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.