利用有限差分時域法求解電磁波問題一般是將整個解
析空間分割成網狀，且同方向的每個網格邊緣長度均維持
相等。當散射物體具有微細結構，必須使用較細均勻網格
以達到可接受的精確度，不過需要耗用大量記憶體和執行
時間。針對此點，替代方案是採用非均勻網格法，對於具
有結構簡單之處以較大網格計算，較小網格套用於結構複
雜之處，但此法僅限用於片段切割區域，每個區域至少有
兩端通達解析空間截斷面，無法做全向性局部細切網格。
補強的作法是使用次單胞法，特點在於當物體邊緣具有曲
面形狀，可針對局部區域將矩形網格變形成合乎該處輪廓
所需之網格形狀。次網格法有別於上述兩種網格類型，特
別另闢一小節討論優缺點。在具非均勻網格解析空間截斷
處採用異方性完美匹配層衰減朝外的電磁波，足以取代
Mur一階吸收邊界與Berenger的完美匹配層成為更優良的
吸收介質，本論文也一併比較特性差異。

The finite-difference time-domain (FDTD) method
has been widely and effectively used for analysis
in many kinds of electromagnetic problems.
Generally, the computational space can be divided
into many lattices with rectangular; and
the length on each of these meshs is equivalent
in unitary aspect. In some of those problems, a
greatly improved accuracy of the solution can be
obtained if a finer discretization is used in
specific regions of the computational space.
There are limitations of the present form of
uniform FDTD. It must increase the computational
cost (memory and CPU time). Concerning the
impression, we are trying to find more efficient
ways of utilizing nonuniform grids. Coarser mesh
for uncomplicated structure and finer mesh for
complicated structure in nonuniform grids.
However, this way can use in part of cutting area
only. There are two edges connects the truncation
of computational space. A similar scheme has been
used with nonuniform FDTD method by a
modification to the mesh scheme. The subcell
method is a very general approach, capable of
analyzing arbitrarily-shaped structures. In local
area the mesh change from rectangular to
irregular. Subgridding method is dissimilar to
the both methods. Furthermore, the anisotropic
PML to decrease the electromagnetic wave from
nonuniform mesh of the computational space. It
have replaced Mur’s first-order absorbing
boundary conditions and Berenger’s PML for
improving computationally efficient. Finally,
compare them with the anisotropic PML in the
essay.

誌謝 Ⅰ
論文摘要 Ⅱ
目錄 Ⅲ
圖表目錄 Ⅴ

第一章 序論 1
1.1 簡介 1
1.2 論文大綱 2

第二章 非均勻網格之有限差分時域法 4
2.1 理論 4
2.2 評估非均勻Yee網格的誤差 7
2.3 注意事項 9

第三章 吸收邊界條件 10
3.1 Mur一階吸收邊界條件 10
3.2 Berenger的PML吸收介質 11
3.2.1 定義PML介質 12
3.2.2 在PML介質內平面波的傳播 13
3.2.3 最佳化參數 14
3.3 異方性完美匹配層 16
3.3.1 異方性介質 16
3.3.2 異方性介質之原理 17
3.3.3 異方性完美匹配層有限差分方程式 25
3.4 數值特性比較 29

第四章 入射波源 33
4.1 邊緣電壓激發方式 33
A. 微帶線饋入電壓源 33
B. 同軸式饋入線電壓源 34
4.2 穿透源 37

第五章 次單胞及次網格 39
5.1 次單胞法 39
5.2 次網格法 43

第六章 應用 51
6.1 同軸線饋入微帶天線 51
6.2 具有交叉式細狹縫結構金屬薄膜的矩形波導管 56
6.3 具有屏蔽盒的微波積體電路 61
6.3.1 簡介 61
6.3.2 數值技術 62
6.3.3 同軸式饋入線的模型 63
6.3.4 非均勻網格技術 65
6.3.5 實體規格 66
6.3.6 計算S21 70
A. 不同吸收邊界 70
B. 圓形表面輪廓描述 74
6.4 次網格法的應用-----微帶線饋入矩形天線 81

第七章 結論 83

參考文獻 85
附錄A 非均勻網格FDTD差分方程式 88
附錄B Mur一階吸收邊界差分方程式 89
附錄C Berenger的完美匹配層非均勻網格差分方程式 90
附錄D異方性完美匹配層非均勻網格差分方程式 93

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