌洪,谭远洋,宗卫华.‘'Fermat原理求解柱2锥系统二阶反射问题”,西安电子科技大学学报,2004,31(4)：497-500.
[18]Joseph B. Keller,"Geometrical Theory of Diffraction", Journal of the Optical Society of America,1962,52(2):116-130.
[19]P. H. Pathak, W. D. Burnside, and R. J. Marhefka,"A uniform GTD analysis of the diffraction of electromagnetic waves by a smooth convex surface," IEEE Transactions on Antennas and Propagation,1980,28(9):631-642.
[20]Pathak P.H., Youngchel Kim."A uniform geometrical theory of diffraction (UTD) for curved edges illuminated by electromagnetic beams", General Assembly and Scientific Symposium,2011:1-4.
[21]Phaebua K., Lertwiriyaprapa T., Phongcharoenpanich C., Pathak PH.."A modified UTD solution for an impedance cylinder surface",8th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology,2011:208-211.
[22]Nan Wang, Hao-Bo Yuan, Xiao-Jie Dang, Chang-Hong Liang,"Edge Diffraction in NURBS-UTD Method", IEEE Transactions on Antennas and Propagation,2012,60(5):2590-2593.
[23]Rao S.M., Wilton D., Glisson A.W.,"Electromagnetic scattering by surfaces of arbitrary shape", IEEE Transactions on Antennas and Propagation,1982,30(3):409-418.
[24]Wilton D., Rao S., Glisson A..."Triangular patch modeling of arbitrary bodies-An electric field integral equation approach for both open and closed bodies", International Symposium on Antennas and Propagation Society,1979, vol.17:151-154.
[25]阮颖铮.雷达截面与隐身技术.北京：国防工业出版社,1998.
[26]Taboada J M, Obelleiro F, Rodriguez."Modeling the physical optics crrents in a hybrid Moment-Method-Physical-Optics code", IEICE transactions on Electronics,2001, E84-C(9):1207-1214.
[27]Gordon W B."High frequency approximation to the physical optics scattering integral", IEEE Transactions on Antennas and Propagation,1994,42(3):427-432.
[28]陈铭.基于NURBS建模技术的物理光学方法研究.西安：西安电子科技大学,2005.
[29]Perez J.., Catedra M.F.,"Application of physical optics to the RCS computation of bodies modeled with NURBS surfaces", IEEE Transactions on Antennas and Propagation,1994,42(10):1404-1411.
[30]Yee K S."Numerical solution of initial boundary value problems involving Maxwell's equation in isotropic media", IEEE Transactions on Antennas and Propagation,1966,14(3):302-1307.
[31]Taflove A, Hagness S C. Computational electrodynamics:the Finite-difference time-domain method,2nd ed. Boston:Artech House,2000.
[32]Taflove A."Prospects for Finite-difference time-domain (FDTD) computational electrodynamics", IEEE Transactions on Antennas and Propagation,2002.
[33]张玉.计算电磁学中的时域方法.西安：西安电子科技大学讲义,2004.
[34]葛德彪,闫玉波.电磁波时域有限差分方法.西安：西安电子科技大学出版社,2002.
[35]张玉.FDTD新技术和矩量法在波导缝隙阵中的应用.西安：西安电子科技大学,2002.
[36]袁伟良.时域有限差分法关键问题研究及其应用.西安：西安电子科技大学,1998.
[37]Baumann D., Gimersky M., Fumeaux C., Vahldieck R..."Accuracy considerations of the FVTD method for radiating structures",2005European Microwave Conference,2005, vol.2.
[38]Isleifson D., Shafai L., Barber D.G.."Numerical rough surface scattering simulations using the FVTD method",15th International Symposium on Antenna Technology and Applied Electromagnetics,2012:1-4.
[39]Cong Deng, Wenlu Yin, Shunlian Chai, Junjie Mao."A Comparative Study of the DGTD Algorithm and the FVTD Algorithm in Computational Electromagnetics", Third International Joint Conference on Computational Science and Optimization,2010, vol.1:56-59.
