Numerical Study of Algebraic Multigrid Methodsfor Solving Linear/Nonlinear Elliptic Problems onSequential and Parallel Computers

• Main Authors: Yu-Chieh Tseng, 曾郁潔
• Other Authors: Feng-Nan Hwang
• Format: Others
• Language: en_US
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/30387129668094877115

碩士 === 國立中央大學 === 數學研究所 === 100 === In the nowadays, Multigrid method plays an important role in the trend of numerical computations. Besides of its advantages of decreasing the iterations and the computation time, parallelization is also a big advantage of the parallel computation, it brings the convience for those researchers who do the research about parallel computation. About the developement of the multigrid already exists for a period of time. Its efficiency and the form of algorithms also have many different versions. In this paper, we will discuss about the result of solving the Poisson-Boltzmann Equations, Convection-Diffusion Equations by using the numerical multigrid method, including the time cost and the effect of solving linear system after using multigird method. And recovering the disadvantages and advantages of multigrid method. Through understanding the concepts of multigrid method, we hope we can using this method to decrease the iterations and cost of time. And extending this method that can be used to solve more linear system problems or linear sparse matrix problems.