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Volume 11, Issue 1
An Algebraic Multigrid Method for Eigenvalue Problems and Its Numerical Tests

Ning Zhang, Xiaole Han, Yunhui He, Hehu Xie & Chun'guang You

DOI: 10.4208/eajam.210918.090519

East Asian J. Appl. Math., 11 (2021), pp. 1-19.

Published online: 2020-11

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  • Abstract

In order to solve eigenvalue problems, an algebraic multigrid method based on a multilevel correction scheme and the algebraic multigrid method for linear equations is developed. The algebraic multigrid method setup procedure is used for construction of an hierarchy and intergrid transfer operators. In this approach, large scale eigenvalue problems are solved by algebraic multigrid smoothing steps in the hierarchy and by low-dimensional eigenvalue problems. The efficacy and flexibility of the method is demonstrated by a number of test examples and the global convergence, which does not depend on the number of eigenvalues wanted, is obtained.

  • Keywords

Algebraic multigrid, multilevel correction, eigenvalue problem.

  • AMS Subject Headings

65N30, 65N25, 65L15, 65B99

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-11-1, author = {Zhang , NingHan , XiaoleHe , YunhuiXie , Hehu and You , Chun'guang}, title = {An Algebraic Multigrid Method for Eigenvalue Problems and Its Numerical Tests}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {11}, number = {1}, pages = {1--19}, abstract = {

In order to solve eigenvalue problems, an algebraic multigrid method based on a multilevel correction scheme and the algebraic multigrid method for linear equations is developed. The algebraic multigrid method setup procedure is used for construction of an hierarchy and intergrid transfer operators. In this approach, large scale eigenvalue problems are solved by algebraic multigrid smoothing steps in the hierarchy and by low-dimensional eigenvalue problems. The efficacy and flexibility of the method is demonstrated by a number of test examples and the global convergence, which does not depend on the number of eigenvalues wanted, is obtained.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.210918.090519}, url = {http://global-sci.org/intro/article_detail/eajam/18410.html} }
TY - JOUR T1 - An Algebraic Multigrid Method for Eigenvalue Problems and Its Numerical Tests AU - Zhang , Ning AU - Han , Xiaole AU - He , Yunhui AU - Xie , Hehu AU - You , Chun'guang JO - East Asian Journal on Applied Mathematics VL - 1 SP - 1 EP - 19 PY - 2020 DA - 2020/11 SN - 11 DO - http://doi.org/10.4208/eajam.210918.090519 UR - https://global-sci.org/intro/article_detail/eajam/18410.html KW - Algebraic multigrid, multilevel correction, eigenvalue problem. AB -

In order to solve eigenvalue problems, an algebraic multigrid method based on a multilevel correction scheme and the algebraic multigrid method for linear equations is developed. The algebraic multigrid method setup procedure is used for construction of an hierarchy and intergrid transfer operators. In this approach, large scale eigenvalue problems are solved by algebraic multigrid smoothing steps in the hierarchy and by low-dimensional eigenvalue problems. The efficacy and flexibility of the method is demonstrated by a number of test examples and the global convergence, which does not depend on the number of eigenvalues wanted, is obtained.

Zhang , NingHan , XiaoleHe , YunhuiXie , Hehu and You , Chun'guang. (2020). An Algebraic Multigrid Method for Eigenvalue Problems and Its Numerical Tests. East Asian Journal on Applied Mathematics. 11 (1). 1-19. doi:10.4208/eajam.210918.090519
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