时域积分方程混合与快速算法及其在分析复杂结构中瞬态电磁效应的应用研究
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摘要
近年来,电子信息系统在功能曰渐强大的同时,也面临着电磁环境曰益复杂和恶劣的问题。随着电磁脉冲武器研制的发展,电磁兼容和电磁干扰问题成为高度研究的问题。高功率电磁脉冲可以通过天线、线缆等注入电子器件与线路,使受辐照的电子设备功能失效甚至损毁。特别是,对于舰船平台,在有限的空间需放置大量不同波段收发设备,如何深入研究外来高功率电磁脉冲对典型器件、系统的耦合机理和损毁效应显得非常迫切和重要。在研究舰船平台EMC问题时,由于真实试验条件有限,花费代价也巨大,受到诸多限制。因此,使用计算电磁学方法进行数值仿真,对问题和设计进行评估、量化和改进,可发挥重要作用。正是本着这样的目标,论文有针对性地研究了时域积分方程混合与快速算法,开发了用于分析电磁脉冲照射下瞬态电磁问题的并行平台,主要研究工作和创新点可归纳为：
1)基于时域积分方程的特性,较为系统地研究了时间步进算法。分析了常用时间基函数波形及其特性,研究了显式和隐式算法；针对时间步进算法后时不稳定性问题,利用新型拉盖尔多项式时间基函数,提出了后时稳定的自适应阶数步进(MOD)求解方法；
2)系统研究了复杂金属-介质组合体目标的电磁特性,建立TD-EFIE-PMCHW方程,研究介质涂覆、金属贴片等不同情形,提出一种处理金属-介质-自由空间三者的交界边(junction)的精确方法,并且研究了卷积计算加速技术,使算法更为有效；
3)研究了时域积分方程与高频方法的混合,提出了TDIE-TDPO混合方法,有效分析了平台上多天线耦合特性；
4)系统研究了自适应积分方法,提出了TD-AIM-MOD快速算法,包括辅助基函数投影矩阵的快速求解、FFT加速Toeplitz矩阵-向量乘积,稀疏矩阵存储技术,以及奇异值分解压缩技术；
5)研究和开发了快速算法TD-AIM-MOD的并行程序,解决了4-D时-空FFT并行求解技术。在此基础上,研究了典型先进舰船桅杆结构及其电磁建模技术,运用并行TD-AIM-MOD方法分析了舰船桅杆典型结构模型的瞬态散射特性。
此外,论文研究还包括了表面电流显示、Vandermonde矩阵方程快速求解、奇异和近奇异积分等技术,进一步完善时域积分积分方程方法求解大规模电磁问题的能力。
In recent years, with rapidly increasing in functionality of the electronic information systems, the electromagnetic environment they have to face becomes more and more complex and harsh. With the development of electromagnetic pulse weapons, the great attention is paid on the electromagnetic compatibility (EMC) and electromagnetic interference (EMI) problems. High-power electromagnetic pulses can be injected through the antennas, wires, cables, and etc. which will cause the electronic devices malfunction and even damaged. In particular, for the ship platform, a number of transceivers in different bands have to be placed in the limited space. So it is of vital important to deeply investigate the coupling mechanism and damage effects of high-power electromagnetic pulses on typical devices and systems. In the study of EMC problems for the ship platform, there are great restrictions on the field measurement due to the required strict testing conditions and cost of resources. Under such circumstance, the numerical simulation is able to play a key role in design evaluation, quantification and improvement of EMC problems. In this dissertation, we focus on the hybrid and fast algorihms based on time domain integral equation (TDIE), and develop the parallel computational platform for the analysis of transient electromagnetic problems under the illumination of electromagnetic pulses. The main research and academic contributions of this dissertation are summarized as follows:
1) Based on the properties of time domain integral equation, firstly, the method of moment for solving the frequency domain integral equation is introduced. Further, the complete derivation of the time-domain integral equation is given, and the marching-on-in-time (MOT) scheme for solving TDIE is studied step by step. The commonly used temporal basis functions are discussed, then the explicit and implicit MOT schems are investigated. Three forms of TDIE formulations, incluindg electric field integral equation, magnetic field integral equation and combined field integral equations are analyzed, respectively.
