FDTD与MPSTD并行算法在电磁散射中的应用研究
摘要
目标的电磁散射特性研究是计算电磁学的一个重要方面,广泛应用于雷达探测、遥感卫星对地观测、目标识别等领域中,具有很高的工程应用价值。目前,获取目标电磁散射特性的技术途径主要有三种:实验测量、解析方法和数值方法。由于数值方法具有快速、准确、低成本等优势,该方法得到了越来越广泛的工程应用。
但是,由于实际目标往往是电大尺寸的,单台计算机在处理速度、内存需求等方面都已远远满足不了计算需求。所以,采用并行计算技术,将计算任务分解成若干可单独执行的小规模计算任务,是一种有效扩大仿真规模,提高仿真效率的途径。此外,计算机集群技术的发展,使利用普通商用计算机通过网络互联来达到并行计算成为可能。
在众多的电磁仿真技术中,时域数值方法是分析复杂系统宽带电磁特性的有力工具,可实现对物理量和物理现象更深刻、更直观的理解,且经过简单的时频变换即可得到宽带范围的频域信息。因此,结合PC集群,开展并行时域算法研究,对解决电大尺寸问题具有很强的现实意义。本文主要工作包括:
1.介绍了并行计算系统的组成,研究了基于分布式内存的MPI并行技术和基于共享内存的OpenMP并行技术,并对并行性能评估参数进行了分析。
2.在研究基于面元模型网格自动生成技术的基础上,以判定网格点和闭合目标关系为出发点,对其中的基本原理和关键步骤进行了详细介绍,并通过实例验证了该方法的可行性与正确性。
3.系统介绍了并行FDTD的算法原理,对其中的区域分割和数据交换进行了深入分析,并通过采用CPML吸收边界,使吸收边界的并行化处理完全融入到FDTD的并行过程中。通过算例,验证了并行FDTD算法的准确性与有效性。在此基础上,采用MPI和OpenMP相结合的两级并行策略,提高了并行性能。
4.在阐述多区域伪谱时域算法(MPSTD)原理的基础上,结合并行FDTD实现原理,对并行MPSTD算法中的区域分割和数据交换进行了分析,初步实现了并行MPSTD算法在电磁散射问题中的应用,并通过算例验证了该算法的准确性与有效性。
The study about EM scattering characteristics is important in electromagnetism, which is widely used on target tracking radar, remote sensing satellites detecting, radar target recognition technology, and it is great valuable to engineering. Nowadays, it consists of three main methods to get the EM scattering characteristics which are named by experiment methods, analytical methods and numerical algorithms. Among them, the numerical algorithms are more and more widely applied in engineering because of the fast, accurate and low-cost advantages.
However, because the practical objects are always electrical large, a single computer's processing speed and memory are far from meeting these needs. Therefore, with the use of parallel computing technology, computing task could be decomposed, and the complexity of simulation can be effectively promoted, the simulation efficiency would also be improved. In addition, with the development of computer cluster technology, it’s possible to achieve parallel computing with the use of common business computers which are connected through network.
Time-domain numerical method is more powerful to analyze the broadband EM characteristics of complex systems than the other full-wave time domain algorithms, which can achieve a deeper, more advanced and intuitive understanding of the physical concepts and phenomena. What’s more, after a simple time-frequency transform, a broadband information on frequency domain could be obtained. Therefore, it has a strong practical significance of carrying out a study on time domain parallel algorithm with the use of PC cluster. The main contributions of the author in this paper are summarized as follows:
1. The composition of Parallel computing system is introduced systematically. The MPI based on distributed memory parallel technology and the OpenMP based on memory-shared parallel technology are studied, and the parallel performance evaluation parameters are deeply discussed.
2. In order to get the relationship of grid points and closed objects, The theory and key procedure of meshing technology based on surface element model is deeply studied. Then the validity and correctness of this technology are demonstrated by certain examples.
3. The theory of parallel FDTD algorithm are introduced, and the method of region division and data exchange are further analyzed, then the parallel processing of absorbing boundary is well embedded into the general FDTD processing by selecting CPML boundary conditions. The accuracy of the parallel FDTD algorithm is verified through the parallel computing of Scattering from a metal sphere, and the validity of the parallel FDTD algorithm is verified by certain examples. Based on the above technology, a two-level strategy is applied by combing MPI and OpenMP, which promotes the performance.
4. Based on the study of Multi-domain pseudo-spectral time-domain (MPSTD) algorithm and the theory of parallel FDTD, the region division and data exchange are studied, and the application of parallel MPSTD algorithm in scattering problems is realized. The veracity and validity of the algorithm are verified by an example.
