### 博碩士論文 942201002 完整後設資料紀錄

 DC 欄位 值 語言 DC.contributor 數學系 zh_TW DC.creator 蔡尚融 zh_TW DC.creator Shang-Rong Cai en_US dc.date.accessioned 2008-7-16T07:39:07Z dc.date.available 2008-7-16T07:39:07Z dc.date.issued 2008 dc.identifier.uri http://ir.lib.ncu.edu.tw:88/thesis/view_etd.asp?URN=942201002 dc.contributor.department 數學系 zh_TW DC.description 國立中央大學 zh_TW DC.description National Central University en_US dc.description.abstract 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。 zh_TW dc.description.abstract 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. en_US DC.subject 非精確牛頓法 zh_TW DC.subject overlapped Schwarz preconditioning zh_TW DC.subject 有限元素法 zh_TW DC.subject 膠體科學 zh_TW DC.subject 三維模擬 zh_TW DC.subject Poisson-Boltzmann 方程式 zh_TW DC.subject Poisson-Boltzmann equation en_US DC.subject 3D simulation en_US DC.subject colloidal science en_US DC.subject inexact Newton en_US DC.subject overlapped Schwarz preconditioning en_US DC.subject finite element method en_US DC.subject parallel processing en_US DC.title 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 zh_TW dc.language.iso zh-TW zh-TW DC.title Parallel Newton-Krylov-Schwarz Algorithms for Finite Element Solution of Three Dimensional Poisson-Boltzmann Equations with Applications in Colloidal Science en_US DC.type 博碩士論文 zh_TW DC.type thesis en_US DC.publisher National Central University en_US