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Volume 27, Issue 1
A Shifted-Inverse Adaptive Multigrid Method for the Elastic Eigenvalue Problem

Bo Gong, Jiayu Han, Jiguang Sun & Zhimin Zhang

DOI: 10.4208/cicp.OA-2018-0293

Commun. Comput. Phys., 27 (2020), pp. 251-273.

Published online: 2019-10

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65N25, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

gongbo@csrc.ac.cn (Bo Gong)

hanjiayu126@126.com (Jiayu Han)

jiguangs@mtu.edu (Jiguang Sun)

zmzhang@csrc.ac.cn (Zhimin Zhang)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-27-251, author = {Gong , BoHan , JiayuSun , Jiguang and Zhang , Zhimin}, title = {A Shifted-Inverse Adaptive Multigrid Method for the Elastic Eigenvalue Problem}, journal = {Communications in Computational Physics}, year = {2019}, volume = {27}, number = {1}, pages = {251--273}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0293}, url = {http://global-sci.org/intro/article_detail/cicp/13321.html} }
TY - JOUR T1 - A Shifted-Inverse Adaptive Multigrid Method for the Elastic Eigenvalue Problem AU - Gong , Bo AU - Han , Jiayu AU - Sun , Jiguang AU - Zhang , Zhimin JO - Communications in Computational Physics VL - 1 SP - 251 EP - 273 PY - 2019 DA - 2019/10 SN - 27 DO - http://doi.org/10.4208/cicp.OA-2018-0293 UR - https://global-sci.org/intro/article_detail/cicp/13321.html KW - Elastic eigenvalue problem, shifted-inverse iteration, adaptive multigrid method. AB -

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.

Gong , BoHan , JiayuSun , Jiguang and Zhang , Zhimin. (2019). A Shifted-Inverse Adaptive Multigrid Method for the Elastic Eigenvalue Problem. Communications in Computational Physics. 27 (1). 251-273. doi:10.4208/cicp.OA-2018-0293
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