但是,由于实际目标往往是电大尺寸的,单台计算机在处理速度、内存需求等方面都已远远满足不了计算需求。所以,采用并行计算技术,将计算任务分解成若干可单独执行的小规模计算任务,是一种有效扩大仿真规模,提高仿真效率的途径。此外,计算机集群技术的发展,使利用普通商用计算机通过网络互联来达到并行计算成为可能。
在众多的电磁仿真技术中,时域数值方法是分析复杂系统宽带电磁特性的有力工具,可实现对物理量和物理现象更深刻、更直观的理解,且经过简单的时频变换即可得到宽带范围的频域信息。因此,结合PC集群,开展并行时域算法研究,对解决电大尺寸问题具有很强的现实意义。本文主要工作包括:
1.介绍了并行计算系统的组成,研究了基于分布式内存的MPI并行技术和基于共享内存的OpenMP并行技术,并对并行性能评估参数进行了分析。
2.在研究基于面元模型网格自动生成技术的基础上,以判定网格点和闭合目标关系为出发点,对其中的基本原理和关键步骤进行了详细介绍,并通过实例验证了该方法的可行性与正确性。
3.系统介绍了并行FDTD的算法原理,对其中的区域分割和数据交换进行了深入分析,并通过采用CPML吸收边界,使吸收边界的并行化处理完全融入到FDTD的并行过程中。通过算例,验证了并行FDTD算法的准确性与有效性。在此基础上,采用MPI和OpenMP相结合的两级并行策略,提高了并行性能。
4.在阐述多区域伪谱时域算法(MPSTD)原理的基础上,结合并行FDTD实现原理,对并行MPSTD算法中的区域分割和数据交换进行了分析,初步实现了并行MPSTD算法在电磁散射问题中的应用,并通过算例验证了该算法的准确性与有效性。
The study about EM scattering characteristics is important in electromagnetism, which is widely used on target tracking radar, remote sensing satellites detecting, radar target recognition technology, and it is great valuable to engineering. Nowadays, it consists of three main methods to get the EM scattering characteristics which are named by experiment methods, analytical methods and numerical algorithms. Among them, the numerical algorithms are more and more widely applied in engineering because of the fast, accurate and low-cost advantages.
However, because the practical objects are always electrical large, a single computer's processing speed and memory are far from meeting these needs. Therefore, with the use of parallel computing technology, computing task could be decomposed, and the complexity of simulation can be effectively promoted, the simulation efficiency would also be improved. In addition, with the development of computer cluster technology, it’s possible to achieve parallel computing with the use of common business computers which are connected through network.
Time-domain numerical method is more powerful to analyze the broadband EM characteristics of complex systems than the other full-wave time domain algorithms, which can achieve a deeper, more advanced and intuitive understanding of the physical concepts and phenomena. What’s more, after a simple time-frequency transform, a broadband information on frequency domain could be obtained. Therefore, it has a strong practical significance of carrying out a study on time domain parallel algorithm with the use of PC cluster. The main contributions of the author in this paper are summarized as follows:
1. The composition of Parallel computing system is introduced systematically. The MPI based on distributed memory parallel technology and the OpenMP based on memory-shared parallel technology are studied, and the parallel performance evaluation parameters are deeply discussed.
2. In order to get the relationship of grid points and closed objects, The theory and key procedure of meshing technology based on surface element model is deeply studied. Then the validity and correctness of this technology are demonstrated by certain examples.
3. The theory of parallel FDTD algorithm are introduced, and the method of region division and data exchange are further analyzed, then the parallel processing of absorbing boundary is well embedded into the general FDTD processing by selecting CPML boundary conditions. The accuracy of the parallel FDTD algorithm is verified through the parallel computing of Scattering from a metal sphere, and the validity of the parallel FDTD algorithm is verified by certain examples. Based on the above technology, a two-level strategy is applied by combing MPI and OpenMP, which promotes the performance.
4. Based on the study of Multi-domain pseudo-spectral time-domain (MPSTD) algorithm and the theory of parallel FDTD, the region division and data exchange are studied, and the application of parallel MPSTD algorithm in scattering problems is realized. The veracity and validity of the algorithm are verified by an example.
引文
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[30]庄钊文,袁乃昌,莫锦军,刘少斌.军用目标雷达散射界面预估与测量[M].科学出版社,北京, 2007.
[31] Nikolaos Drosinos, Nectarios Koziris. Performance Comparison of Pure MPI vs Hybrid MPI-OpenMP Parallelization Models on SMP Clusters[J]. 18th International Parallel and Distributed Processing Symposium, Apr 26-30 2004, Santa Fe, NM, United States, 193-202
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[35]普鑫.一种基于面元模型的FDTD自动网格产生技术.计算机应用, 2006.
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[2] Jensen M A, Fi jany A, and Rahmat-Samii Y. Time-Parallel Computational Strategy for FDTD Solution of Maxwell Equations[J]. IEEE Antennas and Propagation Society International Symp, 1994, Vol.1: 380-383.
[3] Schiavone Guy A, Codreanu Iulian, Palaniappan Ravishankar, et a1. FDTD Speedups Obtained in Distributed Computing on a Linux Workstation Cluster[J]. IEEE Antennas and Propagation Society International Symposium, Salt Lake, UT, USA, 2000, Vol.3:1336-1339.
[4] G-uiffaut C and Mahdjoubi K. A parallel FDTD algorithm using the MPI library[J]. IEEE Antennas and Propagation Magazine, 2001, 43(2); 94-103.