[40]Baumann D., Fumeaux C., Leuchtmann P., Vahldieck R..."Finite-volume time-domain (FVTD) method and its application to the analysis of hemispherical dielectric-resonator antennas", IEEE MTT-S International Microwave Symposium,2003, vol.2:985-988.
[41]Isleifson D., Shafai L., Barber D.G.."Numerical scattering from3D randomly rough surfaces using FVTD", IEEE International Symposium on Antennas and Propagation,2011:3225-3228.
[42]Bonnet P., Ferrieres X., Grando J.., Alliot J.C.."FVTD applied to dielectric or wire structures", International Symposium on Antennas and Propagation Society,1996, vol.3:2126-2129.
[43]贺之莉.基于GiD的并行FDTD及其混合方法研究.西安：西安电子科技大学,2012.
[44]Demir V., Alkan E., Elsherbeni A.Z., Arvas E.."An Algorithm for Efficient Solution of Finite-Difference Frequency-Domain (FDFD) Methods [EM Programmer's Notebook]", IEEE Antennas and Propagation Magazine,2009,51(6):143-150.
[45]Jiunn Nan Hwang."A compact2-D FDFD method for modeling microstrip structures with nonuniform grids and perfectly matched layer", IEEE Transactions on Microwave Theory and Techniques,2005,53(2):653-659.
[46]Hu Xiaojuan, Ge Debiao, Wei Bing."2-D FDFD Analysis of Electromagnetic Scattering by Complex Targets",7th International Symposium on Antennas, Propagation&EM Theory,2006:1-4.
[47]金建铭,王建国译.电磁场有限元方法.西安：西安电子科技大学出版社,1998.
[48]D. P. Bouche, F. A. Molinet, and Mittra."Asympotic and hybrid techniques for electromagnetic scattering", Proc. IEEE,1993,81(12):1658-1684.
[49]G. A. Thiele,"Overview of selected hybrid methods in radiating system analysis", Proc. IEEE,1992,80(1):67-78.
[50]L. N. Medgyesi-Mitschang, D.-S. Wand,"Hybrid methods in computational eletromagnetics:A review", Computer Physics Communications,1991,68(4):76-94.
[51]L. N. Medgyesi-Mitschang, D.-S. Wand,"Hybrid solution for scattering from perfectly conducting bodies of revolution", IEEE Transactions on Antennas and Propagation,1983,34(4):570-583.
[52]L. N. Medgyesi-Mitschang, D.-S. Wand,"Hybrid solutions for large impedance coated bodies of revolution", IEEE Transactions on Antennas and Propagation,1986,34(11):1319-1329.
[53]Chunzhu Dong, Fangzhi Geng, Hongcheng Yin, Chao Wang."New hybridization of PO, SBR, and MoM for scattering by large complex conducting objects", Journal of Systems Engineering and Electronics,2007,18(4):726-730.
[54]Jian-Ming Jin, Feng Ling, Carolan S.T., Song J.M., Gibson W.C., Weng Cho Chew, Cai-Cheng Lu, Kipp, R..."A hybrid SBR/MoM technique for analysis of scattering from small protrusions on a large conducting body", IEEE Transactions on Antennas and Propagation,1998,46(9):1349-1357.
[55]Ling F., Sheng X.Q., Jin J.M.,"Hybrid MoM/SBR and FEM/SBR methods for scattering by large bodies with inhomogeneous protrusions.", International Symposium on Antennas and Propagation Society,1997,2:644-647.
[56]Jin, J.M., Ling, F., Carolan S.T., Song J.M., Gibson W.C., Chew W.C., Lu C.C., Kipp R.."A hybrid SBR/MoM technique for analysis of scattering from small protrusions on a large conducting body", International Symposium on Antennas and Propagation Society,1998,2:1074-1077.
[57]R. E. Hodges, Y. Rahmat-Samii."An iterative current-based hybrid method for complex structures", IEEE Transactions on Antennas and Propagation, Feb.1997,45(2):265-276.
[58]陈晓洁,王萌,梁昌洪,史小卫.“利用PO修正MM-UTD计算机载波导缝隙天线阵的方向图”,电子与信息学报,2008,30(7)：1173-1775.
