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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳宜良 | |
| dc.contributor.author | Ssu-Han Liu | en |
| dc.contributor.author | 劉思瀚 | zh_TW |
| dc.date.accessioned | 2021-05-16T16:22:49Z | - |
| dc.date.available | 2013-07-30 | |
| dc.date.available | 2021-05-16T16:22:49Z | - |
| dc.date.copyright | 2013-07-30 | |
| dc.date.issued | 2013 | |
| dc.date.submitted | 2013-07-22 | |
| dc.identifier.citation | [1] R. Almgren, Variational algorithms and pattern formation in dendritic solidification, Journal of Computational Physics 106 (1993) 337–354.
[2] N. Al-Rawahi, G. Tryggvason, Numerical simulation of dendritic solidification with convection: two-dimensional geometry, Journal of Computational Physics 180 (2002) 471–496. [3] R.P. Beyer, R.J. LeVeque, Analysis of a one-dimensional model for the immersed boundary method, SIAM Journal in Numerical Analysis Vol. 29, No. 2 (Apr., 1992) 332-364. [4] S. Chen, B. Merriman, S. Osher, P. Smereka, A simple level set method for solving Stefan problems, Journal of Computational Physics 135 (1997) 8–29. [5] I.L. Chern, Y.C. Shu, A coupling interface method for elliptic interface problems, Journal of Computational Physics 225 (2007) 2138–2174. [6] J. Glimm, M. J. Graham, J. Grove, X. L. Li, T.M. Smith, D. Tan, F. Tangerman, Q. Zhang, J, front tracking in two and three dimensions, Comp. Math. 7 (1998) 1-12. [7] F. Gibou, R.P. Fedkiw, L.T. Cheng, M. Kang, A second-order- accurate symmetric discretization of the poisson equation on irregular domains, Journal of Computational Physics 176 (2002) 205–227. [8] D. Juric, G. Tryggvason, A front-tracking method for dendritic solidification, Journal of Computational Physics 123 (1996) 127–148. [9] X.M. Jiao, H.Y. Zha, Consistent computation of first- and second-order differential quantities for surface meshes, ACM Solid and Physical Modeling Symposium (2008) 159-170. [10] X.L. Li, J. Glimm, X.M. Jiao, C. Peyser, Y.H. Zhao, Study of crystal growth and solute precipitation through front tracking method, Acta Mathematica Scientia 30B(2) (2010) 377–390. [11] Z.L. Li, Immersed interface methods for moving interface Problems, Numerical Algorithms 14 (1997) 269–293. [12] Z.L. Li, The immersed interface method – a numerical approach for partial differential equations with interfaces, Ph. D. Thesis, University of Washington (1994). [13] Z.L. Li, The immersed interface method: numerical solutions of pdes involving interfaces and irregular domains, SIAM Frontiers in Applied mathematics 33 (2006). [14] Z.L. Li, Fast and accurate numerical approaches for Stefan problems and crystal growth, Numerical Heat Transfer Part B (1999), in press. [15] R.J. LeVeque, Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems, SIAM (2007). | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/6192 | - |
| dc.description.abstract | 由陳宜良教授以及舒宇宸教授所提出的界面耦合法目的在笛卡兒網格下解橢圓介面問題，此方法已被證明是處理界面問題中非常有競爭力的方法。在這篇論文,我們把界面耦合法應用在不同問題上,例如:一維移動界面問題、二維固定界面的熱傳導問題以及二維的融化問題等,我們也提供數值例子來驗證方法的收斂性。 | zh_TW |
| dc.description.abstract | The coupling interface method (CIM) proposed by Chern and Shu aims for solving elliptic complex interface problems in arbitrary dimensions under Cartesian grid. It has been proven that the method is very competitive in dealing with interface problems. In this thesis, we apply the CIM to various problems, including one dimensional moving interface problems, two dimensional diffusion equations with fixed interface, two dimensional melting problems, etc. Numerical examples are presented to test the accuracy of the method in these applications. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-16T16:22:49Z (GMT). No. of bitstreams: 1 ntu-102-R98221001-1.pdf: 10916233 bytes, checksum: eb4dbcf896adb41da2ede6c5359f56d6 (MD5) Previous issue date: 2013 | en |
| dc.description.tableofcontents | 口試委員會審定書 #
誌謝 1 中文摘要 2 ABSTRACT 3 CONTENTS 4 LIST OF FIGURES 5 LIST OF TABLES 7 Chapter 1 Coupling interface method in one dimension 8 Chapter 2 Application to one dimensional moving interface problems 17 Chapter 3 Coupling interface method in two dimensions 48 Chapter 4 Application to two dimensional diffusion equations with fixed interface 60 Chapter 5 Application to two dimensional melting problems 97 Chapter 6 Conclusions 110 REFERENCE 111 | |
| dc.language.iso | en | |
| dc.subject | front tracking method | en |
| dc.subject | coupling interface method | en |
| dc.subject | moving interface problems | en |
| dc.subject | ADI method | en |
| dc.subject | Crank-Nicolson scheme | en |
| dc.subject | melting problems | en |
| dc.title | 界面耦合法在移動界面問題上的應用 | zh_TW |
| dc.title | Solving Some Moving Interface Problems by the Coupling Interface Method | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 101-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 薛克民,舒宇宸 | |
| dc.subject.keyword | 界面耦合法,移動界面問題,交替方向隱式法,克蘭克－尼科爾森方法,融化問題,界面追蹤法, | zh_TW |
| dc.subject.keyword | coupling interface method,moving interface problems,ADI method,Crank-Nicolson scheme,melting problems,front tracking method, | en |
| dc.relation.page | 112 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2013-07-22 | |
| 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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| 檔案 | 大小 | 格式 | |
|---|---|---|---|
| ntu-102-1.pdf | 10.66 MB | Adobe PDF | 檢視/開啟 |
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