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  本文選題：并矢格林函數(shù)　切入點：非均勻采樣　出處：《南京理工大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：積分方程方法和并矢格林函數(shù)是分析平面分層電路電磁特性的重要研究內(nèi)容。本文主要以矩量法為背景,深入研究分層媒質(zhì)并矢格林函數(shù)的精確快速算法。研究內(nèi)容包括兩個部分:第一部分提出了一種新穎的非均勻采樣的矩陣束方法。這種方法的核心思想主要基于一種新的廣義矩陣束方法,通過分段采樣實現(xiàn)譜域并矢格林函數(shù)的平面波展開。具體來說,就是將采樣路徑進行分段,不同的分段路徑采用不同的采樣間隔,然后將路徑上所有的采樣點結(jié)合起來,也就形成本文提出的非均勻采樣的矩陣束方法。采用該矩陣束方法,可以有效的降低譜域格林函數(shù)的計算時間,也可以顯著減少平面波展開的計算時間。第二部分提出了一種可以減少復(fù)鏡像個數(shù)的矩陣束方法。該方法將壓縮感知理論與新穎的非均勻采樣的矩陣束方法相結(jié)合,利用譜域格林函數(shù)的平面波展開的稀疏性和正交匹配追蹤重構(gòu)算法快速實現(xiàn)格林函數(shù)的譜域近似。數(shù)值實驗表明該算法能夠在可控的數(shù)值精度內(nèi),可以有效減少復(fù)鏡像的個數(shù)。復(fù)鏡像個數(shù)的減少,可以用來進一步減少矩量法阻抗矩陣的填充時間,也能進一步提高平面分層電路的計算效率。
[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.
【學(xué)位授予單位】：南京理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TN011

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