[59]D. S. Wang,"Current-based hybrid analysis for surface-wave effects on large scatters", IEEE Transactions on Antennas and Propagation,1991,39(6):839-850.
[60]U. Jakobus, J. Christ, and F. M. Lanstorfer,"PO-MOM analysis of cavity-backed antennas", in IEE8th Int. Conf. Antennas Propgat. Edinburgh, Conf. Pubication Number370, Apr.1993:111-114.
[61]U. Jakobous and F. M. Landstorfer,"Improved PO-MM hybrid formulation for scattering from three dimensional perfectly conducting bodies of arbitrary shape", IEEE Transactions on Antennas and Propagation,1995,43(1):162-169.
[62]U. Jakobus and F. M. Landstorfer,"Improvement of the PO-MM hybrid method by accounting for effects of perfectly conducting wedges", IEEE Transactions on Antennas and Propagation,1995,43(6):1123-1129.
[63]U. Jakobus and F. M. Landstorfer,"Hybrid MOM-PO-FOCK analysis of monopole antennas mounted on curved convex bodies", in Conference Proceedings of the12th Annual Review of Progress in Computational Electromagnetics, Monterey, Mar,1996:101-108.
[64]G. A. Thiele, T. M. Newhouse."Hybrid technique for combining Moment methods with the geometrical theory of diffraction", IEEE Transactions on Antennas and Propagation,1975,23(1):551-558.
[65]Gary Athiele, Thomas Hnewhouse."A hybrid technique for combining Moment methods with the geometrical theory of diffraction", IEEE Transactions on Antennas and Propagation,1975,23(l):62-69.
[66]W. D. Burnside, C. L. Yu, and R. J. Marhefka,"A technique to combine the geometrical theory of diffraction and the Moment method", IEEE Transactions on Antennas and Propagation,1975,28(11):831-839.
[67]E. P. Ekelman, G. A.Thiele,"A hybrid technique for combining the Moment method treatment of wire antennas with the GTD for curved surfaces", IEEE Transactions on Antennas and Propagation,1980,28(11):831-839.
[68]雷继兆,梁昌洪,丁伟,张玉.“并行FDTD-UTD方法分析机载相控阵天线”,电波科学报,20(3),2005.
[69]Yang He-lin, Tang Yan-mei, Lu shu."Analysis of EM Scattering by Electrically Large Coated Object", The20064th Asia-Pacific Conference on Environmental Electromagnetics,2006,869-872.
[70]Chan K.K., Wong S.."Accurate RCS prediction of electrically large jet inlets and engines", Twelfth International Conference on Antennas and Propagation,2003, vol.1,253-256.
[71]Ye Zhao, Min Zhang, Hui Chen."The EM Scattering of Electrically Large Dielectric Rough Sea Surface at240GHz Using a Scale Model", IEEE Transactions on Antennas and Propagation,2012,60(12):5890-5899.
[72]Ming Chen, Yu Zhang, Xun-Wang Zhao, Chang-Hong Liang."Analysis of Antenna Around NURBS Surface With Hybrid MoM-PO Technique.", IEEE Transactions on Antennas and Propagation,2007,55(2):407-413.
[73]Kai Huang, Zhi-Li He, Chang-Hong Liang."Efficient Analysis of Antenna Around Electrically Large NURBS Platform With Accelerating MOM-PO Method", IEEE Antennas and Wireless Propagation Letters,2010, vol.9:134-137.
[74]Bing Hu, Xiaowen Xu, Mang He, Weihua Yu."PO-MOM analysis of an antenna with reflector enclosed in an electrically large radome", International Conference on Microwave Technology and Computational Electromagnetics,2009:115-118.
[75]H. Y. Yee."The design of large waveguide arrays of shunt slots", IEEE Transactions on Antennas and Propagation,1992,40(7):775-781.
[76]RS Elliott. Antenna theory and design. New York:Prentice-Hall, Englewood Cliffs1981.
[77]薛正辉,李伟明,任武.阵列天线分析与综合.北京：北京航空航天大学出版社,2011.
