應用於超大型陣列結構的電磁輻射與散射問題之數值分析

Numerical Analysis of Electromagnetic Radiation/Scattering Problems from Large Array Structures

何賢奎(Hsien-Kwei Ho)

指導教授 ： 陳興義

元智大學/工程學院/電機工程學系/碩士(2001年)

摘要

由於超級大型陣列結構在實際應用上有急速增加的趨勢，近年來研究人員花費了龐大的努力在發展快速且有效的分析技巧以處理超大型陣列問題。
數值分析最引人入勝之處在於它可靠的正確性，陣列結構愈大時其效率變得相當難以忍受。本篇論文探討兩種具有潛力來克服傳統數值技巧─動差法(Moment of Method , MoM)無效率的方法，並能有效的簡化運算複雜度和減少記憶體用量來擴展MoM的應用範圍。
第一種方法推廣前進後退法來處理任意元素形狀的陣列結構，並允許前進後退法處理更廣泛且複雜的陣列問題。前進後退法的好處包括疊代重覆的程序中具備快速收斂特性，並只有O(N)的運算複雜性與記憶體需求。
第二種方法採用離散富利葉轉換(DFT)來表示MoM的未知數，並整合到MoM的程序內。將陣列表面感應電流利用機何線的詮釋與分解，可找出重要的DFT項，這些重要的DFT項一般說來只佔了MoM未知數的一小部分。其優點不但使MoM?迉憚噯じぁ堣Q分顯著的減少而且基底函數間的互相耦合阻抗及輻射場型均可利用射線分解來快速運算，通常只需要少數的射線項就可以正確的預測數值。
最後，這篇論文也研究了銅箔微帶天線的陣列問題。

關鍵字

動差法 ； 前進後退法 ； 光譜加速法

並列摘要

Development of novel analysis techniques to treat large array problems has been great efforts of researchers in years due to the increasing trend to employ very large array structures in the practical applications. Numerical analysis is most attractive due to its reliable accuracy, but it suffers from inefficiency for large array structures. This thesis presents two approaches that potentially overcome the inefficiency of conventional numerical technique of Moment Method (MoM) in terms of computational complexity and memory storage.
The first approach generalizes the forward-backward method (F-BM) to treat array structure with arbitrary element shapes, and allows the F-BM to treate more general array problems The advantages of F-BM includes fast convergence in iterative computation, and O(N) memory requirement and computational complexity.
The second approach employs Discrete Fourier Transform (DFT) representation for MoM unknowns, and integrates with MoM procedure. Through a ray interpretation of the induced currents on array surface, significant DFT terms are identified, which in general is only a small portion of MoM unknowns. The advantages include significant reduction on the number of unknowns in MoM, and efficient computation on the mutual impedance and radiation patterns in terms of ray decompositions, where only a few rays can accurately predict the values.
Finally, an array problem of microstrip patch antennas is studied as well in this thesis.

並列關鍵字

moment method ； forward-backward method ； novel spectral acceleration

參考文獻

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[3]Chou, H.-T. and J. T. Johnson, “A novel acceleration algorithm for the computation of scattering from rough surfaces with the forward-backward method,” Radio Science, Vol. 33, Number 5, pg. 1277-1287, September-October 1998.

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[8]D. Torrungrueng, Joel T. Johnson and H.-T. Chou, Some Issues Related to the Novel Acceleration(NSA) Method for the Fast Computation of Radiation/Scattering from One-Dimensional Extremely Large-Scale Quasi-Planar Structures.,submitted to IEEE transactions on Geoscience and Remote Sensing.