Parallel Multilevel Smoothed Aggregation Schwarz Preconditioned Newton-Krylov Algorithms for Poisson-Boltzmann Problem

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蕭鈞懌(Jun-Yi Xiao) 查詢紙本館藏

畢業系所

數學系

論文名稱

(Parallel Multilevel Smoothed Aggregation Schwarz Preconditioned Newton-Krylov Algorithms for Poisson-Boltzmann Problem)

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摘要(中)

運用多重網格法(Multigrid method)延伸出的演算法, 作為平行 Newton-Krylov-Schwarz 演算法的預處理, 降低迭代次數與計算時間, 加速求得大型鬆弛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, 並進一步探討對稱與非對稱電解質溶液對於電場與電位能的影響. Poisson-Boltzmann 方程式, 為描述帶電膠體粒子於電解液中, 其電位能分佈狀況的方程式. 並進行關於平行效能的研究, 使用多層次法 (Multilevel) 優化迭代次數及時間, 和比較多層次法使用不同聚集方法的效益。

摘要(英)

The use of multi-grid (Multigrid method) extending algorithm as preconditioner parallel Newton-Krylov-Schwarz algorithms to reduce the number of iterations and calculation time determined to accelerate the solution of nonlinear equations large relaxation. The group, this nonlinear system is mediated by the finite element method, as in the
three-dimensional discrete Poisson-Boltzmann equation; in glial scientific applications, do the three-dimensional numerical simulation of charged colloidal particles in the electrolyte, and to further explore symmetric and asymmetric electrolyte solution for electric field and the potential energy of the impact. Poisson-Boltzmann equation for the description of charged colloidal particles in the electrolyte, the potential energy distribution formula. And conduct research on parallel performance, optimization iterations, and time, and compare the effectiveness of different aggregation methods.

關鍵字(中)

★ 平行計算
★ 多重網格法
★ 數值分析

關鍵字(英)

★ Parallel
★ Multilevel
★ Newton-Krylov
★ Poisson-Boltzmann

論文目次

Tables......................................... vi
Figures ......................................... ix
Symbols ........................................ x
1 Introduction . .................................. 1
2 Mathematical model . .............................. 3
3 Solution Algorithm . ............................... 6
3.1 Inexact Newton-Krylov........................... 6
3.2 Calculation of Jacobian matrices...................... 7
3.3 A parallel one-level overlapping Schwarz preconditioner......... 8
3.4 Two-level methods with a parallel coarse preconditioner......... 9
3.5 Multilevel Method: A Parallel Smoothed Aggregation Multigrid Method. 11
3.5.1 Uncoupled Parallel Aggregation Scheme............. 13
3.5.2 MIS-based Parallel Aggregation Scheme............. 14
3.5.3 METIS-based Parallel Aggregation Scheme............ 15
4 Numerical Results . ............................... 16
4.1 Simulation domains............................. 16
4.2 Two Isolated Charged Particles....................... 18
4.3 Parameters study and parallel performance................ 22
5 Conclusions . ................................... 27
5.1 The derivation of Poisson-Boltzmann model in a Asymmetric electrolyte. 30
5.2 Particles Interaction Force......................... 34
5.3 The computation of the non-dimensionalized electrostatic force acting on the charged particles............................ 36
5.4 Richardson’s Extrapolation......................... 40

參考文獻

[1] Mark Adams and John W Demmel. A parallel maximal independent set algorithm.
University of California, Berkeley,Computer Science Division,1998.
[2] Ted D Blacker,William J Bohnhoff, and Tony L Edwards.Cubit mesh generation environment. volume 1 : Users manual. Technical report, Sandia National Labs.,
Albuquerque,NM(United States),1994.
[3] Shang-Rong Cai.Parallelnewton-krylov-schwarz algorithms for finite elementsolution of three dimensional poisson-boltzmann equations with applications in colloidal
science. 中央大學數學系學位論文, pages 1–28,2008.
[4] XIAO-CHUANCAI.Parallel fully coupled schwarz preconditioners for saddle point problems. Electronic Transactions on Numerical Analysis, 22:146–162,2006.
[5] Yun-Long Shao Jong-Shinn Wu Feng-Nan Hwang, Shang-Rong Cai.Parallel newton-krylov-schwarz algorithms for the three-dimensional poisson-boltzmann
equation in numerical simulation of colloidal particle interactions.2010.
[6] Michael W Gee, Christopher M Siefert, Jonathan J Hu, Ray S Tuminaro, and Marzio G Sala. Ml 5.0 smoothed aggregation user’sguide. Technical report,Technical Report SAND2006-2649, Sandia National Laboratories,2006.
[7] Amy Henderson,Jim Ahrens,Charles Law,et al. The ParaView Guide. Kitware Clifton Park,NY,2004.
[8] Mark T Jones and Paul E Plassmann. A parallel graph coloring heuristic. SIAM Journal on Scientific Computing, 14(3):654–669,1993.
[9] George Karypis and Vipin Kumar. A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM Journal on scientific Computing, 20(1):359–392, 1998.

[10] George Karypis, Kirk Schloegel, and Vipin Kumar. Parmetis. Parallel graph partitioning and sparse matrix ordering library. Version, 2, 2003.

[11] Jan Mandel. Hybrid domain decomposition. In Domain Decomposition Methods in Science and Engineering: The Sixth International Conference on Domain Decomposition, June 15-19, 1992, Como, Italy, volume 157, page 103. American Mathematical Soc., 1994.

[12] YVAN NOTAY. An aggregation-based algebraic multigrid method. Electronic

Transactions on Numerical Analysis, 2010.

[13] W.D. Gropp D. Kaushik M.G. Knepley-L.C. McInnes B.F. Smith S. Balay,

K. Buschelman and H. Zhang. Petsc web page. http://www.mcs.anl.gov/petsc/, 2009.

[14] Youcef Saad and Martin H Schultz. Gmres: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on scientific and statistical computing, 7(3):856–869, 1986.

[15] Will J Schroeder, Bill Lorensen, and Ken Martin. The visualization toolkit. Kitware,2004.

[16] Ray S Tuminaro. Parallel smoothed aggregation multigrid: Aggregation strategies on massively parallel machines. In Proceedings of the 2000 ACM/IEEE conference
on Supercomputing, page 5. IEEE Computer Society, 2000.

指導教授

黃楓南(Feng-Nan Hwang)

審核日期

2016-8-18

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