在本論文中，將提出一個結合FDTD與CNDG-FDTD演算法之混合式次網格法。此方法在粗網格區域使用傳統的FDTD演算法，而在細網格區域則引入CNDG-FDTD演算法。由於CNDG方法為無條件穩定，在細網格區域可使用較大的粗網格區域之時間步階尺寸，加速細網格區域的計算時間。此外，因為粗細網格時間步階一致，在粗、細網格邊界可以省略時間上的內插近似，大幅度簡化粗、細網格邊界處理的複雜度。
　　CNDG-FDTD演算法雖然可跳脫CFL穩定條件的限制，節省大量的計算時間得到與傳統FDTD演算法相當近似準確的模擬結果，但是必須比FDTD演算法額外付出最少20%以上的記憶體使用量。本人將提出一個能增加記憶體效率之改良式CNDG-FDTD演算法。此方法不僅保有跳脫CFL穩定條件的特性，節省大量的計算時間外，而且能有效的減縮記憶體使用量。

　In this thesis, a novel subgridding scheme is proposed based on the hybridization of the FDTD and CNDG-FDTD algorithms. The FDTD method is applied to the coarse grid region, while the CNDG-FDTD method is used in the fine grid region. Because of the unconditional stability of the CNDG scheme, the temporal step size can be set equal to that in the coarse grid region to speed up the computation in the fine grid region. Furthermore, the temporal interpolation at the fine and coarse grids interface is no longer necessary and thus the complexity of spatial interpolation is largely reduced.
　As the CNDG-FDTD method is free from the CFL condition restraint, it saves a large amount of CPU time. Numerical results agree very well with that of the FDTD scheme. But it requires a larger amount of computer memory, at least 20% more than the FDTD method. A modified version of the CNDG-FDTD scheme with increased memory efficiency is also presented. It has not only eliminated the restraint of the CFL condition, but also achieved a more efficient saving of CPU time and computer memory requirements.

目錄................................................................................................ I
圖表目錄.........................................................................................III
第一章 序論...................................................................................1
1.1 概述..........................................................................................1
1.2 論文大綱..................................................................................2
第二章 CNDG-FDTD 演算法之分析與模擬..............................3
2.1 顯式差分方法..........................................................................3
2.2 Crank-Nicolson 演算法............................................................5
2.3 Douglas-Gunn 分解法..............................................................7
2.4 CNDG-FDTD 演算法..............................................................10
2.4.1 CN-FDTD 演算法之推導.....................................................10
2.4.2 使用DG 分解法於CN-FDTD 演算法中….......................12
2.5 CNDG-FDTD 數值色散分析...................................................18
2.6 平行板波導結構之模擬...........................................................22
第三章 CNDG-FDTD 演算法與次網格演算法之結合...............25
3.1 次網格法...................................................................................25
3.2 混合式次網格法.......................................................................26
3.2.1 粗網格和細網格區域之電磁場計算....................................26
3.2.2 粗、細網格邊界上的處理.....................................................29
3.3 數值模擬結果............................................................................32
3.3.1 單向翼片波導結構.................................................................32
3.3.2 介電圓柱散射問題.................................................................36
第四章 低記憶體需求之改良式CNDG-FDTD 演算法...............43
4.1 CNDG-FDTD 演算法與散度關係式之結合............................43
4.1.1 在無電荷區域之散度關係式..................................................43
4.1.2 散度關係式引入CNDG-FDTD 演算法................................44
4.2 導體結構之處理.........................................................................49
4.3 激發源區域之處理.....................................................................52
4.4 數值模擬結果..............................................................................53
4.4.1 平行板波導結構之模擬...........................................................53
4.4.2 含兩塊PEC 薄板之波導結構.................................................57
第五章 結論.......................................................................................59
參考文獻..............................................................................................60

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