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Volume 33, Issue 6
Inexact Two-Grid Methods for Eigenvalue Problems

Qun Gu & Weiguo Gao

DOI: 10.4208/jcm.1502-m4539

J. Comp. Math., 33 (2015), pp. 557-575.

Published online: 2015-12

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  • Abstract

We discuss the inexact two-grid methods for solving eigenvalue problems, including both partial differential and integral equations. Instead of solving the linear system exactly in both traditional two-grid and accelerated two-grid method, we point out that it is enough to apply an inexact solver to the fine grid problems, which will cut down the computational cost. Different stopping criteria for both methods are developed for keeping the optimality of the resulting solution. Numerical examples are provided to verify our theoretical analyses.

  • Keywords

Inexact, Two-grid, Eigenvalue, Eigenvector, Finite element method, Convergence rate.

  • AMS Subject Headings

65N25, 65N30, 65B99.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

081018018@fudan.edu.cn (Qun Gu)

wggao@fudan.edu.cn (Weiguo Gao)

  • BibTex
  • RIS
  • TXT
@Article{JCM-33-557, author = {Gu , Qun and Gao , Weiguo}, title = {Inexact Two-Grid Methods for Eigenvalue Problems}, journal = {Journal of Computational Mathematics}, year = {2015}, volume = {33}, number = {6}, pages = {557--575}, abstract = {

We discuss the inexact two-grid methods for solving eigenvalue problems, including both partial differential and integral equations. Instead of solving the linear system exactly in both traditional two-grid and accelerated two-grid method, we point out that it is enough to apply an inexact solver to the fine grid problems, which will cut down the computational cost. Different stopping criteria for both methods are developed for keeping the optimality of the resulting solution. Numerical examples are provided to verify our theoretical analyses.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1502-m4539}, url = {http://global-sci.org/intro/article_detail/jcm/9860.html} }
TY - JOUR T1 - Inexact Two-Grid Methods for Eigenvalue Problems AU - Gu , Qun AU - Gao , Weiguo JO - Journal of Computational Mathematics VL - 6 SP - 557 EP - 575 PY - 2015 DA - 2015/12 SN - 33 DO - http://doi.org/10.4208/jcm.1502-m4539 UR - https://global-sci.org/intro/article_detail/jcm/9860.html KW - Inexact, Two-grid, Eigenvalue, Eigenvector, Finite element method, Convergence rate. AB -

We discuss the inexact two-grid methods for solving eigenvalue problems, including both partial differential and integral equations. Instead of solving the linear system exactly in both traditional two-grid and accelerated two-grid method, we point out that it is enough to apply an inexact solver to the fine grid problems, which will cut down the computational cost. Different stopping criteria for both methods are developed for keeping the optimality of the resulting solution. Numerical examples are provided to verify our theoretical analyses.

Qun Gu & Weiguo Gao. (2020). Inexact Two-Grid Methods for Eigenvalue Problems. Journal of Computational Mathematics. 33 (6). 557-575. doi:10.4208/jcm.1502-m4539
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