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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/22348完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 薛克民 | |
| dc.contributor.author | Chia-Pao Su | en |
| dc.contributor.author | 蘇家寶 | zh_TW |
| dc.date.accessioned | 2021-06-08T04:15:58Z | - |
| dc.date.copyright | 2010-08-10 | |
| dc.date.issued | 2010 | |
| dc.date.submitted | 2010-08-04 | |
| dc.identifier.citation | [1] B. Engquist, H., Holst and O. Runborg, Multi-scale methods for wave propaga-
tion in heterogeneous media, preprint. [2] W. E and B. Engquist, The heterogeneous multi-scale methods, Commun. Math. Sci., 87-133, 2003. [3] A. Abdulle and W. E, Finite di erence heterogeneous multi-scale method for homogenization problems, J. Comput. Phys., 191(1): 18-39, 2003. [4] B. Engquist and Y. H. Tsai, Heterogeneous multiscale methods for sti ordinary di erential equations, Math Comp., 74(252): 1707-1742, 2005. [5] R. J. Leveque, Finite volume methods for hyperbolic problems, Cambridge Uni- versity Press, 2002. [6] W. E and B. Engquist, The heterogeneous multiscale method for homogenization problems, SIAM J. Multiscale Modeling and Simulations, submitted. Available at <http://www.math.princeton.edu/multiscale/> . [7] X. Yue and W. E, Numerical methods for multiscale transport equations and application to two-phase porous media ow, J. Comput. Phys., 210: 656-675, 2005. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/22348 | - |
| dc.description.abstract | 本文中，我們將發展雙曲問題的多尺度方法。我們的方法建立在 HMM 的架構上。HMM 的架構是在 [Commun. Math. Sci. 1 (1) 87] 所提出的。該架構包含兩部分 ：微尺度上的問題(原方程度)和宏觀問題。藉由解宏觀問題，我們所需的計算時間將比直接解原問題，要少得多。除了方法的描述外，我們也呈現一些數值的結果，以及誤差的分析。 | zh_TW |
| dc.description.abstract | In this thesis, we design a numerical method to solve multiscale hyperbolic problems. This method is based on the framework HMM, introduced in [Commun. Math. Sci. 1 (1) 87]. The HMM framework contains two main components: microscopic problem (orginal equation) and macroscopic problem. By solving the macroscopic probem, our cost is much lower than solving the original equation directly. We describe the details of the HMM method and present some numerical results. Finally, we analyze the errors of the HMM method. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-08T04:15:58Z (GMT). No. of bitstreams: 1 ntu-99-R97221005-1.pdf: 710593 bytes, checksum: 016827521e1b470764ed115f950be19e (MD5) Previous issue date: 2010 | en |
| dc.description.tableofcontents | Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
Abstract (in chinese) . . . . . . . . . . . . . . . . . . . . . . . . ii 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Classical numerical methods . . . . . . . . . . . . . . . . . . . . . 3 2.1 The Lax-Friedrich method . . . . . . . . . . . . . . . . . . . . . . 4 2.1.1 Consistency . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1.2 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.3 Modify equation . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Godunov method . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.1 Riemann problem . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.2 Wave propagation form . . . . . . . . . . . . . . . . . . . . . . 9 2.2.3 Modied equation . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3 High resolution method . . . . . . . . . . . . . . . . . . . . . . 10 2.4 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . 11 3 Heterogeneous multiscale method . . . . . . . . . . . . . . . . . . . 15 iv3.1 HMM method . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.1.1 Macro problem . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.1.2 Micro problem. . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.1.3 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.2.1 Linear cases . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.2.2 Nonlinear case . . . . . . . . . . . . . . . . . . . . . . . . . 21 4 Theory of Convergence . . . . . . . . . . . . . . . . . . . . . . . . 22 4.1 Consistency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.2 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.3 Analysis of errors . . . . . . . . . . . . . . . . . . . . . . . . 29 5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 | |
| dc.language.iso | en | |
| dc.subject | 守恆律 | zh_TW |
| dc.subject | 多尺度 | zh_TW |
| dc.subject | HMM | zh_TW |
| dc.subject | 數值方法 | zh_TW |
| dc.subject | 雙曲問題 | zh_TW |
| dc.subject | HMM | en |
| dc.subject | conservation laws. | en |
| dc.subject | hyperbolic problem | en |
| dc.subject | numerical method | en |
| dc.subject | multiscale | en |
| dc.title | 雙曲問題的多尺度方法 | zh_TW |
| dc.title | Multiscale method for hyperbolic problems | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 98-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 牛仰堯,郭志禹 | |
| dc.subject.keyword | 多尺度,HMM,數值方法,雙曲問題,守恆律, | zh_TW |
| dc.subject.keyword | multiscale,HMM,numerical method,hyperbolic problem,conservation laws., | en |
| dc.relation.page | 36 | |
| dc.rights.note | 未授權 | |
| dc.date.accepted | 2010-08-04 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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