以平行 Newton-Krylov-Schwarz 演算法解 Poisson-Boltzmann 方程式的有限元素解在膠體科學上的應用

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：68

、訪客IP：18.191.46.36

姓名

蔡尚融(Shang-Rong Cai) 查詢紙本館藏

畢業系所

數學系

論文名稱

以平行 Newton-Krylov-Schwarz 演算法解 Poisson-Boltzmann 方程式的有限元素解在膠體科學上的應用
(Parallel Newton-Krylov-Schwarz Algorithms for Finite Element Solution of Three Dimensional Poisson-Boltzmann Equations with Applications in Colloidal Science)

相關論文

★ 非線性塊狀高斯消去牛頓演算法在噴嘴流體的應用	★ 最小平方有限元素法求解對流擴散方程以及使用Bubble函數的改良
★ Bifurcation Analysis of Incompressible Sudden Expansion Flows Using Parallel Computing	★ Parallel Jacobi-Davidson Algorithms and Software Developments for Polynomial Eigenvalue Problems in Quantum Dot Simulation
★ An Inexact Newton Method for Drift-DiffusionModel in Semiconductor Device Simulations	★ Numerical Simulation of Three-dimensional Blood Flows in Arteries Using Domain Decomposition Based Scientific Software Packages in Parallel Computers
★ A Parallel Fully Coupled Implicit Domain Decomposition Method for the Stabilized Finite Element Solution of Three-dimensional Unsteady Incompressible Navier-Stokes Equations	★ A Study for Linear Stability Analysis of Incompressible Flows on Parallel Computers
★ Parallel Computation of Acoustic Eigenvalue Problems Using a Polynomial Jacobi-Davidson Method	★ Numerical Study of Algebraic Multigrid Methods for Solving Linear/Nonlinear Elliptic Problems on Sequential and Parallel Computers
★ A Parallel Multilevel Semi-implicit Scheme of Fluid Modeling for Numerical Low-Temperature Plasma Simulation	★ Performance Comparison of Two PETSc-based Eigensolvers for Quadratic PDE Problems
★ A Parallel Two-level Polynomial Jacobi-Davidson Algorithm for Large Sparse Dissipative Acoustic Eigenvalue Problems	★ A Full Space Lagrange-Newton-Krylov Algorithm for Minimum Time Trajectory Optimization
★ Parallel Two-level Patient-specific Numerical Simulation of Three-dimensional Rheological Blood Flows in Branching Arteries	★ A Markov Chain Multi-elimination Preconditioner for Elliptic PDE Problems on GPU

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

摘要(中)

運用平行的Newton-Krylov-Schwarz 演算法，求大型稀鬆非線性方程式組的解，此非線性系統是介由有限元素法，作離散化在三維的Poisson-Boltzmann 方程式；於膠質科學的應用中，做帶電膠質微粒在電解液中的三維數值模擬。Poisson-Boltzmann 方程式，為描述帶電膠體粒子於電解液中，其電位能分佈情形的方程式。並進行關於平行效能的研究，討論使用 LU 和 ILU 作為不同的preconditioner 的條件下作比較，其結果顯示，在使用32 顆處理器時，可達的58 % 效率。

摘要(英)

We employ the Newton-Krylov-Schwarz algorithms for solving a large sparse nonlinear system of equations arising from the finite element discretization of three dimensional Poisson-Boltzmann equation (PBE) in the application in colloidal science. The method do the numerical simulation in three dimensional space for the charged colloidal particles in a electrolyte. The PBE is used to describe the distribution of electrostatic potential in a colloidal system. We validate our code by computing the electrostatic forces of their interactions on the charged colloidal particles, and the results agree with other published data. we also conduct parallel performance
study on a parallel machine, and the result shows that our code reachs 58% efficiency up to 32 processors.

