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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 許文翰(Wen-Hann Sheu) | |
| dc.contributor.author | Yu-Wei Chang | en |
| dc.contributor.author | 張育瑋 | zh_TW |
| dc.date.accessioned | 2021-06-16T10:17:16Z | - |
| dc.date.available | 2015-08-26 | |
| dc.date.copyright | 2013-08-26 | |
| dc.date.issued | 2013 | |
| dc.date.submitted | 2013-08-17 | |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/60401 | - |
| dc.description.abstract | 本論文是在非交錯網格上提出三維時域有限差分法(FDTD)求解馬克斯威爾方程。
本文的方法是在時域內透過電場和磁場的零散度條件(亦即高斯定律)以求解法拉第定律和安培定律。 所提出的數值方法於時間離散上使用具辛結構(Symplectic)二級二階之Runge-Kutta方法，在經過長時間模擬後仍得以保持馬克思威爾方程的能量守恆性質； 另透過法拉第及安培旋度方程空間微分項的推導，得到在色散關係上相當準確的解。 本文所提出的數值方法在空間上具有四階準確，且能有效減少實解相速度與數值相速度的誤差。 本文所提出的數值方法亦顯著降低了因時域有限差分所造成的明顯地數值色散誤差以及各向異性誤差。 除了本文所做的基礎分析外，亦證實了本文所提出的數值方法在具辛結構與色散關係上具有良好的保持性，尤其在針對經長時間馬克斯威爾方程的數值模擬後，其效果尤為顯著。 | zh_TW |
| dc.description.abstract | An explicit finite-difference scheme for
solving the three-dimensional Maxwell's equations in non-staggered grids is presented in time domain. Our aim is to solve the Faraday's and Ampere's equations in time domain within the discrete zero-divergence context for the electric and magnetic fields (or Gauss's law). The local conservation laws in Maxwell's equations are also numerically preserved all the time using the explicit second-order accurate symplectic partitioned Runge-Kutta temporal scheme. Following the method of lines, the spatial derivative terms in the semi-discretized Faraday's and Ampere's equations are then properly discretized to get a dispersively very accurate solution. This proposed fourth-order accurate space centered scheme minimizes the difference between the exact and numerical phase velocities. The significant dispersion and anisotropy errors manifested normally in finite difference time domain methods are therefore much reduced. In addition to the fundamental study performed on the proposed scheme, the dual-preserving (symplecticity and dispersion relation equation) wave solver is numerically demonstrated to be efficient for use to get in particular long-term accurate Maxwell's solutions. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T10:17:16Z (GMT). No. of bitstreams: 1 ntu-102-R00525072-1.pdf: 43296126 bytes, checksum: e046cf82ffa99e0fa551955763ab15d9 (MD5) Previous issue date: 2013 | en |
| dc.description.tableofcontents | 誌謝 --- i
摘要 --- iii 符號說明 -- iv 第一章 緒論 -- 1 1.1 前言 -- 1 1.2 文獻回顧 -- 2 1.3 研究動機 -- 3 1.4 研究木喵 -- 3 1.5 論文大綱 -- 4 第二章 電磁波方程 - 馬克斯威爾方程式 --5 2.1 法拉第/安培/高斯方程組及其推導 --5 2.2 法拉第/安培方程組之數學特性 --6 2.3 軸向完全匹配吸收層方程之推導 --8 第三章 數值方法 --19 3.1 FDTD之非交錯網格系統 --19 3.2 具辛結構之PRK時間離散 --21 3.3 空間離散方程之推導 --23 第四章 具色散關係保持性離散方程之數值分析 --28 4.1 三維空間離散分析 --28 4.1.1 積分域之影響 --30 4.1.2 不同Cr數之影響 --31 4.1.3 角度變化下之係數分佈 --31 4.2 數值穩定性分析 --33 4.3 各向異性與數值色散之分析 --35 4.3.1 數值色散關係式與實解色散關係式之一致性(consistency) --35 4.3.2 數值色散關係分析(Numerical dispersion analysis) --36 4.3.3 數值相速度與群速度之分析(Numerical phase velocity and group velocity analysis) --36 4.4 數值分析之結果與討論 --38 第五章 數值模擬之結果 --52 5.1 程式之驗證 --53 5.2 實際題目之求解 --55 5.2.1 波源設置 --55 5.2.2 全場/散射場 --56 5.2.3 等位函數法 --57 5.2.4 實際題目模擬枝節果 --58 第六章 結論 --83 6.1 研究成果與討論 --83 6.2 未來工作與展望 --84 參考文獻 --79 | |
| dc.language.iso | zh-TW | |
| dc.subject | 馬克斯威爾方程 | zh_TW |
| dc.subject | 非交錯網格 | zh_TW |
| dc.subject | 零散度 | zh_TW |
| dc.subject | 四階準確 | zh_TW |
| dc.subject | 色散關係 | zh_TW |
| dc.subject | 實解相速度和數值相速度 | zh_TW |
| dc.subject | dispersion relation equation | en |
| dc.subject | exact and numerical phase velocities. | en |
| dc.subject | non-staggered grids | en |
| dc.subject | zero-divergence | en |
| dc.subject | fourth-order | en |
| dc.title | 在非交錯網格下發展一具最佳數值色散關係式之三維時域有限差分方法以求解馬克斯威爾方程 | zh_TW |
| dc.title | Development of a dispersively optimized 3D FDTD solver for solving Maxwell's equations in non-staggered grids | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 101-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 薛文証(Wen-Jeng Hsueh),林長壽(Chang-Shou Lin),黃聰明(Tsung-Min Hwang),王偉仲(Weichung Wang) | |
| dc.subject.keyword | 馬克斯威爾方程,非交錯網格,零散度,四階準確,色散關係,實解相速度和數值相速度, | zh_TW |
| dc.subject.keyword | non-staggered grids,zero-divergence,fourth-order,dispersion relation equation,exact and numerical phase velocities., | en |
| dc.relation.page | 88 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2013-08-17 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 工程科學及海洋工程學研究所 | zh_TW |
| 顯示於系所單位： | 工程科學及海洋工程學系 | |
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