Adaptive Multigrid Method for Eigenvalue Problem

Adaptive Multigrid Method for Eigenvalue Problem

Year:    2022

Author:    Fei Xu, Qiumei Huang, Shuangshuang Chen, Hongkun Ma

International Journal of Numerical Analysis and Modeling, Vol. 19 (2022), Iss. 1 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2022-IJNAM-20346

International Journal of Numerical Analysis and Modeling, Vol. 19 (2022), Iss. 1 : pp. 1–18

Published online:    2022-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    Eigenvalue problem adaptive multigrid method multilevel correction convergence optimal complexity.

Author Details

Fei Xu

Qiumei Huang

Shuangshuang Chen

Hongkun Ma