A Shifted-Inverse Adaptive Multigrid Method for the Elastic Eigenvalue Problem

Authors

  • Bo Gong Beijing Computational Science Research Center, Beijing 100193, China.
  • Jiayu Han School of Mathematical Sciences, Guizhou Normal University, Guiyang, 550025, China.
  • Jiguang Sun Department of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931, USA.
  • Zhimin Zhang Beijing Computational Science Research Center, Beijing, 100193, China.

DOI:

https://doi.org/10.4208/cicp.OA-2018-0293

Keywords:

Elastic eigenvalue problem, shifted-inverse iteration, adaptive multigrid method.

Abstract

A shifted-inverse iteration is proposed for the finite element discretization of the elastic eigenvalue problem. The method integrates the multigrid scheme and adaptive algorithm to achieve high efficiency and accuracy. Error estimates and optimal convergence for the proposed method are proved. Numerical examples show that the proposed method inherits the advantages of both ingredients and can compute low regularity eigenfunctions effectively.

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Published

2020-03-06

Issue

Vol. 27 No. 1 (2020)

Section

Articles