臺灣博碩士論文加值系統

本論文提出一個將數值動差法一般化的技巧。對任意形狀的三維複雜物體表面以三角平板來近似，並利用積分方程計算其散射場，此積分方程可轉變為矩陣方程式。方程式中關於不同點之相互作用矩陣不會因為散射體幾何狀況與邊界條件不同而改變。經過這樣的整理，可以歸納出計算不同電磁散射問題的固定程序。另一方面，在求解矩陣方程時，是以共軛梯度法來得到電磁流係數值，於是我們利用修改過後的多階層快速多極計算法來加速共軛梯度法中矩陣-向量相乘的速度，可將原來矩陣-向量相乘的計算量由 縮減為 ，其中N為未知數個數。因此在PC工作環境上，能處理較大尺寸的三維複雜物體。

In this thesis, we outline a generalized form of the method of moment technique. Integral equation formulations are used to solve for the scattering field of a three-dimensional complex object of arbitrary shape modeled by triangularly faceted surfaces and then are transformed into matrix equations, in which the matrices involving two-point interaction are independent of the geometry and boundary conditions of scatterers. This allows a unified procedure to be implemented for different scattering problems. In addition, the conjugate gradient method (CGM) is used to solve the matrix equation for the unknown expansion coefficients of the surface electric and magnetic current. We use the multilevel fast multipole algorithm (MLFMA) to speed up the matrix-vector multiplication in the CGM. The MLFMA reduces the complexity of a matrix-vector multiplication from to , where N is the number of unknowns. This algorithm requires less memory, and hence, large-sized complex objects and more practical problems can be solved on a PC.

目錄
摘要………………………………………………………………………i
目錄……………………………………………………………………iii
第一章 緒論……………………………………………………………1
1.1 研究動機與目的………………………………………………1
1.2 簡介……………………………………………………………2
1.3 文獻回顧……………………………………………………2
1.4 章節概要……………………………………………………3
第二章 數值理論分析與公式…………………………………………4
2.1三角平板近似物體……………………………………………4
2.2數值方法………………………………………………………4
2.2.1積分方程………………………………………………4
2.2.2數值動差法的一般化…………………………………7
2.2.2.1 、 、 矩陣………………………………8
2.2.2.2基底函數的一般化……………………………10
2.2.2.3如何決定基底函數……………………………14
2.2.2.4運算子…………………………………………16
2.2.3 數值積分………………………………………………17
2.2.3.1 奇異點的處理……………………………19
2.3共軛梯度法(CG)……………………………………………21
2.4 快速多極計算法(FMM)……………………………………22
2.4.1 FMM演算法…………………………………………23
2.5 多階層快速多極記算法(MLFMA)…………………………26
2.6 多極點展開式的極點數與方向取樣 ………………………29
2.6.1 極點個數的決定………………………………………29
2.6.2 方向取樣個數的決定…………………………………30
2.7 遠場雷達截面積 ……………………………………………30
第三章 數值程式實作…………………………………………………44
3.1 程式架構與類別 ……………………………………………45
3.1.1 基本類別………………………………………………45
3.1.2 應用類別………………………………………………46
3.2 程式流程 ……………………………………………………47
3.2.1 前續資料處理…………………………………………48
3.2.2 核心數值計算程式……………………………………49
3.2.3 後續處理………………………………………………50
第四章 計算結果與討論………………………………………………60
4.1 導體球………………………………………………………60
4.2 塗層導體球…………………………………………………60
4.3圓球體……………………………………………………61
4.4 橢球體………………………………………………………62
4.5 多球體………………………………………………………62
第五章 結論……………………………………………………………74
附錄A 邊界條件與輸入檔格式………………………………………75
參考文獻 ………………………………………………………………77

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