三维矢量散射的时域积分方程解及时频互推技术

【作者】 赵青；

【导师】 聂在平；

【作者基本信息】 电子科技大学 ， 电磁场与微波技术， 2004， 硕士

【摘要】 在电磁领域，随着对宽带信息的需求的不断增加，越来越需要能够直接求解时域中的电磁散射问题。直接在时域上求解目标电磁散射特性的方法不需要逐个对不同频点进行计算，而是直接求出整个宽频带上的目标电磁信息。因此，本文需要研究如何利用时域方法来求解任意形状目标的瞬态电磁散射。 时域方法又可以分为时域积分方程(TDIE)方法和时域微分方程(TDDE)方法。TDIE法和TDDE法相比具有以下优势：首先，对导体目标而言TDIE的计算区域是目标表面，因而比TDDE具有更少的计算量；第二，TDIE通过格林函数自动满足辐射边界条件，所以不需要额外的截断边界条件；第三，TDIE具有很小的网格色散误差。因此，是基于时间步进技术(MOT)的TDIE求解技术在近年来广受关注。研究表明，主要有两个原因阻碍MOT算法的广泛采用。一是MOT方法的后时不稳定性；另外MOT方法具有相当的计算复杂性，这使得对一些电大尺寸目标的精确分析几乎是不可能的。 本文针对MOT算法的后时不稳定性采用了一种隐式(implicit)时间步进算法能够较为有效的推迟其不稳定性发生的时间。在此基础上，本文采用了矩阵束方法来对时域响应进行外推。数值计算结果表明在给出足够的已知时域数据基础上，矩阵束方法能外推出一定范围内的时域数据。但是，此方法对数据有比较严格的要求，并且外推的范围有限。针对这些问题，本文时域早时响应和频域低频信息利用基于连带Hermit多项式的时频互推方法来获得时域的晚时响应和频域的高频信息。数值结果表明这种方法不但能够正确的互推出时、频域内的未知数据，而且由于只需要提供稳定的早时数据从而绕开了后时不稳定性的问题。另外，由于此方法只需要提供频域上的低频信息却能获得高频信息因而很大程度上节约了计算量和计算时间。此方法的采用避开了单独的时域、频域算法的缺陷，而且比仅采用单独的时、频域算法都更节省时间和计算量。但是，此方法的互推精度取决于关键参数的选择，本文分析推导出一些重要参数的选取原则，并基于这些原则获得的参数初值采用了一种自适应优化算法来获得最优参数。更多还原

【Abstract】 In the electromagnetic field, the demands for the time-domain electromagnetic methods keep raising as the demand for the wide-band information is increasing. The frequent-domain methods(such as MOM, FEM etc.) need to compute at every different frequent points in order to get wide band information. But by using the time-domain methods we can work out the whole wide band electromagnetic response of the subjects straightly. So, that’s why we have to pay more attention on the study of time-domain methods. In this work, we are going to do some research about time-domain integral equation method.Time-domain methods include the time-domain differential equation (TDDE) method and the time-domain integral equation (TDIE) methods. TDIE method has some advantages compared with TDDE method: Firstly, the compute area is just on the surface of the conducting subjects that means fewer unknown quantities; Secondly, there is no need of absorb boundary condition (ABC) for the TDIE method; Thirdly, there is smaller dispersion error. Therefore, Marching on-in-time(MOT) algorithm is getting more and more attention nowadays. Research shows that two shortcomings block in the spreading of this method. One is the late-time instability; the other is the computational complexity which make it impossible to accurately analysis the electrically large object subjects.This paper use the implicit MOT algorithm in order to delay the instability of explicit MOT algorithm. The examples show that it can get some effect. Then we use the matrix-pencil algorithm to interpolation/extrapolation the unknown data in some range, result shows that it can get correct response if enough known data is provided. This paper also uses the simultaneous interpolation/extrapolation algorithm to get the late-time electromagnetic responses and the high-frequency electromagnetic data by the early-time and low-frequency responses. It was proved to be an effective method by the computational results. It can not only work out the accurate responses, but also avoid the late-time instability in time domain as we only need early-time stable data. And the most important thing is that it can cut the computational cost and time as there is no need to compute the high-frequency electromagnetic responses. But the success of this algorithm depends on the accurate choose of the key parameters. In this paper, we derivative some principles of how to get the right initial value of this key parameters, then based on these initial value, we use a optimal method to get their optimal values.更多还原