非参数估计在分层媒质并矢格林函数快速计算中的应用

发布时间：2018-03-04 21:33

本文选题：并矢格林函数　切入点：非均匀采样　出处：《南京理工大学》2017年硕士论文　论文类型：学位论文

【摘要】：积分方程方法和并矢格林函数是分析平面分层电路电磁特性的重要研究内容。本文主要以矩量法为背景,深入研究分层媒质并矢格林函数的精确快速算法。研究内容包括两个部分:第一部分提出了一种新颖的非均匀采样的矩阵束方法。这种方法的核心思想主要基于一种新的广义矩阵束方法,通过分段采样实现谱域并矢格林函数的平面波展开。具体来说,就是将采样路径进行分段,不同的分段路径采用不同的采样间隔,然后将路径上所有的采样点结合起来,也就形成本文提出的非均匀采样的矩阵束方法。采用该矩阵束方法,可以有效的降低谱域格林函数的计算时间,也可以显著减少平面波展开的计算时间。第二部分提出了一种可以减少复镜像个数的矩阵束方法。该方法将压缩感知理论与新颖的非均匀采样的矩阵束方法相结合,利用谱域格林函数的平面波展开的稀疏性和正交匹配追踪重构算法快速实现格林函数的谱域近似。数值实验表明该算法能够在可控的数值精度内,可以有效减少复镜像的个数。复镜像个数的减少,可以用来进一步减少矩量法阻抗矩阵的填充时间,也能进一步提高平面分层电路的计算效率。
[Abstract]:The integral equation method and dyadic Green's function are important research contents in analyzing the electromagnetic characteristics of planar layered circuits. In this paper, the exact and fast algorithm of dyadic Green's function for layered media is studied. The research includes two parts: in the first part, a novel nonuniform sampling matrix beam method is proposed. The core idea of this method is mainly based on. A New Generalized Matrix Beam method, The plane wave expansion of dyadic Green's function in spectral domain is realized by piecewise sampling. Specifically, the sampling path is segmented, the different segmented paths are divided into different sampling intervals, and all the sampling points on the path are combined together. The nonuniform sampling matrix beam method proposed in this paper is also formed. By using the matrix beam method, the computing time of Green's function in spectral domain can be reduced effectively. In the second part, a matrix beam method which can reduce the number of complex images is proposed, which combines the compressed sensing theory with the novel nonuniform sampling matrix beam method. The spectral domain approximation of Green's function is realized quickly by using the sparse of plane wave expansion of the Green's function in spectral domain and the reconstruction algorithm of orthogonal matching tracing. The numerical experiments show that the algorithm can be used in controllable numerical accuracy. The reduction of the number of complex images can be used to further reduce the filling time of the impedance matrix of the method of moments and to further improve the computational efficiency of planar layered circuits.
【学位授予单位】：南京理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN011

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