設計師設計產品時，除了要盡量避免訊號失真外，有時也會刻意將輸入的訊號以非常態方式傳播。例如軍用飛機可以在機身表面塗上特殊材料，能令電磁輻射碰觸至機身時造成不正常的反射及散射，使得雷達欲偵測其動向時無法獲得預想中的資訊。這種特殊塗料就是俗稱的隱形材料，而各向異性介質便是其中一種原料選擇。
FDTD是常用分析電磁波的時域演算法，但由於常用的Yee網格在各向異性介質的分析上有些劣勢，而在相同問題上能有較好表現的Lebedev網格因此慢慢地被重視。不過Lebedev除了善於處理各向異性介質外，必須承擔很多數值上的缺點，例如較大的數值色散和複雜地波源激發等。
因此，本文提出了一種結合以上提及兩種網格的方法，以達到在模擬各向異性介質問題時能夠同時擁有Yee網格的高效率與Lebedev的準確率，進而能更有效且準確地處理各向異性介質問題。

When designers design products, they will avoid the distortion of signal as possible. However, they sometimes may make input signal propagate in unusual form. For instance, military airplanes can be coated with special material on the body surface, and it cannot cause normal reflection and scattering when radiations touch on the body surface. Therefore, radars will not receive expected information to predict their movements. This special material is commonly known as invisible material, and anisotropic material is one of the choice of materials.
FDTD is widely used in analysis of electromagnetic wave. Since there are a few disadvantages on the analysis of anisotropic material with Yee’s grid, Lebedev grid becomes famous because of its better results on the same issue. However, except the advantages, Lebedev grid may face a lot of trouble, such as bigger numerical distortion and complicated excitation.
As a result, this thesis will provide a method which combines two kinds of grid that have been mentioned above to have both of their advantages and achieve higher accuracy and efficiency. Therefore, the issue of anisotropic material can be solved more efficiently and accurately.

目錄
論文審定書+i
誌謝+ii
中文摘要+iii
英文摘要+iv
目錄+v
圖表目錄+vii
第一章 緒論+1
1.1研究目的與方法+1
1.2 論文大綱+3
第二章 FDTD演算法+4
2.1 FDTD介紹+4
2.1.1 FDTD公式推導+4
2.2 數值色散與穩定準則+8
2.3 吸收邊界+8
2.4 FDTD模擬+10
2.5 FDTD方法處理各向異性介質+11
第三章 Lebedev網格+16
3.1 選用Lebedev網格的原因+16
3.2 Lebedev網格介紹+17
3.3 Lebedev網格內波源的分散式激發+18
第四章 Yee網格與Lebedev網格的連結+23
4.1 兩種網格的優劣比較+23
4.2 結合使用的基本配置+23
4.3 結合使用的互相耦合+24
4.3.1 Yee網格中的電磁場透過磁場耦合至Lebedev網格+26
4.3.2 Lebedev網格中的電磁場透過電場耦合至Yee網格+27
4.4 運用與步驟+28
第五章 結合後的應用與模擬+29
5.1 平面波激發+29
5.2 方法穩定性測試+31
5.3 準確率與共振頻率+35
5.4 介質層結構模擬+37

 
圖表目錄
圖2-1 FDTD-Yee網格中最小單位網格電磁場配置圖+7
圖2-2 電磁場一維空間與時間運算示意圖+7
圖2-3 吸收邊界示意圖+9
圖2-4 APML空間示意圖+10
圖3-1 六角網格式意圖+16
圖3-2 Lebedev網格式意圖+17
圖3-3 Lebedev網格內磁場環積分示意圖+19
圖3-4 Lebedev網格內波源的分散式激發+20
圖3-5 Lebedev網格內波源的單點激發結果+21
圖3-6 Lebedev網格內波源的分散式激發結果+21
圖4-1 兩種網格結合運用配置圖+24
圖4-2 當k=2n.時 在連結面x=x0上的場量分布圖+25
圖4-3 當k=2n+1.時 在連結面x=x0上的場量分布圖+25
圖5-1 平面波激發是意圖+29
圖5-2 在時間步階n=110時Yee網格區域全波波形+30
圖5-3 在時間步階n=110時Lebedev網格區域全波波形+30
圖5-4 在時間步階n=110時全波波型+31
圖5-5 單純Yee網格之共振腔模型結構示意圖+32
圖5-6 兩種網格結合使用之共振腔模型示意圖+33
圖5-7 連結後模擬共振腔在Yee網格區域的時域波形+34
圖5-8 連結後模擬共振腔在Lebedev網格區域的時域波形+35
圖5-9 共振腔頻率響應圖+36
表5-1 共振腔的共振模態+37
圖5-10介質模擬模型示意圖+38
表5-2 介質m1之各項參數+38
圖5-11YZ方向激發之高斯波時域波形+39
圖5-12平面波入射介質m1的Y分量入射波與穿透波+41
圖5-13平面波入射介質m1的Z分量入射波與穿透波+41

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