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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 陳宜良(I-Liang Chern) | |
dc.contributor.author | Xian-Wen Dong | en |
dc.contributor.author | 董憲文 | zh_TW |
dc.date.accessioned | 2021-06-08T07:27:35Z | - |
dc.date.copyright | 2008-07-14 | |
dc.date.issued | 2008 | |
dc.date.submitted | 2008-07-09 | |
dc.identifier.citation | [1] P. Debye-HÄuckel , Physik.Z. 24, 185 (1923).
[2] Michael J. Holst, The Poisson-Boltzmann equation: Analysis and multilevel numerical solution, Applied Mathematics and CRPC, California Institute of Technology. (1994). [3] M. Holst and F. Saied, Multi-Grid solution of the Poisson-Boltzmann Equation J. Comput. Chem., 14 (1993), pp. 105-113. [4] I-Liang Chern, Jian-Guo Liu andWei-ChengWang, Accurate Evaluation of Electrostatics for Macromolecules in Solution, (2005). [5] I-Liang Chern and Yu-Chen Shu, A Coupling Interface Method for Elliptic Interface Problems, (2007). [6] M. Brezina, R. Falgout, S. MacLachlan, T. Manteu®el, S. McCormick, and J.Ruge, Adaptive Algebraic Multigrid, SIAM J. Sci. Comput. 27 (2005), pp. 1261-1286. [7] A. J. Cleary , R, D Falgout, V. E. HENSON, and J. E. Jones, Coarse-grid selection for parallel algebraic multigrid, in Proc. of the Fifth International Symposium on Solving Irregularly Structured Problems in Parallel, vol. 1457 of Lecture Notes in Computer Science, New York, (1998). [8] Weihua Geng, Sining Yu, and Guowei Wei , Treatment of charge singularities in implicit solvent models , J. Chem. Phys 127,(2007) [9] M. F. Sanner, A. J. Olson, and J. C. Spehner, REDUCED SURFACE: an Efficient Way to Compute Molecular Surfaces, Biopolymers 38, 305, (1996). [10] M. Holst, Multilevel methods for the Poisson-Boltzmann equation, Ph.D. thesis, Numerical Computing Group, University of Illinois at Urbana-Champaign,(1994). [11] Lee, B. and Richards, F.M. J.Mol.Biol. 55, (1971),pp. 379-400. [12] R. E. Bank and D. J. Rose, Analysis of a multilevel iterative method for nonlinear finite element equations, Math. Comp., 39 (1982), pp. 453-465. | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/26826 | - |
dc.description.abstract | 在此篇論文中,我們利用數值方法研究了在三維空間中的波瓦松-波茲曼方程式,並以此來計算分子在溶液中的靜電勢能。在研究過程中有三點困難之處:第一,分子在溶液中形成的邊界,內外的電介質係數為不連續且差異懸殊。第二,分子的電荷會產生出位能的奇異性質。第三,在溶液中所得到的靜電勢能反應是非線性的。
於是我們採取了以下幾個步驟一一來解決這些困難的地方:首先,對第一點而言,我們採取藕合界面方法來處理橢圓界面問題;其次,針對第二點,自由空間中的電位能可以用來將靜電勢能中的奇異部份取出;最後,關於第三點非線性的部份,我們使用阻尼牛頓法以達到二階收斂。 在數值的觀察上,我們利用水分子做探測器以得到其收斂速度以及計算結果,並測試了恐水性的蛋白質(代碼:1crn)和親水性的蛋白質(代碼:1DNG)。顯示此方法確實對於分子周圍的電位能與電場均可以達到二階的準確度。 | zh_TW |
dc.description.abstract | In this paper, we study the Poisson-Boltzmann equation (PBE) in three dimensions numerically for computing the electrostatic potential for molecules in solvent. There are three numerical difficulties:(i) discontinuity of the dielectric coefficients large contrast across the boundaries of the macromolecules and solvent, (ii) potential singularity arisen from point charges of the macromolecules, (iii) nonlinearities of the solvent response. We take the following steps to resolve these difficulties. For (i), we adopt the coupling interface
method, which can deal with elliptic interface problems with large jumps of elliptic coefficients across interfaces. For (ii), the point charge potential in free space is used to remove the singularity of the potential. For (iii), we implement the damped Newton's method to achieve quadratic convergence. Numerical investigation for convergence rate and computation solution are performed for test probe and for a hydrophobic protein (PDB ID:1crn) and a hydrophilic protein (PDB ID:1DNG). It is shown the method is second-order accurate even for both the electric potential and the electric field around the molecular boundary. | en |
dc.description.provenance | Made available in DSpace on 2021-06-08T07:27:35Z (GMT). No. of bitstreams: 1 ntu-97-R95221025-1.pdf: 3025270 bytes, checksum: 658b469cb57259444df2793358336dd7 (MD5) Previous issue date: 2008 | en |
dc.description.tableofcontents | 1. Introduction…………………………………………1
1.1 Poisson-Boltzmann equation ………………………1 1.2 Construction of the molecule surface …………3 2. Coupling interface method………………………6 2.1 CIM1 in one dimension……………………………7 2.2 CIM2 in one dimension ……………………………8 2.3 CIM in d-dimension ……………………………10 3. Treatment of nonlinear PBE ……………………12 3.1 Newton's method …………………………………12 3.2 Treatment of singularities ………………………13 3.3 Nonlinear iteration for the correction potential ……14 3.4 Summary of the algorithm ………………………15 4. Multigrid methods for solving PBE with discontinuous coefficients……………………16 4.1 Multigrid methods in general…………………………16 4.2 The Algebraic Multigrid method………………………16 4.3 3-dimension discretization…………………………18 5. Numerical experiments…………………………20 6. Conclusion…………………………………………28 References…………………………………………………29 | |
dc.language.iso | en | |
dc.title | 分子在溶液中靜電勢能之演算法 | zh_TW |
dc.title | Fast Algorithm for Solving Electrostatic Potential of Macromolecules in Solvent | en |
dc.type | Thesis | |
dc.date.schoolyear | 96-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 張建成,林榮信 | |
dc.subject.keyword | 靜電勢能,波瓦松-波茲曼方程式,藕合界面方法,阻尼牛頓法,多重網格法, | zh_TW |
dc.subject.keyword | Poisson-Boltzmann equation,electrostatic potential,coupling interface method,Multigrid method, | en |
dc.relation.page | 29 | |
dc.rights.note | 未授權 | |
dc.date.accepted | 2008-07-10 | |
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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