[5] Su Mehmet F, E1-Kady Ihab,Bader David A. et a1. A novel FDTD application featuring OpenMP-MPI hybrid parallelization[J]. Proceedings of International Conference on Parallel Processing, Aug 15-18 2004, Montreal, Que, Canada, 373-379.
[6] Wenhua Yu, Hashemi M R, Raj Mittra, et a1. Massively Parallel Conformal FDTD on a BlueGene Supercomputer[J]. IEEE Trans. On Advanced Packaging, 2007, 30(2): 335-341.
[7] Wenhua Yu, Yongjun Liu, Tao Su, et a1. A Robust Parallel Conformal Finite-Difference Time-Domain Processing Package Using the MPI Library[J].IEEE Antennas and Propagation Magazine, 2005, 47(3):39-59.
[8]闫玉波,葛宁,郑美艳.网络并行FDTD方法分析电大目标电磁散射[J].电子学报, 2003.06.
[9]陈星,黄卡玛.构建基于Windows和MPI的Beowulf并行计算系统[J].计算机工程与应用, 2003.04.
[10]杨虎.多区域时域伪谱算法在电磁分析中的理论和应用研究[D].国防科学技术大学, 2006.
[11] A.V.Kabakian. A spectral algorithm for electromagnetic wave scattering in the time domain Application to RCS computation[C]. Proc.Of27th AIAA Plasma dynamics and Lasers Conference. 1996. New Orleans, AIAA,2334-2337.
[12]刘瑜.混合并行技术在FDTD计算中的应用研究[J].电子科技大学学报, 2009.03.
[13] Srisukh Y, Nehrbass J, Teixeira F L et al. An approach of automatic grid generation in three-dimensional FDTD simulations of complex geometries[J]. IEEEAntennas and Propagation Magazine, 2002, 44(4): 75-80
[14] Baolin Yang. Spectral methods and absorbing boundary conditions for Maxwell’s Equations[D]. Brown University. 1998.
[15] B.LYang, J.S.Hesthaven. Multidomain pseudospectral computation of Maxwell’s equation in 3-D general curvilinear coordinates[J]. Applied Numerical. Mathematics, 2000, 33:282-289.
[16] Y.Shi, T.Su, C.H.Liang. Multidomain pseudospectral time-domain method for computation of electromagnetic scattering by bodies of revolution[J]. Microwave and Optical Technology Letters, 2005, 47(1): 92-96
[17] Jiang Yong-jin, Chai Shun-lian, Mao Jun-jie. CV-PB patching conditions for inter-faces in multidomain pseudospectral time-domain[C]. IEEE 4th International Conference on Microwave and Millimeter Wave Technology Proceedings. 2005.3:368-372.
[18]卢光辉,陈瀚,王浩刚.并行处理技术在电大尺寸复杂目标电磁散射中的应用[J],电子学报, 2003.06.
[19]聂在平,方大纲.目标与环境电磁散射特性建模[M].国防工业出版社,北京, 2009.
[20]潘晓敏,计算电磁学中的并行技术及其应用,中国科学院[D], 2006.04
[21]肖运辉,计算电磁学中的并行矩量法及在集群环境中的实现,西安电子科技大学[D], 2006
[22] Conway, ME, A Multi porcessor System Design[J], Porc. AFlPS Fall Joint Computer Conf, Vol 4: 139-146, 1963.
[23] Flynn Michael J. Some computer organizations and their effectiveness[J]. IEEE Trans. on Computers, 1972, 21(9): 948-960.
[24] Timothy G Mattson, Beverly A Sanders, and Bema L Massingill[J]. Paaerns for Parallel Programming. Boston: Addison—Wesley Pub. Co. 2005, 5-17.
[25]莫则尧,袁国兴.消息传递并行编程环境MPI[M].科学出版社,北京, 2001.
[26] http://www-unix.mcs.anl.gov/mpi/mpich/
[27] Yee K S.Numerical solution of initial boundary value problems involving Maxwell equations in isotropic media[J]. IEEE Trans. Antennas Propagation, 1966, l7(5): 302·307.
[28]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,西安, 2003.
[29]梁晓冰.基于MPI的电磁场时域有限差分法的网络并行研究[D].国防科学技术大学[D], 2004.
[30]庄钊文,袁乃昌,莫锦军,刘少斌.军用目标雷达散射界面预估与测量[M].科学出版社,北京, 2007.
[31] Nikolaos Drosinos, Nectarios Koziris. Performance Comparison of Pure MPI vs Hybrid MPI-OpenMP Parallelization Models on SMP Clusters[J]. 18th International Parallel and Distributed Processing Symposium, Apr 26-30 2004, Santa Fe, NM, United States, 193-202
[32]多核系列教材编写组.多核程序设计[M].北京:清华大学出版社, 2007.
[33]张玉.电磁场并行计算[M],西安电子科技大学出版社,西安, 2006.
[34]张林波,迟学斌,莫则尧等.并行计算导论[M].清华大学出版社,北京, 2006.
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