2) Due to the late time instability of marching-on-in-time scheme, the marching-on-in-degree (MOD) scheme is proposed, and it is proven to be very late time stable. The novel temporal basis function based on Laguerre polynomials is introduced, then the formulations and process of MOD for anaysing metallic and dielectric structures are derived and explained in detail. Further, an adaptive MOD scheme based on2-norms is developed, which improves the computation efficiency of MOD.
3) The electromagnetic characteristics of dielectric-metallic composite structures are studied, and the TD-EFIE-PMCHW formulations are derived. Different circumstances are taken into account, incluing dielectric coating, metallic patch, and etc. A compact and effective treatment of junctions among dielectic, metallic component and free space is proposed. The technique of accelerating the convolution in MOD recursion is studied.
4) The hybridization of TDIE and high frequency method, and TDIE-TDPO hybrid method are proposed. For solving the muti-scale problems, the target is divided into TDIE region and TDPO region, according to the respective advantages of the two methods. Compared to the full TDIE solution, the hybrid method reduces the calculation consumption. TDIE-TDPO method is utilized to analyze the coupling characteristics of multiple antennas on the platform.
5) The adaptive integral method is studied systematically. Based on this, the TD-AIM-MOD fast algorithm is proposed. In the implementation of TD-AIM-MOD method, several techniques are adopted, such as fast solution of projection matrix based on auxiliary basis function, the Toeplitz matrix-vector multiplication accelerated by FFT, sparse matrix storage and sparse matrix-vertor multiplication. Due to reduce the memory requirement of the near field correction matrix, the technique of singular value decomposition compression is introduced.
6) The parallel TD-AIM-MOD fast algorithm is developed.4-D spatial-temporal FFT is solved by parallel. Numerical examples are provided to analyze the parallel efficieny of the proposed algorithm.
7) Some typical modern ship mast structures are studied, and the required modeling techniques for electromagnetic simulation are also investigated. Further, a series of tower mast structures for simulation are established by using3ds Max and HFSS. Numerical simulations are given to analyze the transient scattering characteristics of these typical ship mast structures by using the proposed parallel TD-AIM-MOD fast algorithm.
In addition, in this dissertation, the surface current display, fast solution of equations formed by Vandermode matrix, singular and nearly singular integral are studied. They together improve the capabilities of TDIE method for solving large-scale electromagnetic problems.
1)基于时域积分方程的特性,较为系统地研究了时间步进算法。分析了常用时间基函数波形及其特性,研究了显式和隐式算法；针对时间步进算法后时不稳定性问题,利用新型拉盖尔多项式时间基函数,提出了后时稳定的自适应阶数步进(MOD)求解方法；
2)系统研究了复杂金属-介质组合体目标的电磁特性,建立TD-EFIE-PMCHW方程,研究介质涂覆、金属贴片等不同情形,提出一种处理金属-介质-自由空间三者的交界边(junction)的精确方法,并且研究了卷积计算加速技术,使算法更为有效；
3)研究了时域积分方程与高频方法的混合,提出了TDIE-TDPO混合方法,有效分析了平台上多天线耦合特性；
4)系统研究了自适应积分方法,提出了TD-AIM-MOD快速算法,包括辅助基函数投影矩阵的快速求解、FFT加速Toeplitz矩阵-向量乘积,稀疏矩阵存储技术,以及奇异值分解压缩技术；
5)研究和开发了快速算法TD-AIM-MOD的并行程序,解决了4-D时-空FFT并行求解技术。在此基础上,研究了典型先进舰船桅杆结构及其电磁建模技术,运用并行TD-AIM-MOD方法分析了舰船桅杆典型结构模型的瞬态散射特性。
此外,论文研究还包括了表面电流显示、Vandermonde矩阵方程快速求解、奇异和近奇异积分等技术,进一步完善时域积分积分方程方法求解大规模电磁问题的能力。
In recent years, with rapidly increasing in functionality of the electronic information systems, the electromagnetic environment they have to face becomes more and more complex and harsh. With the development of electromagnetic pulse weapons, the great attention is paid on the electromagnetic compatibility (EMC) and electromagnetic interference (EMI) problems. High-power electromagnetic pulses can be injected through the antennas, wires, cables, and etc. which will cause the electronic devices malfunction and even damaged. In particular, for the ship platform, a number of transceivers in different bands have to be placed in the limited space. So it is of vital important to deeply investigate the coupling mechanism and damage effects of high-power electromagnetic pulses on typical