TY - JOUR
T1 - A Cascadic Multigrid Method for Eigenvalue Problem
AU - Han , Xiaole
AU - Xie , Hehu
AU - Xu , Fei
JO - Journal of Computational Mathematics
VL - 1
SP - 74
EP - 90
PY - 2017
DA - 2017/02
SN - 35
DO - http://doi.org/10.4208/jcm.1608-m2014-0135
UR - https://global-sci.org/intro/article_detail/jcm/9764.html
KW - Eigenvalue problem, Cascadic multigrid, Multilevel correction scheme, Finite
element method.
AB - <p style="text-align: justify;">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.</p>