[78]卢礼芬.环境电磁兼容控制基础.北京：兵器工业出版社,1989.
[79]张玉.FDTD与矩量法的关键技术及并行电磁计算应用研究,西安电子科技大学,2004.
[80]张玉.电磁场并行计算.西安：现代电子科技大学出版社,2006.
[81]Yu Zhang, Tapan K. Sarkar, Parallel Solution of Integral Equation-based EM Problems in the Frequency Domain, Hoboken, New Jersey:John Wiley&Sons,2009.
[82]Barry Wilkinson Michael Allen,陆鑫达等译.并行程序设计.北京：机械工业出版社,2002.
[83]都志辉.高性能计算并行编挥技术——MPI并行程序.北京：清华大学出版社,2001.
[84]G. S. Almasi, A. Gottlieb. Highly Parallel Computing, Benjamin-Cummings, Redwood City, CA,1989.
[85]Lawrence Livermore National Laboratory."Introduction to Parallel Computing," High Performance Computing Training,2007.
[86]J. S. Shang."Computational Electromagnetics," ACM Computing Surveys,1996,28(1):97-99.
[87]Cheng G. A. Dataflow-based software integration model in parallel and distributed computing and applications. USA:Syraucuse University,1996.
[88]A. Rubinstein, F. Rachidi, M. Rubinstein, and B. Reusser."A Parallel Implementation of NEC for the Analysis of Large Structures," IEEE Transactions on Electromagnetic Compatibility,2003,45(2):177-188.
[89]Y. Zhang, T. K. Sarkar, P. Ghosh, M. Taylor, and A. De."Highly Efficient Parallel Schemes Using Out-of-Core Solver for MoM," IEEE Applied Electromagnetics Conference-AEMC, Kolkata, India,2007.
[90]Yu Zhang, Taylor, M., Sarkar, T., De, A., Mengtao Yuan, Hongsik Moon, and Changhong Liang."Parallel in-core and out-of-core solution of electrically large problems using the RWG basis functions," IEEE Antennas and Propagation Magazine,2008,50(5):84-94.
[91]Yu Zhang, van de Geijn, R.A., Taylor, M.C., and Sarkar, T.K.."Parallel MoM Using Higher-Order Basis Functions and PLAPACK In-Core and Out-of-Core Solvers for Challenging EM Simulations," IEEE Antennas and Propagation Magazine,2009,51(5):42-60.
[92]Jingyan Mo, Liang Shen, Bing Wei, Weidong Fang, and Ying Yan,"RCS computation of engine by parallel higher-order MoM with out-of-core technique," IET International Radar Conference,2013.
[93]Ming Chen, Meng Wang, Yu Zhang, and Chang-Hong Liang,"Parallel NURBS PO method based on the Ludwig algorithm and its application to the RCS computation", Asia-Pacific Microwave Conference,2005.
[94]Yan, Y., Zhao, H., Zhang, Y., Zhao, X.W., Liang, C.H., Garcia-Donoro, D., and Sarkar, T.K.,"Parallel computation of Radar Cross Section of target with coatings", The5th European Conference on Antennas and Propagation (EUCAP),2011.
[95]Ying Yan, Wei-Xin Zhao, Xun-Wang Zhao, Yu Zhang, and Chang-Hong Liang."Parallel Computation of RCS of Electrically Large Platform with Coatings Modeled with NURBS Surfaces", International Journal of Antennas and Propagation, vol.2012,2012.
[96]J Edlund."A parallel, iterative method of moments and physical optics hybrid solver for arbitrary surfaces", Licentiate thesis,2001.
[97]Yu Zhang, Xun-Wang Zhao, Donoro, D.G., Sio-Weng Ting, and Sarkar, T.K."Parallelized Hybrid Method With Higher-Order MoM and PO for Analysis of Phased Array Antennas on Electrically Large Platforms", IEEE Transactions on Antennas and Propagation,2010.
[98]Ying Yan, Xun-Wang Zhao, and Chang-Hong Liang."Analysis of wire antenna around dielectric or coated object using parallel MoM-PO technique", IET International Radar Conference,2013.
