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

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題名:	Parallel Multilevel Smoothed Aggregation Schwarz Preconditioned Newton-Krylov Algorithms for Poisson-Boltzmann Problem
作者:	蕭鈞懌;Xiao,Jun-Yi
貢獻者:	數學系
關鍵詞:	平行計算;多重網格法;數值分析;Parallel;Multilevel;Newton-Krylov;Poisson-Boltzmann
日期:	2016-08-18
上傳時間:	2016-10-13 14:48:13 (UTC+8)
出版者:	國立中央大學
摘要:	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。;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.
顯示於類別:	[數學研究所] 博碩士論文

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