FDTD网络并行计算及ADI-FDTD方法研究
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摘要
本文采用区域分解技术将FDTD计算区域分割成多个子域进行分别计算,各个子区域在边界处与其相邻的子区域进行切向场值的数据交换以使整个迭代进行下去。根据FDTD迭代式的特点,相邻子域之间有半个网格的重叠区域。三维FDTD计算域分割方式和二维FDTD计算域分割方式相同,每个子域的编号为其在整个计算域的空间位置。给出了FDTD子域间同步计算的技术,即采用同步消息传递和阻塞函数同步两种手段。并行FDTD中吸收边界、输出边界和总场边界被分配到不同的子域内,对这三大边界的特殊处理,增加了编程的复杂度。
本文应用基于消息传递(Message Passing)模式的网络并行计算系统来实现FDTD并行计算方法,消息传递的并行计算平台采用PVM (Parallel Virtual Machine)并行系统。并行FDTD计算方法采用主从式的编程模式。并行程序分为主控程序(master)和从程序(slave)两部分。主控程序主要负责进程的生成、初始化、收集并显示计算结果等功能;从程序主要执行实际FDTD计算,其负载由主控程序分配。最后,给出了网络并行程序的流程图,详细的介绍了程序中各个模块的具体功能。
利用并行FDTD方法分析了二维和三维目标的电磁散射问题。给出了复杂目标(金属机翼和NASA杏仁体)和实用目标(导弹目标)的RCS计算结果。为了更精确的模拟弹头的外形轮廓,采用超椭球(Superspheroid)几何体来模拟导弹弹头的雷达罩。随后,给出了超回转椭球体的参数方程,并确定用来模拟导弹弹头Von Karman外形尺寸的参数设置。计算结果表明,采用一定参数下的超椭球几何体弹头比球冠状弹头有效的减小后向RCS。并行FDTD方法在处理电大尺寸实用目标的电磁散射问题上有更为实际的意义。
本文给出并行FDTD方法的并行加速比、并行效率和其它性能指标的测试结果。给出并行计算所需内存的估计公式,分析了内存估计结果与测试结果之间存在差异的原因。分析了FDTD并行计算性能与粒度、数据通讯量之间的关系。最后,通过计算三维复杂目标金属机翼目标的RCS,给出并行加速比和并行效率的测试结果。通过分析测试结果,指出网络通信性能和进程间的负载平衡影响并行计算的加速比。
给出一维Crank-Nicolson时域有限差分(C-N FDTD)方法在分层介质中的应用。给出一维C-N FDTD方法两种迭代求解方式:一种按照Holland编号方式电场和磁场分量交替排列构成三对角条带矩阵方程,一次性将电场和磁场格点的场值求出;另一种是按照交替方向隐式(ADI)差分格式要求仅使电场分量排列构成三对角条带矩阵方程,然后利用求出的空间各处电场分量迭代解出同时刻的磁场分量。随后,分析讨论
Based on a spatial decomposition of the regular grid structure, the FDTD computation space is divided into some sub-domains. Then the fields inside each sub-domain are computed on an individual processor with a small amount of data being communicated from neighboring sub-domains. According to the characteristic of FDTD computation formulas, there is an overlapping region between adjacent sub-domains, so that data communication is needed. The partition for 3D FDTD domain is the same as the one made for 2D FDTD domain. The identifier for each sub-domain is defined as the three-dimensional spatial location in the entire simulation domain. Some synchronization to be performed in all processes is required. Two main pathways that are use of blocking messages and use of barriers can be pursued to achieve the goal. It is worth noting that the domain partition leads to increased complexity in programming while the absorbing boundary, total-field scattered-field boundary and near-to-far field extrapolation boundary are located in different sub-domains.
A parallel algorithm for the FDTD method on a distributed network by using the message-passing module is presented. The parallel platform of PVM system is applied to the implementation of FDTD parallel algorithm. The structure of the parallel program adopts a master-slave organization. Then the parallel program is divided into two parts of master program and slave program. The functions of the master program mainly include the creation of process, the initialization of iterative, the collection and display of the computation results, and so on. Similarly, the functions of the slave program mainly include the execution of FDTD computation, and the load of slave process is distributed by master process. Finally, flow diagrams of the parallel FDTD program are given, and the concrete functions of each module are discussed in detail.
