臺灣博碩士論文加值系統

過去有許多學者運用各種計算方法來分析在橫向磁場、橫向電場平面波或高斯波束入射作用下，平面嵌有半圓形凹槽或半橢圓形凹槽的散射問題，而較少看到凹槽形狀為淺橢圓形的研究。所以，本論文主要是求解淺橢圓形凹槽的Helmholtz散射問題，其中求解的凹槽形狀，有單一半橢圓形凹槽、單一淺橢圓形凹槽、多個半橢圓形凹槽及多個淺橢圓形凹槽。本文根據領域媒親法，引入輔助邊界將整個計算領域分割成數個子領域，以分離變數法求得滿足控制方程式及部分邊界條件的各子領域波場表示式，藉由輔助邊界上的連續條件及邊界條件，利用選點法來建構聯立方程式求得各子領域之未定係數。本文的數值計算結果與參考文獻分別做一比較，比對結果皆吻合。根據本文數值計算結果可知：在多個凹槽時，相鄰凹槽的間距愈小，則對散射影響愈顯著，凹槽的間距愈大，則對散射影響越微小。

The problems scattering of TM, TE plane waves or Gaussian beam by a semi-circular or semi-elliptical channel were analyzed by lots of scholars and solved by applying different numerical methods in past. However, the related investigations on the scattering problems of the shallow elliptical channels are rare. Hence, the main purpose of this thesis is to solve the Helmholtz scattering problems of shallow elliptical channels, including of single semi-elliptical channel, single shallow elliptical channel, multiple semi-elliptical, and shallow elliptical channels. Based on the region-matching technique, the auxiliary boundaries are introduced to divide the entire computational region into several sub-regions. The expression of the wave field in each sub-region satisfied the governing equation and partial boundary condition is derived through separation of variables. By employing the continuity conditions at the auxiliary boundaries, the boundary conditions, and constructing simultaneous equations by means of the collocation method, the unknown coefficients can be determined. The computational solutions in present are matched well with the solutions from reference. According to the computational results in case that the waves impinge upon multiple channels, the distance between neighborhoods of channels is the narrower, the effect of mutual interaction on the scattered field is the more obvious.

中文摘要 i
英文摘要 ii
目錄 iii
表目錄 vi
圖目錄 vii
第一章 緒論 1
1－1 前言 1
1－2 文獻回顧 1
1－3 研究動機、目的及方法 2
1－4 研究內容與架構 3
第二章 理論分析 4
2－1 單一半橢圓形凹槽的Helmholtz散射 4
2－1－1 TM平面波入射 4
2－1－2 TE平面波入射 7
2－1－3 TM高斯波束入射 10
2－1－4 TE高斯波束入射 14
2－2 多個半橢圓形凹槽的Helmholtz散射 18
2－2－1 TM平面波入射 18
2－2－2 TE平面波入射 22
2－2－3 TM高斯波束入射 26
2－2－4 TE高斯波束入射 31

2－3 單一淺橢圓形凹槽的Helmholtz散射 36
2－3－1 TM平面波入射 36
2－3－2 TE平面波入射 40
2－3－3 TM高斯波束入射 44
2－3－4 TE高斯波束入射 48
2－4 多個淺橢圓形凹槽的Helmholtz散射 52
2－4－1 TM平面波入射 52
2－4－2 TE平面波入射 57
2－4－3 TM高斯波束入射 63
2－4－4 TE高斯波束入射 68
2－5 散射遠場的計算 74
第三章 數值計算例與討論 82
3－1 單一半橢圓型凹槽的計算結果 82
3－1－1 TM平面波入射 82
3－1－2 TE平面波入射 88
3－1－3 TM高斯波束入射 92
3－1－4 TE高斯波束入射 97
3－2 多個半橢圓形凹槽的計算結果 101
3－2－1 兩個半橢圓形凹槽 101
3－2－1－1 TM平面波入射 101
3－2－1－2 TE平面波入射 111
3－2－1－3 TM高斯波束入射 118
3－2－1－4 TE高斯波束入射 125
3－2－2 三個半橢圓形凹槽 132
3－2－2－1 TM平面波入射 132
3－2－2－2 TE平面波入射 140
3－2－2－3 TM高斯波束入射 147
3－2－2－4 TE高斯波束入射 154
3－3 單一淺橢圓形凹槽的計算結果 161
3－3－1 TM平面波入射 161
3－3－2 TE平面波入射 167
3－3－3 TM高斯波束入射 171
3－3－4 TE高斯波束入射 176
3－4 多個淺橢圓形凹槽的計算結果 180
3－4－1 兩個淺橢圓形凹槽 180
3－4－1－1 TM平面波入射 180
3－4－1－2 TE平面波入射 188
3－4－1－3 TM高斯波束入射 193
3－4－1－4 TE高斯波束入射 200
3－4－2 三個淺橢圓形凹槽 206
3－4－2－1 TM平面波入射 206
3－4－2－2 TE平面波入射 213
3－4－2－3 TM高斯波束入射 219
3－4－2－4 TE高斯波束入射 225
第四章 結論 231
參考文獻 233

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