A CASCADIC MULTIGRID METHOD FOR EIGENVALUE PROBLEM  

作　　者：Xiaole Han Hehu Xie Fei Xu 

机构地区：[1]IAPCM, Institute of Applied Physics and Computational Mathematics, Beijing 100093, China [2]LSEC, NCMIS, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China [3]Beijing Institute for Scientific and Engineering Computing, Beijing University of Technology, Beijing 100124, China

出　　处：《Journal of Computational Mathematics》2017年第1期74-90,共17页计算数学（英文）

基　　金：Acknowledgments. This work is supported in part by the National Natural Science Foundation of China （NSFC 91330202, 11371026, 11001259, 11031006, 2011CB309703） and the National Center for Mathematics and Interdisciplinary Science, CAS.

摘　　要：A cascadic multigrid method is proposed for eigenvalue problems based on the multilevel correction scheme. With this new scheme, an eigenvalue problem on the finest space can be solved by linear smoothing steps on a series of multilevel finite element spaces and nonlinear correcting steps on special coarsest spaces. Once the sequence of finite element spaces and the number of smoothing steps are appropriately chosen, the optimal convergence rate with the optimal computational work can be obtained. Some numerical experiments are presented to validate our theoretical analysis.A cascadic multigrid method is proposed for eigenvalue problems based on the multilevel correction scheme. With this new scheme, an eigenvalue problem on the finest space can be solved by linear smoothing steps on a series of multilevel finite element spaces and nonlinear correcting steps on special coarsest spaces. Once the sequence of finite element spaces and the number of smoothing steps are appropriately chosen, the optimal convergence rate with the optimal computational work can be obtained. Some numerical experiments are presented to validate our theoretical analysis.

关 键 词：Eigenvalue problem Cascadic multigrid Multilevel correction scheme Finiteelement method. 

分 类 号：O241.82[理学—计算数学] O241.6[理学—数学]