時域有限差分法(FDTD)可以非常成功的模擬各種電磁波的現象,一般情形下時域有限差分法在處理電磁問題時皆以Cartesian正交座標系為主,但是在曲面結構的問題上,使用傳統的時域有限差分法是較困難求得精確解,這是因為在Yee演算法上是使用staircasing近似,為了改善此缺點,所以使用保形時域有限差分法(Conformal FDTD)去分析曲面結構,保形時域有限差分法使用規則時域有限差分法的磁場計算式,將其沿著曲線的電場值引入保形長度的修正項,所以保形時域有限差分法可以更適用於模擬曲面的結構。
動差法是將積分方程轉化為矩陣方程。動差法(Moment Method)的主要瓶頸在於造成滿矩陣及巨額的計算量。保形時域有限差分法直接從Maxwell方程式近似得到,可避免使用更多的數學公式。本論文使用保形時域有限差分法來模擬圓柱與球形體散射之雷達截面積(RCS)值,並將保形時域有限差分法與動差法(Moment Method)來做比較,從中可得知在層狀結構中保形時域有限差分法會比動差法更省記憶體容量與CPU時間。

FDTD can successfully simulate various kinds of phenomena of electromagnetic waves. Mainly, we use orthogonal Cartesian coordinate in general situations when we deal with the electromagnetic problems, but the curved geometry of the problem makes it difficult to obtain accurate results using conventional FDTD algorithm because of staircasing. To analyze curved geometry using Conformal FDTD can improve this shortcoming. The Conformal FDTD uses the regular FDTD equation for updating the magnetic field by using the electric field values along the distorted
contours, that are appropriately weighted with lengths of the contours. The Conformal FDTD technique is well suited for handling such curved geometries.
The moment method is used to convert the integral equation into a matrix equation.The major drawback of moment method (MoM) is the full matrix generation and huge computation time. The CFDTD directly approximates the differential operators in the Maxwell curl equation, and avoids using more mathematic formulae. This thesis uses Conformal FDTD to simulate RCS value of the cylinder and sphere and compare Conformal FDTD with Moment Method. We know that Conformal FDTD will save memory requirement and CPU time even more than Moment Method in layered structure.

目錄……………………………………………..Ⅰ
圖表目錄……………………………………………..IV
第一章 序論…………………………………………..1
1.1 研究動機與目的………………………………….1
1.2 論文大綱………………………………………….2
第二章 基本數值方法………………………………..4
2.1 FDTD數值法……………………………………...4
2.2 Conformal FDTD : 二維情況…………………….9
2.3 Conformal FDTD : 三維情況…………………...12
2.4 Conformal FDTD 的面積處理………………….13
2.5 Conformal FDTD 的介質處理………………….14
2.5.1 加權平均處理法………………………………14
2.5.2 線性的加權平均處理法………………………15
2.6 Conformal FDTD 的三維的公式……………….16
2.7 近場與遠場的轉換……………………………...18
2.8 雷達截面積……………………………………...23
第三章 動差法………………………………………25
3.1 介電體…………………………………………...25
3.2 導磁體…………………………………………...27
3.3 導磁與介電體………………………………...29
3.4 病態矩陣………………………………………...30
第四章 圓柱的散射…………………………………32
4.1 平面波入射……………………………………...32
4.1.1 正向入射平面波: TMz 極化…………………..32
4.1.2 正向入射平面波: TEz 極化…………………...32
4.2 解析解…………………………………………...33
4.2.1 圓柱散射: TMz 極化…………………………..33
4.2.2 遠場的散射場: TMz 極化……………………..34
4.2.2.1 金屬圓柱的遠場散射場: TMz 極化………….35
4.2.2.2 介質圓柱的遠場散射場: TMz 極化………….35
4.2.2.3 介質塗層金屬圓柱的遠場散射場: TMz 極化.35
4.2.3 圓柱散射: TEz 極化…………………………...36
4.2.4 遠場的散射場: TEz 極化……………………...37
4.2.4.1 金屬圓柱的遠場散射場: TEz 極化………..37
4.2.4.2 介質圓柱的遠場散射場: TEz 極化………..38
4.2.4.3 介質塗層金屬圓柱的遠場散射場: TEz 極化.38
4.3 數值結果………………………………………...38
4.3.1 完全導體圓柱…………………………………38
4.3.2 介質塗層導體圓柱……………………………39
4.3.3 以一個週期性8×8 圓柱狀矩形陣列塗層於介質
圓柱..…………………………………………………40
4.3.4 以兩層不同介質塗層於導體圓柱……………42
第五章 球的散射……………………………………44
5.1 平面波入射……………………………………...44
5.2 解析解…………………………………………...45
5.2.1 波轉換…………………………………………45
5.2.2 向量位結構……………………………………46
5.2.3 遠場的散射場…………………………………49
5.3 數值結果………………………………………...50
5.3.1 完全導體圓球…………………………………50
5.3.2 介質球…………………………………………51
5.3.3 介質塗層導體球………………………………53
5.3.4 以兩種不同介質塗層導體球…………………54
第六章 結論…………………………………………56
參考文獻……………………………………………58

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