The EM scattering problems of 2D and 3D objects are analyzed by using the parallel FDTD method. The radar cross sections (RCS) of complex objects of metallic wing and NASA almond and practical object of missile are presented. In order to exactly imitate the contour of the missile warhead in the FDTD modeling, the superspheroid body is successfully applied. Then, the coefficient design of the superspheroidal equation, which can be modeling a number of shapes, such as Von Karman radome available for missile warhead is discussed. The calculated results of the back scattering demonstrate that the
本文应用基于消息传递(Message Passing)模式的网络并行计算系统来实现FDTD并行计算方法,消息传递的并行计算平台采用PVM (Parallel Virtual Machine)并行系统。并行FDTD计算方法采用主从式的编程模式。并行程序分为主控程序(master)和从程序(slave)两部分。主控程序主要负责进程的生成、初始化、收集并显示计算结果等功能;从程序主要执行实际FDTD计算,其负载由主控程序分配。最后,给出了网络并行程序的流程图,详细的介绍了程序中各个模块的具体功能。
利用并行FDTD方法分析了二维和三维目标的电磁散射问题。给出了复杂目标(金属机翼和NASA杏仁体)和实用目标(导弹目标)的RCS计算结果。为了更精确的模拟弹头的外形轮廓,采用超椭球(Superspheroid)几何体来模拟导弹弹头的雷达罩。随后,给出了超回转椭球体的参数方程,并确定用来模拟导弹弹头Von Karman外形尺寸的参数设置。计算结果表明,采用一定参数下的超椭球几何体弹头比球冠状弹头有效的减小后向RCS。并行FDTD方法在处理电大尺寸实用目标的电磁散射问题上有更为实际的意义。
本文给出并行FDTD方法的并行加速比、并行效率和其它性能指标的测试结果。给出并行计算所需内存的估计公式,分析了内存估计结果与测试结果之间存在差异的原因。分析了FDTD并行计算性能与粒度、数据通讯量之间的关系。最后,通过计算三维复杂目标金属机翼目标的RCS,给出并行加速比和并行效率的测试结果。通过分析测试结果,指出网络通信性能和进程间的负载平衡影响并行计算的加速比。
给出一维Crank-Nicolson时域有限差分(C-N FDTD)方法在分层介质中的应用。给出一维C-N FDTD方法两种迭代求解方式:一种按照Holland编号方式电场和磁场分量交替排列构成三对角条带矩阵方程,一次性将电场和磁场格点的场值求出;另一种是按照交替方向隐式(ADI)差分格式要求仅使电场分量排列构成三对角条带矩阵方程,然后利用求出的空间各处电场分量迭代解出同时刻的磁场分量。随后,分析讨论
Based on a spatial decomposition of the regular grid structure, the FDTD computation space is divided into some sub-domains. Then the fields inside each sub-domain are computed on an individual processor with a small amount of data being communicated from neighboring sub-domains. According to the characteristic of FDTD computation formulas, there is an overlapping region between adjacent sub-domains, so that data communication is needed. The partition for 3D FDTD domain is the same as the one made for 2D FDTD domain. The identifier for each sub-domain is defined as the three-dimensional spatial location in the entire simulation domain. Some synchronization to be performed in all processes is required. Two main pathways that are use of blocking messages and use of barriers can be pursued to achieve the goal. It is worth noting that the domain partition leads to increased complexity in programming while the absorbing boundary, total-field scattered-field boundary and near-to-far field extrapolation boundary are located in different sub-domains.
A parallel algorithm for the FDTD method on a distributed network by using the message-passing module is presented. The parallel platform of PVM system is applied to the implementation of FDTD parallel algorithm. The structure of the parallel program adopts a master-slave organization. Then the parallel program is divided into two parts of master program and slave program. The functions of the master program mainly include the creation of process, the initialization of iterative, the collection and display of the computation results, and so on. Similarly, the functions of the slave program mainly include the execution of FDTD computation, and the load of slave process is distributed by master process. Finally, flow diagrams of the parallel FDTD program are given, and the concrete functions of each module are discussed in detail.
The EM scattering problems of 2D and 3D objects are analyzed by using the parallel FDTD method. The radar cross sections (RCS) of complex objects of metallic wing and NASA almond and practical object of missile are presented. In order to exactly imitate the contour of the missile warhead in the FDTD modeling, the superspheroid body is successfully applied. Then, the coefficient design of the superspheroidal equation, which can be modeling a number of shapes, such as Von Karman radome available for missile warhead is discussed. The calculated results of the back scattering demonstrate that the
引文
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