[99]Y. Zhang, A. De, B. H. Jung, and T. K. Sarkar."A Parallel Marching-on-in-Time Solver", IEEE AP-S&USNC/URSI Symposium,2008.
[100]Shi, Y, and Jin, JM."OpenMP parallized MOD solution of the time-domain EFIE accerlerated by the AC A algorithm", MICROWAVE AND OPTICAL TECHNOLOGY LETTERS,2012,54(5):1206-1212.
[101] T. Marshall.“Numerical Electromagnetics Code (Method of Moments),”Numerical Electromagnetics Code NEC2Unofficial Home Page,2002.
[102] R. A. van de Geijn. Using PLAPACK—Parallel Linear Algebra Package, MITPress, Cambridge, MA,1997.
[103] S. M. Rao, D. R. Wilton, and A. W. Glisson.“Electromagnetic Scattering bySurfaces of Arbitrary Shape,” IEEE Transactions on Antennas and Propagation,1982,30(3):409–418.
[104] T. Cwik, R. A. van de Geijn, and J. E. Patterson.“The Application of ParallelComputation to Integral Equation Models of Electromagnetic Scattering,”Journal of the Optical Society of America,1994,11(4):1538–1545.
[105] L. S. Blackford, J. Choi, A. Cleary, E. D’Azevedo, J. Demmel, I. Dhillon, J.Dongarra, S. Hammarling, G. Henry, A. Petitet, K. Stanley, D. Walker, and R. C.Whaley. ScaLAPACK User’s Guide, Society for Industrial Mathematics,Philadelphia, PA,1997.
[106] U. Jakobus.“Parallel Computation of Electromagnetic Fields Based on IntegralEquations,” Penn State Citeseer,1999.
[107] Lawrence Livermore National Laboratory.“Message Passing Interface (MPI),”High Performance Computer Training,2008.
[108] Oak Ridge National Laboratory.“PVM: Parallel Virtual Machine,” ComputerScience and Mathematics,2008.
[109] Y. Zhang, T. K. Sarkar, H. Moon, A. De, and M. C. Taylor.“Solution of LargeComplex Problems in Computational Electromagnetics Using Higher OrderBasis in MoM with Parallel Solvers”, IEEE Antennas and Propagation SocietyInternational Symposium,2007:5620–5623.
[110] Y. Zhang, T.K. Sarkar, X.W.Zhao, D. García-Do oro, W.X.Zhao, M.Salazar-Palma and S.W. Ting. Higher Order Basis Based Integral EquationSolver (HOBBIES). Hoboken, NJ: Wiley,2012.
[111] J. S. Asvestas.“The Physical Optics Method in Electromagnetic Scattering”,Journal of Mathematical Physics,1980,21(2):290–299.
[112] J. Edlund. A Parallel, Iterative Method of Moments and Physical Optics HybridSolver for Arbitrary Surfaces, Uppsala University,2001.
[113] Y. Zhang, X. W. Zhao, M. Chen, and C. H. Liang.“An Efficient MPI VirtualTopology Based Parallel, Iterative MoM-PO Hybrid Method on PC Clusters”,Journal of Electromagnetic Waves and Applications,2006,20(5):661–676.
[114] T. K. Sarkar, E. Arvas, and S. M. Rao.“Application of FFT and the ConjugateGradient Method for the Solution of Electromagnetic Radiation fromElectrically Large and Small Conducting Bodies”, IEEE Transactions onAntennas and Propagation,1986,34(5):635–640.
[115] E. Bleszynski, M. Bleszynski, and T. Jaroszewicz.“AIM: Adaptive IntegralMethod for Solving Large-Scale Electromagnetic Scattering and RadiationProblems”, Radio Science,1996,31(5):1225–1251.
[116] V. Rokhlin.“Rapid Solution of Integral Equations of Scattering Theory in TwoDimensions”, Journal of Computational Phyics,1990, Vol.86:414–439.