devices and systems. In the study of EMC problems for the ship platform, there are great restrictions on the field measurement due to the required strict testing conditions and cost of resources. Under such circumstance, the numerical simulation is able to play a key role in design evaluation, quantification and improvement of EMC problems. In this dissertation, we focus on the hybrid and fast algorihms based on time domain integral equation (TDIE), and develop the parallel computational platform for the analysis of transient electromagnetic problems under the illumination of electromagnetic pulses. The main research and academic contributions of this dissertation are summarized as follows:
1) Based on the properties of time domain integral equation, firstly, the method of moment for solving the frequency domain integral equation is introduced. Further, the complete derivation of the time-domain integral equation is given, and the marching-on-in-time (MOT) scheme for solving TDIE is studied step by step. The commonly used temporal basis functions are discussed, then the explicit and implicit MOT schems are investigated. Three forms of TDIE formulations, incluindg electric field integral equation, magnetic field integral equation and combined field integral equations are analyzed, respectively.
2) Due to the late time instability of marching-on-in-time scheme, the marching-on-in-degree (MOD) scheme is proposed, and it is proven to be very late time stable. The novel temporal basis function based on Laguerre polynomials is introduced, then the formulations and process of MOD for anaysing metallic and dielectric structures are derived and explained in detail. Further, an adaptive MOD scheme based on2-norms is developed, which improves the computation efficiency of MOD.
3) The electromagnetic characteristics of dielectric-metallic composite structures are studied, and the TD-EFIE-PMCHW formulations are derived. Different circumstances are taken into account, incluing dielectric coating, metallic patch, and etc. A compact and effective treatment of junctions among dielectic, metallic component and free space is proposed. The technique of accelerating the convolution in MOD recursion is studied.
4) The hybridization of TDIE and high frequency method, and TDIE-TDPO hybrid method are proposed. For solving the muti-scale problems, the target is divided into TDIE region and TDPO region, according to the respective advantages of the two methods. Compared to the full TDIE solution, the hybrid method reduces the calculation consumption. TDIE-TDPO method is utilized to analyze the coupling characteristics of multiple antennas on the platform.
5) The adaptive integral method is studied systematically. Based on this, the TD-AIM-MOD fast algorithm is proposed. In the implementation of TD-AIM-MOD method, several techniques are adopted, such as fast solution of projection matrix based on auxiliary basis function, the Toeplitz matrix-vector multiplication accelerated by FFT, sparse matrix storage and sparse matrix-vertor multiplication. Due to reduce the memory requirement of the near field correction matrix, the technique of singular value decomposition compression is introduced.
6) The parallel TD-AIM-MOD fast algorithm is developed.4-D spatial-temporal FFT is solved by parallel. Numerical examples are provided to analyze the parallel efficieny of the proposed algorithm.
7) Some typical modern ship mast structures are studied, and the required modeling techniques for electromagnetic simulation are also investigated. Further, a series of tower mast structures for simulation are established by using3ds Max and HFSS. Numerical simulations are given to analyze the transient scattering characteristics of these typical ship mast structures by using the proposed parallel TD-AIM-MOD fast algorithm.
In addition, in this dissertation, the surface current display, fast solution of equations formed by Vandermode matrix, singular and nearly singular integral are studied. They together improve the capabilities of TDIE method for solving large-scale electromagnetic problems.
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