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Volume 19, Issue 1
Adaptive Multigrid Method for Eigenvalue Problem

Fei Xu, Qiumei Huang, Shuangshuang Chen & Hongkun Ma

Int. J. Numer. Anal. Mod., 19 (2022), pp. 1-18.

Published online: 2022-03

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  • Abstract

In this paper, we propose a type of adaptive multigrid method for eigenvalue problem based on the multilevel correction method and adaptive multigrid method. Different from the standard adaptive finite element method applied to eigenvalue problem, with our method we only need to solve a linear boundary value problem on each adaptive space and then correct the approximate solution by solving a low dimensional eigenvalue problem. Further, the involved boundary value problems are solved by some adaptive multigrid iteration steps. The proposed adaptive algorithm can reach the same accuracy as the standard adaptive finite element method for eigenvalue problem but evidently reduces the computational work. In addition, the corresponding convergence and optimal complexity analysis are derived theoretically and numerically, respectively.

  • Keywords

Eigenvalue problem, adaptive multigrid method, multilevel correction, convergence, optimal complexity.

  • AMS Subject Headings

65F15, 65N15, 65N25, 65N30, 65N50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-19-1, author = {Xu , FeiHuang , QiumeiChen , Shuangshuang and Ma , Hongkun}, title = {Adaptive Multigrid Method for Eigenvalue Problem}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2022}, volume = {19}, number = {1}, pages = {1--18}, abstract = {

In this paper, we propose a type of adaptive multigrid method for eigenvalue problem based on the multilevel correction method and adaptive multigrid method. Different from the standard adaptive finite element method applied to eigenvalue problem, with our method we only need to solve a linear boundary value problem on each adaptive space and then correct the approximate solution by solving a low dimensional eigenvalue problem. Further, the involved boundary value problems are solved by some adaptive multigrid iteration steps. The proposed adaptive algorithm can reach the same accuracy as the standard adaptive finite element method for eigenvalue problem but evidently reduces the computational work. In addition, the corresponding convergence and optimal complexity analysis are derived theoretically and numerically, respectively.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/20346.html} }
TY - JOUR T1 - Adaptive Multigrid Method for Eigenvalue Problem AU - Xu , Fei AU - Huang , Qiumei AU - Chen , Shuangshuang AU - Ma , Hongkun JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 1 EP - 18 PY - 2022 DA - 2022/03 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/20346.html KW - Eigenvalue problem, adaptive multigrid method, multilevel correction, convergence, optimal complexity. AB -

In this paper, we propose a type of adaptive multigrid method for eigenvalue problem based on the multilevel correction method and adaptive multigrid method. Different from the standard adaptive finite element method applied to eigenvalue problem, with our method we only need to solve a linear boundary value problem on each adaptive space and then correct the approximate solution by solving a low dimensional eigenvalue problem. Further, the involved boundary value problems are solved by some adaptive multigrid iteration steps. The proposed adaptive algorithm can reach the same accuracy as the standard adaptive finite element method for eigenvalue problem but evidently reduces the computational work. In addition, the corresponding convergence and optimal complexity analysis are derived theoretically and numerically, respectively.

Fei Xu, Qiumei Huang, Shuangshuang Chen & Hongkun Ma. (2022). Adaptive Multigrid Method for Eigenvalue Problem. International Journal of Numerical Analysis and Modeling. 19 (1). 1-18. doi:
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