[117] X. C. Nie, L. W. Li, and N. Yuan.“Precorrected-FFT Algorithm for SolvingCombined Field Integral Equations in Electromagnetic Scattering”, IEEEAntennas and Propagation Society International Symposium,2002, Vol.3:574–577.
[118] J. M. Song, C. Lu, and W. Chew.“Multilevel Fast Multipole Algorithm forElectromagnetic Scattering by Large Complex Objects”, IEEE Transactions onAntennas and Propagation,1997,45(10):1488–1493.
[119] J. Song, C. Lu, W. Chew, and S. Lee.“Fast Illinois Solver Code (FISC)”, IEEEAntennas and Propagation Magazine,1998,40,(3):27–34.
[120] S. Velamparambil, J. Schutt-Aine, J. Nickel, J. Song, and W. Chew.“SolvingLarge Scale Electromagnetic Problems Using a Linux Cluster and ParallelMLFMA”, IEEE Antennas and Propagation Society International Symposium,1999, Vol.1:636–639.
[121] S. Velamparambil and W. Chew.“Analysis and Performance of a DistributedMemory Multilevel Fast Multipole Algorithm”, IEEE Transactions on Antennasand Propagation,2005,53(8):2719–2727.
[122] S. Velamparambil, J. Song, and W. C. Chew.“Parallelization of Multilevel FastMultipole Algorithm on Distributed Memory Computers in Fast and EfficientAlgorithms”, Computational Electromagnetics, Chap.4, Artech House, Boston,MA,2001.
[123] M. Nilsson. A Parallel Shared Memory Implementation of the Fast MultipoleMethod for Electromagnetics, Technical Report2003-049, Department ofInformation Technology, Scientific Computing, Uppsala University, Uppsala,Sweden, Oct.2003.
[124]Velamparambil, S.., Weng Cho Chew, Jiming Song."10million unknowns:is it that big?" IEEE Antennas and Propagation Magazine.,2003,45(2):43-58.
[125]Fang Wu, Yaojiang Zhang, Zaw Zaw Oo, Erping Li."Parallel Multilevel Fast Multipole Method for Solving Large-Scale Problems", IEEE Antennas and Propagation Magazine,2005,47(4):110-118.
[126]S. M. Rao and T. K. Sarkar."Numerical Solution of Time Domain Integral Equations for Arbitrarily Shaped Conductor/Dielectric Composite Bodies" IEEE Transactions on Antennas and Propagation,2002,50(12):1831-1837.
[127]B. H. Jung, Z. Ji, T. K. Sarkar, M. Salazar-Palma and M. Yuan."A Comparison of Marching-on-in-time Method with Marching-on-in-degree Method for the TDIE Solver", Progress in Electromagnetics Research,2007, Vol.70:281-296.
[128]B. M. Kolundzija, J. S. Ognjanovic, T. K. Sarkar, and R. F. Harrington, WIPL: Electromagnetic Modeling of Composite Wire and Plate Structures, Artech House, Boston,1995.
[129]B. M. Kolundzija, J. S. Ognjanovic, and T. K. Sarkar, WIPL-D:Electromagnetic Modeling of Composite Metallic and Dielectric Structures, Software and User's Manual, Artech House, Boston,2000.
[130]B. M. Kolundzija, J. S. Ognjanovic, and T.K. Sarkar,"Analysis of Composite Metallic and Dielectric Structures-WIPL-D Code," Proceedings of17th Applied Computational Electromagnetics Conference, pp.246-253, Monterey, CA, March2001.
[131]B. M. Kolundzija,"Electromagnetic Modeling of Composite Metallic and Dielectric Structures," IEEE Transactions on Microwave Theory Techniques, Vol.47, pp.1021-1032, July1999.
[132]B. D. Popovic and B. M. Kolundzija, Analysis of Metallic Antennas and Scatterers, IEE Electromagnetic Wave Series, No.38, London,1994.
[133]B. D. Popovic and B. M. Kolundzija, Analysis of Metallic Antennas and Scatterers, IEE Electromagnetic Wave Series, No.38, London,1994.
