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

• Main Authors: Jun-Yi Xiao, 蕭鈞懌
• Other Authors: Feng-Nan Hwang
• Format: Others
• Language: en_US
• Published: 2016
• Online Access: http://ndltd.ncl.edu.tw/handle/s7re35

碩士 === 國立中央大學 === 數學系 === 104 === 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.