Introduction to Multigrid Methods系列讲座
本讲教师：Jaap van der Vegt
课程内容简介: Multigrid methods can provide very efficient iterative methods for the solution of large systems of (non)linear algebraic equations, resulting for instance from the discretization of partial differential equations. In a multigrid method several coarsened approximations of the algebraic system and well-designed smoothers are used to accelerate the convergence of the iterative method. This can result in very efficient iterative methods, but if one wants to develop new multigrid algorithms or understand the performance of existing algorithms, then multilevel analysis is indispensible. In this class an outline of basic multigrid and iterative methods will be given and mathematical techniques to understand and predict their performance will be discussed. No prior knowledge of multigrid or iterative methods will be required. After this class you should be able to use basic iterative and multigrid methods, analyze and (approximately) predict multigrid performance using multilevel analysis and apply these techniques to improve and test multigrid algorithms. The main applications will be from numerical discretizations of partial differential equations. Reference: U. Trottenberg, C.W. Oosterlee, A. Schüller, Multigrid, Academic Press, ISBN 0-12-701070-X, 2001.