[134]D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler,"Potential Integrals for Uniform and Linear Source Distributions on Polygonal and Polyhedral Domains," IEEE Transactions on Antennas and Propagation, Vol.32, No.3, pp.276-281, March1984.
[135]Fernandez-Recio, R., Jurado-Lucena, A., Errasti-Alcala, B., Poyatos-Martinez, D.,"RCS Measurements and Predictions of different Targets for RadarBenchmark Purpose”, Electromagnetics in Advanced Applications (ICEAA),2009.
[136]上海超级计算中心“魔方”计算机用户手册：http://www.ssc.net.cn/
[137] S.M. Rao, D.R. Wilton, and A.W. Glisson,“Electromagnetic Scattering bySurfaces of Arbitrary Shape,” IEEE Transactions on Antennas and Propagation,Vol.30, No.5, pp.409-418,1982.
[138] S. M. Rao, C. C. Cha, R. L. Cravey, and D. L. Wilkes,“ElectromagneticScattering from Arbitrary Shaped Conducting Bodies Coated with LossyMaterials of Arbitrary Thickness,” IEEE Transactions on Antennas andPropagation, Vol.39, No.5, pp.627–631, May1991.
[139] R. F. Harrington, Field Computation by Moment Methods, IEEE Series onElectromagnetic Waves. New York: IEEE,1993.
[140] Schleher, D. Curtis, Electronic Warfare in the Information Age, Artech House,Norwood, Massachusetts,1999.
[141] Jenn, David C., Radar and Laser Cross Section Engineering, AIAA EducationsSeries, Washington D.C.,1995.
[142] Skolnik, Merill I., Introduction to Radar Systems,3rd Edition, McGraw Hill,New York,2001.
[143] Garrido, Elmo Jr., Graphical User Interface for a Physical Optics Radar CrossSection Prediction Code, Master’s Thesis, Naval Postgraduate School, Monterey,California, September2000.
[144] Moreira, Fernando J. S., and Prata, Aluizio Jr.,“A Self Predictor-CorrectorAlgorithm for Efficient Evaluation of Reflector Antenna Radiation Integrals,”IEEE Transactions on Antennas and Propagation, vol.42, no.2, pp.246-254,February,1994.
[145] U.Jakobous. F.M.Landstorfer,Improved PO-MOM hybrid formulation forscattering from three dimensional perfectly conducting bodies of arbitrary shape,IEEE Trans. On AP, Feb.1995,43:162-169.
[146] U. Jakobus and F. M. Landstorfer,“Improvement of the PO-MM hybrid methodby accounting for effects of perfectly conducting wedges”, IEEE Trans. onAntennas and Propagat.,1995,43(6):1123-1129.
[147] U. Jakobus and F. M. Landstorfer,“Hybrid MOM-PO-FOCK analysis ofmonopole antennas mounted on curved convex bodies”, ConferenceProceedings of the12th Annual Review of Progress in ComputationalElectromagnetics, Monterey, Mar,1996:101-108.
[148] Lei, J.-Z., C.-H. Liang, W. Ding, and Y. Zhang,“Analysis of airbornephased-array antennas using hybrid method of parallel FDTD and UTD”,Chinese Journal of Radio Science, Vol.24, No.1,2009.
[149] Wang, M., C.-H. Liang, and Y. Zhang,“Combining UTD with MM for patternprediction of the antenna in complex environment”, Chinese Journal of RadioScience, Vol.22, No.3,508-512,2007.
[150] Z. L. He, K. Huang, and C. H. Liang,“ANALYSIS OF COMPLEX ANTENNAAROUND ELECTRICALLY LARGE PLATFORM USING ITERATIVVECTOR FIELDS AND UTD METHOD”, Progress In ElectromagneticsResearch M, Vol.10,103-117,2009.
[151] Beak Ho Jung, T.K. Sarkar,“Time-Domain Eleetric-Field Integral EquationWith Central Finite Difference”, Microwave And Optical Technology Letters,December2001,vol.31,NO.6,429一435.
[152] Beak Ho Jung, T.K. Sarkar,“Time-Domain CFIE For The Analysis Of TransientScattering From Arbitrarily Shaped3D Condueting Objects”, Microwave AndOptical Technology Letters, August2002,vol.34,NO.4,289-296.