關鍵字(中)

★ 非精確牛頓法
★ overlapped Schwarz preconditioning
★ 有限元素法
★ 膠體科學
★ 三維模擬
★ Poisson-Boltzmann 方程式

關鍵字(英)

★ Poisson-Boltzmann equation
★ 3D simulation
★ colloidal science
★ inexact Newton
★ overlapped Schwarz preconditioning
★ finite element method
★ parallel processing

論文目次

List of Tables ii
List of Figures iii
Notations iv
1 Introduction 1
2 Poisson-Boltzmann model in a symmetric electrolyte 4
3 Finite element method for Poisson-Boltzmann equation 7
4 Newton-Krylov-Schwarz algorithm 9
4.1 Inexact Newton method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4.2 Krylov iterative methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4.3 Overlapping Schwarz preconditioner . . . . . . . . . . . . . . . . . . . . . . . . . 10
5 Software developments 12
5.1 Toolkits and workflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
5.2 Particles Interaction Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
6 Numerical Results 17
6.1 Simulation domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
6.2 Two Isolated Charged Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
6.3 Two Charged Particles in a Charged Cylindrical Pore . . . . . . . . . . . . . . . 21
6.4 Parameters study and parallel performance . . . . . . . . . . . . . . . . . . . . . 24
7 Conclusions 26
Bibliography 27

參考文獻

[1] A. E. Larsen and D. G. Grier, Like-charged attraction in metastable colloidal crystallites ,
Nature, 385 (1997), pp. 230-233.
[2] J. E. Sader, D. Y. C. Chan, Long-range electrostatic attractions between identically charged
particles in confined geometries: an unsolved problem , J. Colloid Interface Sci., 213 (1999),
pp. 268-269.
[3] J.E. Sader, D. Y. C. Chan, Long-range electrostatic attractions between identically charged
particles in confined geometries and the Poisson-Boltzmann theory , Langmuir 16, (2000),
pp. 324-331.
[4] D. J. Griffiths, Introduction to electrodynamics 3rd ed. , Prentice Hall, (1999).
[5] J. H. Masliyha, S. Bhattacharjee, Electrokinetic and Colloid Transport Phenomena John
Wiley & Sons. New Jersey, (2006)
[6] C. Johnson, Numerical Solution of Partial Differential Equations by the Finite Element
Method , Cambridge University Press, Cambriage, (1987)
[7] Thomas J. R. Hughes, The Finite Element Method: Linear Static and Dynamic Finite
Element Analysis , Dover Publication, (2000)
[8] P. E. Dyshlovenko, Adaptive numerical method for Poisson-Boltzmann equation and its
application , Comput. Phys. Comm., 147 (2002) pp. 335-338.
[9] P.E. Dyshlovenko, Adaptive mesh enrichment for the Poisson-Boltzmann equation , J.
Comput. Phys., 172 (2001) pp. 198-208.
[10] X.-C. Cai, W. D. Gropp, D. E. Keyes, R. G. Melvin, D. P. Young, Parallel Newton-Krylov-
Schwarz algorithms for the transonic full potential equation , SIAM J. Sci. Comput., 19
(1998) pp. 246-265.
[11] Y. Saad and M. H. Schultz, GMRES: A generalized minimal residual algorithm for solving
nonsymmetric linear systems , SIAM J. Sci. Comput., 7 (1986) pp. 865-869.
[12] B. Smith, P. Bjorstad, W. Gropp, Domain Decomposition: Parallel Multilevel Methods for
Elliptic Partial Differential Equations , Cambridge University Press, (1996)
[13] G. Karypis, METIS homepage, http://www.cs.umn.edu/ karypis/
[14] S. Balay, K. Buschelman, W. E. Gropp, D. Kaushik, M. Knepley, L. C. McInnes, B. F.
Smith, H. Zhang Portable, Extensible Toolkit for Scientific Computation (PETSc) home
page, http://www.mcs.anl.gov/petsc/ , (2008)
[15] Online CUBIT User’s Manual, http://cubit.sandia.gov/documentation.html , Sandia National
Laboratories, (2006).
[16] Abaqus file format, http://www.simulia.com/
[17] Visualization ToolKit (VTK) homepage, http://www.vtk.org/
[18] ParaView homepage, http://www.paraview.org/

指導教授

黃楓南(Feng-Nan Hwang)

審核日期

2008-7-16

推文