时域积分方程快速算法及并行计算的研究与应用
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摘要
时域积分方程(TDIE)方法在雷达目标隐身和反隐身技术研究、雷达目标特性分析与识别、复杂天线系统设计、现代电子系统电磁兼容性分析等领域表现出特别的优势,已成为计算电磁学领域的研究热点之一。然而,TDIE传统的数值解法—时间步进算法(MOT)在实现中面临两方面的问题:数值解不稳定和计算效率低。本文的目的就是发展有效、快速的时域积分方程求解方法,并将其应用于工程实践。
论文首先对良导体电磁散射问题中电场积分方程(EFIE)、磁场积分方程(MFIE)和混合场积分方程(CFIE)的建立方法,以及时域积分方程的离散和求解过程进行了深入研究,系统分析了导致MOT算法不稳定的因素,在算法谐振模式基础上提出了误差一致性原则,完善了MOT算法稳定性理论。为了提高计算精度,深入研究了阻抗矩阵元素计算中的奇异迟滞边界积分问题,提出了一种通过坐标轴变换解析计算奇异积分的方法。在此基础上还提出了一种精确求解时滞积分的解析方法。
为了降低MOT算法的高计算量和存储量,论文重点研究了MOT的三种快速算法,分别为时域自适应算法(TD-AIM)、时域平面波算法(PWTD)、时域积分方程与高频近似混合算法。在TD-AIM算法研究中,对算法的基本思想、一般步骤、理论依据以及各个算子的具体实现方法进行了详细阐述。在PWTD算法研究中,对算法的基本理论进行了深入研究,提出了一种利用出射表和入射表改进聚集、转移和投射的新方法,并且投射方式采用标准子信号前向贡献式投射。该方法不但降低了内存需求,大幅度提高了计算规模,而且投射方式有利于时间点的对齐,降低了投射次数,提高了计算速度和精度。在混合算法研究中,提出了一种一致性绕射理论(UTD)与时域积分方程混合的算法,为求解电大平台电磁兼容问题提供了一条有效途径。
基于.NET Remoting技术,实现了MOT、TD-AIM、PWTD算法的分布式并行计算,从而可充分利用现有的网络计算资源高效解决实际工程问题。
基于上述算法的研究,设计和开发了快速电磁计算软件包,论文展示了软件包的结构,并利用该软件包对一些工程电磁问题进行了仿真计算。计算结果验证了软件包的有效性和通用性,也展现了时域积分方程快速算法的优点。
In the areas of radar stealth and anti-stealth, radar target identification, complex antenna system design and EMC analysis of modern electric systems, time domain integral equation (TDIE) has provided an appealing avenue and has become considerable interest in the computational electromagnetic community. However, marching-on-in-time (MOT) based on TDIE solver has been suffered from numerical instability and low computational efficiency. The purpose of this thesis is to develop an effective, fast method for solving time-domain integral equation, and to apply it to engineering practice.
Derivations of time domain EFIE, MFIE and CFIE in the transient analysis of electromagnetic wave scattering from perfect electrical conducting objects are reviewed firstly in this thesis, and the solving procedures of TDIE are elaborated. Then the causes of MOT instability are systematically studied, and the error consistency principle is proposed based on the algorithm resonant mode, which consummates the stability theory of MOT algorithm. An analytical calculation method is proposed to improve the calculation accuracy of impedance matrix elements by shifting and rotating the coordinates. In addition, a precise analytical method for solving time-delay integration is proposed.
Three accelerated MOT algorithms, named Time Domain Adaptive Integral Method (TD-AIM), Plane Wave Time Domain (PWTD) and hybrid method of high-frequency approximation coupled TDIE respectively, are presented to reduce the computational complexity and memory requirement of classical MOT. Firstly, the basic ideas, the general processes, the theory foundation and the implementation of the operators of the TD-AIM are elaborated. Secondly, PWTD algorithm is studied deeply in this thesis. The outgoing rays table and incoming rays table strategy which uses a new forward contribution project method is presented. This strategy reduces the memory requirements and greatly increases the size of the calculation on the one hand, and on the other hand it is conducive to the alignment point in time, reducing the number of projection to enhance the computing speed and accuracy. Lastly, coupling process and realization method of UTD and TDIE are elaborated.
Distributed and parallel computation for algorithm of MOT, TD-AIM and PWTD is realized based on .NTE Remoting technology, which enables efficiently and adequately using of modern network computing resources to solve practical engineering problems.