[153] Beak Ho Jung, T.K. Sarkar, ZhongJi, Young-seek Chung.“Time-DomainAnalysis Of Condueting Wire Antanna And Scatterers”, Microwave And OpticalTechnology Letters, vol.38, September2003,NO.6,433-436.
[154] Young-seek Chung, T.K. Sarkar, Beak Ho Jung,“Solution Of A Time-DomainMagnetic-Field Integral Equation For Arbitrarily Closed Conducting BodiesUsing An Unconditionally Stable Methodology”, Microwave And OpticalTechnology Letters, December2002,vol.35,NO.6,493-499.
[155] Zhong Ji, T.K. Sarkar, Beak Ho Jung, Young-seek Chung,“A Stable SolutionOf Time-Domain Electric Field Integral Equation For Thin-Wire AntennasUsing the Laguerre Polynomials”, IEEE Transactions On Antennas AndPropagation, October2004,Vol.52,NO.10.
[156] B.H.Jung, Y.S.Chung, T.K.Sarkar.“Time-Domain EFIE, MFIE and CFIEFormulations Using Laguerre Polynomials As Temporal Basis Functions for TheAnalysis of Transient Scattering From Arbitrary Shaped Conducting Struetures”,PIER39,2003,1-45.
[157]蔡明娟.时域积分方程在分析介质问题中的算法研究与应用.长沙:国防科技大学研究生院，2006.
[158]周东明.时域积分方程快速算法及其应用研究.长沙:国防科技大学研究生院，2006.
[159]王映明.时域递推法研究.长沙:国防科技大学研究生院，1990.
[160] S. M. Rao, Time domain electromagnetics. Acdemic press, New York,1999.
[161] S. M. Rao, T. K. Sarkar,“An alternative version of the time-domain electricfield integral equation for arbitrarily shaped conductors”, IEEE Trans. AntennasProp., Vol.41, pp.831-834,1993.
[162] T. K. Sarkar and J. Koh,“Generation of a wide-band electromagnetic responsethrough a laguerre expansion using early–time and low-frequency data”, IEEETrans. Microwave Theory Tech., Vol.50, pp.1408-1416,2002.
[163] B. H. Jung, T. K. Sarkar, S. W. Ting, Y. Zhang, Z. Mei, Z. Ji, M. Yuan, A. De,M. Salazar-Palma, S. M. Rao, Time and Frequency Domain Solutions of EMProblems Using Integral Equations and a Hybrid Methodology. Wiley, IEEEpress,2010.
[164] K. Zhao, M. Vouvakis, and J.-F. Lee,“The adaptive cross approximationalgorithm for accelerated method of moment computations of EMC problems”,IEEE Trans. Electromagn. Compat., vol.47, no.4, Nov.2005.
[165] R. Coifman, V. Roknlin, S. Wandzura,“The fast multipole method for the waveequation: A pedestrian prescription”, IEEE Trans. Antennas Propag., vol.35, no.3, pp.7-12,1993.
[166] E. Bleszynski, M. Bleszynski, and T. Jaroszewicz,“AIM: Adaptive integralmethod for solving large-scale electromagnetic scattering and radiationproblems,” Radio Sci., vol.31, no.5, pp.1225–1251, May1996.
[167] C. F.Wang and J.M. Jin,“Adaptive integral solution of combined field integralequation,” Microw. Opt. Tech. Lett., vol.19, no.5, pp.321–328, Dec.1998.
[168] J. R. Phillips and J. K. White,“A precorrected-FFT method for electrostaticanalysis of complicated3-D structures,” IEEE Trans. Comput. Aided Des. Integr.Circuits Syst., vol.16, no.10, pp.1059–1072, Oct.1997.
[169] M. Bebendorf,“Approximation of boundary element matrices,” Numer. Math.,vol.86, no.4, pp.565-589,2000.
[170] Yousef Saad, Iterative Methods for Sparse Linear Systems. Boston: PWSPublishing Company,1996.