【作者】 徐利明；

【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， 2005， 博士

【摘要】 平面分层介质中的电磁辐射与散射数值分析在雷达目标与环境一体化建模、地球物理探测、遥测遥感、微带天线或电路仿真和信号完整性分析等诸多领域具有强烈的工程应用需求。本文深入研究了求解平面分层介质中三维目标电磁散射的积分方程方法及其关键技术。 首先讨论了适用于分层介质中任意位置、任意跨嵌导体目标电磁散射计算的混合位积分方程方法。构建了适当的积分方程和格林函数来避免目标跨界面给数值计算带来的复杂性。鉴于格林函数在分层介质问题中的重要性,本文独立推导了任意分层介质背景格林函数的谱域表达式。使用这些公式,很容易将均匀空间电磁散射方法扩展到分层介质情况。这些工作为格林函数快速计算方法的实现以及积分方程的矩量法(MoM)高效求解打下了基础。 本文还着重研究了分层介质尤其是半空间背景中格林函数索末菲积分的各种快速计算方法,包括直接积分方法、基于最陡下降路径的快速积分方法和离散复镜像方法等。这些方法的实现为分层介质中的复杂三维目标的电磁散射建模提供了前提条件。本文还提出了一种在角谱平面利用最陡下降路径法进行快速计算的方法。另外,为了克服近界面、跨界面目标问题中格林函数计算效率低下的问题,本文引入了一种高效的格林函数计算方法—空间列表与插值算法。 在格林函数高效计算方法的基础上,本文利用基于RWG基函数的MoM法来求解分层介质混合位积分方程,对其中的重要问题作了讨论(包括入射场计算、奇异性积分处理计算等),并提出了几种有效的方法来加快阻抗矩阵填充过程。利用这些方法实现了半空间背景下的三维导体目标电磁散射的建模分析。也将其用于微带贴片天线散射问题。数值结果表明,这些方法具有很高的精度和计算效率。 还利用体积分方程来实现对半空间背景中的介质体电磁散射问题的求解。采用两种不同的方法推导了适用于体积分方程的半空间电场型并矢格林函数。提出了一种针对格林函数的快速算法来克服常规格林函数求解方法计算效率低下的问题,实现了埋地介质目标电磁散射的快速求解。 为了提高积分方程方法求解复杂电磁问题的效率,本文还对一种针对矩量法的矩阵降阶技术—特征基函数方法(CBFM)—作了研究。讨论了其中的关键问题,提出了一种生成CBF全局矩阵的新方法,用以降低阻抗矩阵生成过程中的计更多还原

【Abstract】 Numerical analysis methods for electromagnetic radiation and scattering by objects in planar multilayered media have urgent need in many applications such as integrated modeling of radar targets and environments, geophysics exploration, remote sensing, microstip antenna and circuit simulation and signal integrality analysis and so on. This dissertation studies the integral equation method and its key techniques for three-dimensional scattering problems in multilayered media.In the first, the multilayered media mixed potential integral equation (MM-MPIE) method is discussed in a general sense. The proper integral equation and corresponding Green’s functions (GFs) are formulated for objects arbitrarily located in multilayered media background and for overcoming the complexity resulted from the case of object penetrating the interfaces. Due to the importance of Green’s functions for multilayered media problems, the dissertation has independently derived out the spectral representations of the GFs, by which the efficient algorithms for free space problems can be easily extended to multilayered media case. The derivations lay a good foundation for the efficient evaluation of GFs and the fast solving of scattering problems by the method of moments (MoM).As key techniques for solving the multilayered media problems by integral equation method, the methods to evaluate the Sommerfeld integrals for GFs are investigated in details, including the direct integration method, the fast integration method along the steepest decent path (SDP), the discrete complex images method (DCIM) and so on. These techniques guarantee the realization and fast solving of the electromagnetic scattering by complex objects in multilayered media. A novel and efficient method for GFs evaluation is proposed, which is based on integrating the Sommerfeld integrals along SDP on angular spectrum plane. In addition, another efficient approach, namely the spatial tabulation and interpolation, for GFs evaluation are introduced into MoM solving.Based on the efficient evaluation methods of GFs, the MoM procedure based on the RWG basis functions are used to solve the MM-MPIE and the pivotal techniques are investigated, including calculation of incident field, treatment of singular integral,更多还原