研究生: |
許智詠 Hsu, Chih-Yung |
---|---|
論文名稱: |
界面演化基於水平集方法與耦合界面法的一個收斂性研究 Interface Evolution Based on Level Set Method and Coupling Interface Method: A Convergence Study |
指導教授: |
舒宇宸
Shu, Yu-Chen |
學位類別: |
碩士 Master |
系所名稱: |
理學院 - 數學系應用數學碩博士班 Department of Mathematics |
論文出版年: | 2014 |
畢業學年度: | 102 |
語文別: | 英文 |
論文頁數: | 54 |
中文關鍵詞: | 水平集方法 、耦合界面法 、隱式溶劑模型 、形狀導數 |
外文關鍵詞: | level set method, coupling interface method, implicit-solvent model, shape derivative |
相關次數: | 點閱:99 下載:2 |
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在這篇碩士論文中,我們假設分子曲面被隱式溶劑模型中的自由能決定,並且
我們要找出它的穩定態,換句話說,去模擬合理的分子曲面。在這個模型裡面,分子上的速度被橢圓界面問題的電位之梯度決定。水平集方法被用來追蹤並移動界面,而且橢圓界面問題被耦合界面法在卡式網格點上求解。在這個研究中,我們提出由變數變換導出的斜向座標系統在那些例外點上來精準的二階估計導數。結果顯示我們得到正解跟它的梯度的二階估計。數值測試上,配合斜向座標系統的耦合界面法做出正解與梯度的二階估計。我們綜合我們提出的方法,對於球形界面可以做出二階的收斂。最後我們藉著最小化隱式溶劑模型中的自由能來演示真實的複雜分子界面(1D63)移動。
In this thesis, we suppose the molecular surfaces determined by free-energy of the implicit solvent model, and nd its steady state, in other words, to simulate the rational molecular surfaces. In the model, the speed of interface depends on the gradient of the electrostatic potential and its gradient which are derived from the elliptic interface problem. The interface is tracked and moved by the level set method and the elliptic interface problem is solved by coupling interface method on Cartesian grid. In this study, we propose oblique coordinate systems by changing variables at the exceptional points in order to approximate the second order derivatives accurately. As a result, we get second-order approximation for the solution and its gradient. The numerical tests for the coupling interface method with oblique coordinate systems show the secondorder approximation for the solution and its gradients. For moving interface problems, we show the second-order convergence for a moving spherical interface by the proposed method. At nal, we demonstrate the molecular surface of real molecule (1D63) by for complex interfaces by minimizing the free energy based on the implicit solvent model.
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