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

发布时间：2018-05-29 04:04

本文选题：时域积分方程 + 时间步进　；参考：《浙江大学》2014年博士论文

【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。
[Abstract]:In recent years, electronic information system (EIS) has become more and more powerful, but it also faces the problem of complex and bad electromagnetic environment. With the development of electromagnetic pulse weapon (EMP), electromagnetic compatibility (EMC) and electromagnetic interference (EMI) have been studied. High power electromagnetic pulses can be injected into electronic devices and circuits through antennas, cables, etc., which invalidate or even destroy the function of irradiated electronic devices. In particular, for the ship platform, a large number of transceiver devices in different bands need to be placed in the limited space. It is very urgent and important to study the coupling mechanism and damage effect of the system. In the study of ship platform EMC problem, due to the real test conditions are limited, the cost is also huge, so it is limited. Therefore, numerical simulation with computational electromagnetics can play an important role in evaluating, quantifying and improving the problem and design. With this aim in mind, this paper studies the mixing and fast algorithm of time domain integral equation, and develops a parallel platform for analyzing transient electromagnetic problems under electromagnetic pulse irradiation. The main research work and innovation points can be summarized as follows: 1) based on the characteristic of time domain integral equation, the time step algorithm is studied systematically. In this paper, the waveform and characteristics of the time basis function are analyzed, and the explicit and implicit algorithms are studied, and the new Laguerre polynomial time basis function is used to solve the time instability problem of the time step algorithm. An adaptive order step mod (MOD) method is proposed to solve the problem. 2) the electromagnetic characteristics of complex metal-dielectric combination are studied systematically, the TD-EFIE-PMCHW equation is established, the different cases such as medium coating and metal patch are studied, and an accurate method to deal with the boundary junctions of metal-media-free space is proposed. And the accelerating technology of convolution calculation is studied to make the algorithm more effective. 3) the mixing of the time domain integral equation and the high frequency method is studied, and the TDIE-TDPO hybrid method is proposed. The coupling characteristics of multiple antennas on the platform are analyzed effectively. 4) the adaptive integration method is studied systematically, and the fast algorithm of TD-AIM-MOD is proposed, including the fast solution of the projection matrix of auxiliary basis function, the fast solution of the Toeplitz matrix and vector product, the storage technology of sparse matrix, and the technique of singular value decomposition and compression. 5) the parallel program of fast algorithm TD-AIM-MOD is studied and developed, and the parallel solution technology of 4-D space-time FFT is solved. On this basis, the typical advanced ship mast structure and its electromagnetic modeling technology are studied, and the transient scattering characteristics of the typical ship mast structure model are analyzed by using the parallel TD-AIM-MOD method. In addition, the paper also includes the surface current display Vandermonde matrix equation fast solution, singular and near singular integration and other techniques to further improve the time-domain integral equation method for solving large-scale electromagnetic problems.
【学位授予单位】：浙江大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TM15

【参考文献】