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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 薛克民(Keh-Ming Shyue) | |
| dc.contributor.author | Yu-An Chen | en |
| dc.contributor.author | 陳昱安 | zh_TW |
| dc.date.accessioned | 2021-06-15T12:26:47Z | - |
| dc.date.available | 2016-08-24 | |
| dc.date.copyright | 2016-08-24 | |
| dc.date.issued | 2016 | |
| dc.date.submitted | 2016-08-10 | |
| dc.identifier.citation | (1) R. J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations, Steady State and Time Dependent Problems, SIAM, 2007
(2) R. J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, 2002 (3) R. J. LeVeque, Numerical Methods for Conservation Laws, Brikhauser-Verlag, Basel, 1990 (4) W. Cai, S. Deng, An upwinding embedded boundary method for Maxwell's equations in media with material interfaces: 2D case, Journal of Computational Physics 190 (2003) 159-183 (5) C. Xue, S. Deng, An upwinding boundary condition capturing method for Maxwell's equations in media with material interfaces, Journal of Computational Physics 225 (2007) 342-362 (6) C. Zhang, R. J. LeVeque, The immersed interface method for acoustic wave equations with discontinuous coefficients, Wave Motion 25(3) (1997) 237-263 (7) S. Deng, On the immersed interface method for solving time-domain Maxwell’s equations in materials with curved dielectric interfaces, Computer Physics Communications 179(2008) 791-800 (8) S. Zhao, G. W. Wei, High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces, Journal of Computational Physics 200(2004) 60-103 (9) T. Aslam, A partial differential equation approach to multidimensional extrapolation, Journal of Computational Physics 193(2003) 349-355 (10) B. Lombard, J. Piraux, Numerical treatment of two-dimensional interfaces for acoustic and elastic waves, Journal of Computational Physics 195(2004), 90-116 (11) K. Umashankar, A. Taflove, Computational Electrodynamics, Artech Hourse, Boston, 1993 (12) A. Taflove, S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, third ed, Artech Hourse, Boston, 2005 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/49958 | - |
| dc.description.abstract | 此篇論文主要是在探討線性雙曲線型偏微分方程式系統界面問題的數值方法。在界面上，通常需要滿足邊界條件，而系統的參數在此也是不連續的。這樣的問題在物理模擬中很常見。譬如說，電磁波從一個介質傳遞至另一個介質中。雙曲線型偏微分方程的標準數值方法通常只試用於係數為連續函數的情況，而在界面問題上，這些方法會失效。因此，在界面週邊必須要做特殊處理。我們介紹兩種以卡式坐標系網格為基準的方法 - 'Ghost Fluid'方法及 'Immersed Interface'方法 - 來處理不連續的邊界條件。 | zh_TW |
| dc.description.abstract | In this thesis, we investigate the numerical techniques for solving interface problem of linear hyperbolic system of equations with piecewise constant coefficients and jump conditions across the interface. Such problem arises naturally in practical physics, for example, electromagnetic waves propagating from one material to the other. Standard numerical techniques for solving hyperbolic systems fail near the interface, and special treatments must be offered. Two Cartesian-based methods, 'ghost fluid method' and 'immersed interface method', are introduced to catch the jump discontinuity. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T12:26:47Z (GMT). No. of bitstreams: 1 ntu-105-R03246009-1.pdf: 1154971 bytes, checksum: 313d157bf44fa9ea034aeb299bfecbe0 (MD5) Previous issue date: 2016 | en |
| dc.description.tableofcontents | 致謝 i
中⽂摘要 ii Abstract iii Contents iv List of Figures vii List of Tables xv 1 Introduction 1 1.1 Model problems 1 1.2 Literature review 13 1.3 Thesis goal 15 2 Hyperbolic Problem without Interface 16 2.1 One-dimensional numerical method 17 2.1.1 Scheme of choice 19 2.1.2 Lax-wendroff method 19 2.1.3 CFL condition 20 2.2 Two-dimensional numerical method 22 2.2.1 Lax-wendroff method 23 2.3 Numerical results 24 2.3.1 Scalar case 25 2.3.2 System case 28 3 One-Dimensional Hyperbolic Problem with Interfaces 31 3.1 Ghost fluid method 34 3.2 Immersed interface method 39 3.3 Numerical results 43 3.3.1 Scalar case with continuous jump condition 43 3.3.2 Scalar case with discontinuous jump condition 46 3.3.3 System case with continuous jump condition 49 3.3.4 System case with discontinuous jump condition 52 4 Two-Dimensional Hyperbolic Problem with Interfaces 56 4.1 Ghost fluid method 59 4.2 Immersed interface method 62 4.3 Numerical results 69 4.3.1 Quasi one-dimensional case 69 4.3.2 Two-dimensional case with rectangular-shaped interface 75 5 Conclusion 83 Appendices 85 A Smoothing method 85 B Interface jump conditions for two-dimensional Maxwell’s equations in immersed interface method 86 References 91 | |
| dc.language.iso | en | |
| dc.subject | immersed interface 方法 | zh_TW |
| dc.subject | 線性雙曲線型偏微分方程式 | zh_TW |
| dc.subject | 界面問題 | zh_TW |
| dc.subject | ghost fluid 方法 | zh_TW |
| dc.subject | Immersed Interface Method | en |
| dc.subject | Linear hyperbolic system | en |
| dc.subject | Interface problem | en |
| dc.subject | Ghost Fluid Method | en |
| dc.title | 雙曲線型線性偏微分方程式界面問題的數值方法 | zh_TW |
| dc.title | Numerical Schemes for Linear Hyperbolic Problems with Interfaces | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 104-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 郭志禹(Chih-Yu Kuo),牛仰堯 | |
| dc.subject.keyword | 線性雙曲線型偏微分方程式,界面問題,ghost fluid 方法,immersed interface 方法, | zh_TW |
| dc.subject.keyword | Linear hyperbolic system,Interface problem,Ghost Fluid Method,Immersed Interface Method, | en |
| dc.relation.page | 92 | |
| dc.identifier.doi | 10.6342/NTU201602171 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2016-08-10 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 應用數學科學研究所 | zh_TW |
| 顯示於系所單位： | 應用數學科學研究所 | |
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