Year: 2017
Author: Xiaole Han, Hehu Xie, Fei Xu
Journal of Computational Mathematics, Vol. 35 (2017), Iss. 1 : pp. 74–90
Abstract
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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1608-m2014-0135
Journal of Computational Mathematics, Vol. 35 (2017), Iss. 1 : pp. 74–90
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Eigenvalue problem Cascadic multigrid Multilevel correction scheme Finite element method.
Author Details
-
A type of full multigrid method for non-selfadjoint Steklov eigenvalue problems in inverse scattering
Xie, Manting | Xu, Fei | Yue, MeilingESAIM: Mathematical Modelling and Numerical Analysis, Vol. 55 (2021), Iss. 5 P.1779
https://doi.org/10.1051/m2an/2021039 [Citations: 4] -
A Bootstrap Multigrid Eigensolver
Brannick, James | Cao, ShuhaoSIAM Journal on Matrix Analysis and Applications, Vol. 43 (2022), Iss. 4 P.1627
https://doi.org/10.1137/20M131151X [Citations: 1] -
A type of cascadic multigrid method for coupled semilinear elliptic equations
Xu, Fei | Huang, QiumeiNumerical Algorithms, Vol. 83 (2020), Iss. 2 P.485
https://doi.org/10.1007/s11075-019-00690-1 [Citations: 4] -
Cascadic adaptive finite element method for nonlinear eigenvalue problem based on complementary approach
Xu, Fei | Huang, QiumeiJournal of Computational and Applied Mathematics, Vol. 372 (2020), Iss. P.112720
https://doi.org/10.1016/j.cam.2020.112720 [Citations: 1] -
A cascadic multigrid method for nonsymmetric eigenvalue problem
Yue, Meiling | Xie, Hehu | Xie, MantingApplied Numerical Mathematics, Vol. 146 (2019), Iss. P.55
https://doi.org/10.1016/j.apnum.2019.07.007 [Citations: 2]