The design ideas of the rapid electromagnetic computation package are described. At the same time, the package structure and some engineering calculation results are shown. On the one hand these examples verify the effectiveness and versatility of the package, and on the other hand the advantages of time domain integral equation’s fast algorithms are demonstrated.
论文首先对良导体电磁散射问题中电场积分方程(EFIE)、磁场积分方程(MFIE)和混合场积分方程(CFIE)的建立方法,以及时域积分方程的离散和求解过程进行了深入研究,系统分析了导致MOT算法不稳定的因素,在算法谐振模式基础上提出了误差一致性原则,完善了MOT算法稳定性理论。为了提高计算精度,深入研究了阻抗矩阵元素计算中的奇异迟滞边界积分问题,提出了一种通过坐标轴变换解析计算奇异积分的方法。在此基础上还提出了一种精确求解时滞积分的解析方法。
为了降低MOT算法的高计算量和存储量,论文重点研究了MOT的三种快速算法,分别为时域自适应算法(TD-AIM)、时域平面波算法(PWTD)、时域积分方程与高频近似混合算法。在TD-AIM算法研究中,对算法的基本思想、一般步骤、理论依据以及各个算子的具体实现方法进行了详细阐述。在PWTD算法研究中,对算法的基本理论进行了深入研究,提出了一种利用出射表和入射表改进聚集、转移和投射的新方法,并且投射方式采用标准子信号前向贡献式投射。该方法不但降低了内存需求,大幅度提高了计算规模,而且投射方式有利于时间点的对齐,降低了投射次数,提高了计算速度和精度。在混合算法研究中,提出了一种一致性绕射理论(UTD)与时域积分方程混合的算法,为求解电大平台电磁兼容问题提供了一条有效途径。
基于.NET Remoting技术,实现了MOT、TD-AIM、PWTD算法的分布式并行计算,从而可充分利用现有的网络计算资源高效解决实际工程问题。
基于上述算法的研究,设计和开发了快速电磁计算软件包,论文展示了软件包的结构,并利用该软件包对一些工程电磁问题进行了仿真计算。计算结果验证了软件包的有效性和通用性,也展现了时域积分方程快速算法的优点。
In the areas of radar stealth and anti-stealth, radar target identification, complex antenna system design and EMC analysis of modern electric systems, time domain integral equation (TDIE) has provided an appealing avenue and has become considerable interest in the computational electromagnetic community. However, marching-on-in-time (MOT) based on TDIE solver has been suffered from numerical instability and low computational efficiency. The purpose of this thesis is to develop an effective, fast method for solving time-domain integral equation, and to apply it to engineering practice.
Derivations of time domain EFIE, MFIE and CFIE in the transient analysis of electromagnetic wave scattering from perfect electrical conducting objects are reviewed firstly in this thesis, and the solving procedures of TDIE are elaborated. Then the causes of MOT instability are systematically studied, and the error consistency principle is proposed based on the algorithm resonant mode, which consummates the stability theory of MOT algorithm. An analytical calculation method is proposed to improve the calculation accuracy of impedance matrix elements by shifting and rotating the coordinates. In addition, a precise analytical method for solving time-delay integration is proposed.
Three accelerated MOT algorithms, named Time Domain Adaptive Integral Method (TD-AIM), Plane Wave Time Domain (PWTD) and hybrid method of high-frequency approximation coupled TDIE respectively, are presented to reduce the computational complexity and memory requirement of classical MOT. Firstly, the basic ideas, the general processes, the theory foundation and the implementation of the operators of the TD-AIM are elaborated. Secondly, PWTD algorithm is studied deeply in this thesis. The outgoing rays table and incoming rays table strategy which uses a new forward contribution project method is presented. This strategy reduces the memory requirements and greatly increases the size of the calculation on the one hand, and on the other hand it is conducive to the alignment point in time, reducing the number of projection to enhance the computing speed and accuracy. Lastly, coupling process and realization method of UTD and TDIE are elaborated.
Distributed and parallel computation for algorithm of MOT, TD-AIM and PWTD is realized based on .NTE Remoting technology, which enables efficiently and adequately using of modern network computing resources to solve practical engineering problems.
The design ideas of the rapid electromagnetic computation package are described. At the same time, the package structure and some engineering calculation results are shown. On the one hand these examples verify the effectiveness and versatility of the package, and on the other hand the advantages of time domain integral equation’s fast algorithms are demonstrated.
引文
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