【作者】 蔡明娟；

【导师】 何建国；

【作者基本信息】 国防科学技术大学 ， 电子科学与技术， 2006， 博士

【摘要】 本论文研究介质体的时域散射和辐射问题。通过时域边界积分方程(BIE)和时间递推方法(MOT)求解这类问题,相对于时域有限差分法(FDTD),它在内存、计算时间、计算精度上都比较有优势,并且有新的快速算法发展空间。因此本文的研究都围绕这种方法展开。本文首先从时变电磁场的对称形式的Maxwell方程组出发,基于等效原理和边界条件,推导了针对解决在无界自由空间中存在的均匀介质散射问题的基于等效电流源和等效磁流源的各种时域电磁场积分方程,包括时域电场积分方程(TD-EFIE)、时域磁场积分方程(TD-MFIE)和时域耦合积分方程(包含时域PMCHW耦合积分方程和时域Müller耦合积分方程)三种形式。这是本论文重要的理论基础。论文研究了用时间递推方法求解时域Müller耦合积分方程。其过程涉及介质体的建模剖分和数据提取、算法实现过程中的一些数学推导、矩阵元素的求解、计算后参数的提取和处理等问题。论文推导了矩阵元素的求解计算公式,并用若干算例说明了所推导的公式的正确性,也说明了算法实现的正确性。在求解奇异积分时,提出了一种改进的求解MOT算法中奇异积分的方法。这种方法在原来对时间项参与计算的简化近似求解的基础上,提出了新的计算公式,提高了计算的精度。这种计算方法有利于分析电磁干扰等对精度敏感的问题。论文研究了用Laguerre多项式作为时间基函数的MOT算法。推导了利用Laguerre多项式的伽略金求解过程,并提供了算例。对其中一些重要的计算步骤提供了优化算法。算法实现过程中在时间域做了伽略金内积,因而在计算过程中消除了MOT算法以前存在的晚时不稳定性。采用Laguerre多项式作为时间基函数时,计算过程中除了通常的对空间基函数的伽略金内积,还有对时间基函数的伽略金内积,这种方法将时间变量从计算过程中完全分离了出来。对于源的伽略金积分,对比各种方法,最后选用了Gauss-Laguerre求积方法。采用MOT算法分析了终端渐变的圆柱形介质棒天线。给出了天线近区时域波形、天线方向图、以及天线结构参数变化时天线特性的变化。这比历来介质棒天线的近似分析要可靠的多。论文最后研究了目前正在发展的时域平面波算法(PWTD),它是MOT算法的加速算法。本文推导了算法中的关键方程;完整地阐述了PWTD算法的思想和实现的聚集、转移和发散的三个过程;阐述了二层PWTD-MOT算法的实现思想,结合分析介质问题的时域耦合积分方程——Müller方程,从理论上分析了用PWTD加速MOT算法的实现。更多还原

【Abstract】 The scattering and radiation of dielectric bodies in time domain are thoroughly studied in this paper. Compared with finite-difference time-domain (FDTD) method, when utilizing the boundary integral equation (BIE) and marching-on in-time (MOT) scheme to solve these questions, it has the advantage over computer memory, computer time and accuracy of results. Also, there is a new algorithm to enhance the speed of the marching-on in-time scheme. So the studies in this paper surround the MOT scheme.Several integral equations of electromagnetic field in time domain, which express the scattering of homogeneous dielectric bodies in free space, are formulated in this paper using the equivalence electric currents and magnetic currents according to the symmetry Maxwell equations in time domain, the equivalence principle and boundary condition. These integral equations include the electric field integral equation in time domain, the magnetic field integral equation in time domain and the coupled integral equations in time domain ( the PMCHW equations and the Müller equations). These are the important bases in theory of this paper.It’s researched how to resolve the Müller equations in time domain using the marching-on in-time scheme. The procedure includes the model building, data extraction, some mathematical formulations in realizing the algorithm, resolving the matrix elements, the parameter extraction and the post process after the simulation, etc. The formulations of the matrix elements are deduced in this paper. An improved method to resolving the singular integrals in the MOT scheme is presented, which gives the new formulations on the approximate resolving to the time parts in the normal method and can improve the accuracy of results. The new method is better to analyzing the sensitive questions on accuracy such as electromagnetic interference (EMI).The MOT scheme is also studied based on the Laguerre polynomials as the temporal basis function in this paper. The procedure on Galerkin testing is deduced when using the Laguerre polynomials, and some examples are given. Some optimize method in the computation are supplied. When realizing the algorithm, the Galerkin testing is done in time domain, so the late-time instabilities existing previously are eliminated in the procedure. Based on the Laguerre polynomials as the temporal basis function, there has not only the Galerkin testing to the spatial basis function but also to the temporal basis function, therefore the time variable is separated from the space variable completely in this method. For the integral of Galerkin testing on the source, the Gauss-Laguerre method is chose after the comparing of several integral methods.The dielectric rod antenna, which end changes gradually, is analyzed using the MOT scheme. The wave shapes in near space, radiation patterns and the antenna characteristic changed with the changeable structure parameter are given. The MOT method is more reliable than the approximate analytical method.The plane-wave time-domain (PWTD) algorithm is researched, which can enhance the speed of the MOT method. We deduce the key formulation in PWTD algorithm, expatiate the idea and the three steps in the procedure of PWTD algorithm, formulate the idea of two-level PWTD enhanced MOT method and analyze how to resolve Müller coupled integral equation in time domain using PWTD enhanced MOT method in theory.更多还原