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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 許文翰(Wen-Hann Sheu) | |
dc.contributor.author | Yu-Chieh Wang | en |
dc.contributor.author | 王豫潔 | zh_TW |
dc.date.accessioned | 2021-05-15T17:50:31Z | - |
dc.date.available | 2016-08-22 | |
dc.date.available | 2021-05-15T17:50:31Z | - |
dc.date.copyright | 2014-08-22 | |
dc.date.issued | 2014 | |
dc.date.submitted | 2014-08-19 | |
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dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/4946 | - |
dc.description.abstract | 本論文是在交錯網格上發展一三維時域有限差分法(FDTD),以求解馬克斯威爾方程。本文的方法是在時域內,在滿足電場和磁場的零散度條件(亦即高斯定律)的架構下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方面使用具辛結構(Symplectic)之二級二階之Runge-Kutta方法,在經過長時間模擬後,解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,以期求得在色散關係上相當準確的解。
為了達到最佳數值色散性質,本文所提出的數值方法能在時間上和空間上保有相當好的收斂,且能有效地減少實解相速度與數值相速度的誤差,而得以顯著地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。本研究證實了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。本文亦在三種典型具代表性之色散介質Debye、Lornetz、Drude模型電磁波的模擬,透過計算,證明了文中所發展之數值方法於馬克斯威爾方程組在與頻率獨立和頻率相依上的有效性及在長時間模擬下的準確度。 | zh_TW |
dc.description.abstract | An explicit finite-difference scheme for solving the three-dimensional Maxwell's equations in staggered grids is presented in time domain. The aim of this thesis 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 proposed 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. To achieve the goal of getting the best dispersive characteristics, this centered scheme minimizes the difference between the exact and numerical phase velocities with good rates of convergence are demonstrated for the problem. The significant dispersion and anisotropy errors manifested normally in finite difference time domain methods are therefore much reduced. 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. The emphasis of this study is also placed on the accurate modelling of EM waves in the dispersive media of the Debye, Lorentz and Drude types. Through the computational exercises, the proposed dual-preserving solver is computationally demonstrated to be efficient for use to predict the long-term accurate Maxwell's solutions for the media of frequency independent and dependent types. | en |
dc.description.provenance | Made available in DSpace on 2021-05-15T17:50:31Z (GMT). No. of bitstreams: 1 ntu-103-R01525048-1.pdf: 40965369 bytes, checksum: 8e67a2b5619cfb191b45472cadfc58bb (MD5) Previous issue date: 2014 | en |
dc.description.tableofcontents | 誌謝 -- i
摘要 -- ii Abstract -- iii 符號說明 -- v 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 研究目標 -- 4 1.5 論文大綱 -- 4 第二章 電磁波方程 - 馬克斯威爾方程式 -- 6 2.1 法拉第/安培/高斯方程組及其推導 -- 6 2.2 法拉第/安培方程組之數學特性 -- 7 2.3 色散介質 -- 9 2.4 卷積完美匹配吸收層 -- 10 第三章 數值方法 -- 20 3.1 FDTD之交錯網格系統 -- 20 3.2 具辛結構之PRK時間離散 -- 22 3.3 空間離散方程之推導 -- 24 第四章 具色散關係保持性離散方法之分析 -- 29 4.1 三維空間離散分析 -- 29 4.1.1 積分域之影響 -- 31 4.1.2 不同Cr數之影響 -- 32 4.1.3 角度變化下之係數分佈 -- 32 4.2 數值穩定性之分析 -- 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 -- 53 5.1 程式之驗證 -- 54 5.2 色散介質中CPML吸收性的驗證 -- 56 5.3 實際題目之求解 -- 57 5.3.1 全場/散設場 -- 58 5.3.2 等位函數法 -- 58 5.3.3 實際題目模擬之結果 -- 59 第六章 結論 -- 93 6.1 研究成果與討論 -- 93 6.2 未來工作與展望 -- 94 參考文獻 -- 79 | |
dc.language.iso | zh-TW | |
dc.title | 在三維色散介質中模擬電磁波的傳遞行為 | zh_TW |
dc.title | Prediction of electromagnetic wave propagation in three-dimensional dispersive media | en |
dc.type | Thesis | |
dc.date.schoolyear | 102-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 李佳翰(Jia-Han Li),王偉仲(Wei-Chung Wang),張宏鈞(Hung-Chun Chang),楊亦松(Yi-Song Yang) | |
dc.subject.keyword | 馬克斯威爾方程,交錯網格,色散關係,實解相速度和數值相速度,Debye介質,Lorentz介質,Drude介質, | zh_TW |
dc.subject.keyword | staggered grids,dispersion relation equation,exact and numerical phase velocities,Debye,Lorentz,Drude, | en |
dc.relation.page | 98 | |
dc.rights.note | 同意授權(全球公開) | |
dc.date.accepted | 2014-08-20 | |
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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