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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳宜良(I-Liang Chern) | |
| dc.contributor.author | Yu-Chun Lin | en |
| dc.contributor.author | 林煜鈞 | zh_TW |
| dc.date.accessioned | 2021-06-12T18:34:18Z | - |
| dc.date.available | 2009-08-28 | |
| dc.date.copyright | 2007-08-28 | |
| dc.date.issued | 2007 | |
| dc.date.submitted | 2007-07-31 | |
| dc.identifier.citation | [ 1] A. Brandt, S.F McCormick, and J. W. Ruge, Algebraic multigrid (AMG) for sparse matrix equations, in Sparsity and Its Applications, D.J. Evans, ed., Cambridge University Press, Cambridge, 1984
[ 2] AN Tikhonov and AA Samarskii, Homogeneous difference schemes, USSR Comput. Math. And Math. Phys. 1 5–67 , 1962 . [ 3] I-Liang Chern, Jian-Guo Liu and Wei-Cheng Wang , Accurate Evaluation of Electrostatics for Macromolecules in Solution ,methods and applications of analysis,Vol.10, No.2, pp.309-308, June 2003, 2005. [ 4] I-Liang Chern and Yu-Chen Shu, A Coupling Interface Method for Elliptic Interface Problems , Journal of Computational Physics, 2007 . [ 5] M Holst and F Saied, Multigrid solution of the Poisson-Boltzmann equation, Journal of Computational Chemistry 14 (1993), 105–113. [ 6] P. Debye-H ckel , Physik. Z , 24 , pp185 ,1923. [ 7] Wolfgang. Hackbusch：Multi-Grid Methods and Applications, Springer-Verlag, 1985 . [ 8] Xu-Dong Liu and Thomas C. Sideris, Convergence of the ghost fluid method for elliptic equations with interfaces, Mathematics of Computation 72 (2003), no. 244, 1731–1746 . | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/28027 | - |
| dc.description.abstract | We present a first order accurate method for solving the partial differential equation, Poisson-Boltzmann Equation
where the coefficients is assumed to be discontinuous across an interface and the source term is allowed to be a delta function. In one-dimension, we take a finite differential approach. Near the discontinuities, the unknown is approximated by a piecewise function. We extend it in two dimensions by taking a dimension-by-dimension in discretization. The underlying grid is regular. We also present two efficient iterative solvers; the algebraic multigrid method to solve the resulting linear system, and the Newton’s method to solve the corresponding nonlinear equations. The main point of this article is to propose an initialization based on geometric multigrid method to reduce number of Newton’s iterations. We show by numerical experiments that total CPU time is nearly proportional to the number of unknowns. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-12T18:34:18Z (GMT). No. of bitstreams: 1 ntu-96-R93221035-1.pdf: 1913716 bytes, checksum: 3609820b86bfcf88ce846d1e8127a2f0 (MD5) Previous issue date: 2007 | en |
| dc.description.tableofcontents | Abstract . 1
I.Introduction………………………………………………2 I.1 About the Poisson-Boltzmann Equation……..…..2 I.2 Fast Algorithm for Solving Poisson-Boltzmann Equation…….….…................................4 II.Approach for solving PBE……………………….……5 II.1.Multigrid method …….……….……………………5 II.2 Algebraic Multigrid Method……………………….7 II.3 Newton method………….……………………………10 III.Multigrid Method for Solving the PBE with discontinuous coefficients……………………………12 III.1.Multigrid Method for Solving the Poisson Boltzmann Equation with Discontinuous Coefficients in One-Dimension…………............................….12 III.2.Multigrid Method for Solving the Poisson Boltzmann Equation with Discontinuous Coefficients in Two-Dimension……..………...........................17 III.3.Operator Review……………………….…………21 IV.Numerical Experiments………………………………22 IV.1 One-dimensional examples……….………..…..22 IV.2 Two-dimensional examples……………………….29 V.Conclusion……………………………………………..38 VI.References…………………………………………….39 | |
| dc.language.iso | en | |
| dc.subject | 波瓦松-波茲曼方程 | zh_TW |
| dc.subject | 多重網格法 | zh_TW |
| dc.subject | algebraic multigrid method | en |
| dc.subject | newton | en |
| dc.subject | Poission-Boltzmann equation | en |
| dc.title | 波瓦松-波茲曼方程之多重網格解法 | zh_TW |
| dc.title | Multigrid Method for Solving Poisson-Boltzmann Equation | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 95-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 周謀鴻(Mo-Hong Chou),薛克民(KEH-MING SHYUE) | |
| dc.subject.keyword | 多重網格法,波瓦松-波茲曼方程, | zh_TW |
| dc.subject.keyword | algebraic multigrid method,newton,Poission-Boltzmann equation, | en |
| dc.relation.page | 39 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2007-08-01 | |
| 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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