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Volume 13, Issue 1
Local and Parallel Finite Element Algorithm Based on Multilevel Discretization for Eigenvalue Problems

X.-L. Han, Y. Li, H.-H. Xie & C.-G. You

Int. J. Numer. Anal. Mod., 13 (2016), pp. 73-89.

Published online: 2016-01

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  • Abstract

In this paper, a local and parallel algorithm based on the multilevel discretization is proposed for solving the eigenvalue problem by the finite element method. With this new scheme, the eigenvalue problem solving in the finest grid is transferred to solutions of the eigenvalue problems on the coarsest mesh and a series of solutions of boundary value problems on each level mesh. Therefore this type of multilevel local and parallel method improves the overall efficiency of solving the eigenvalue problem. Some numerical experiments are presented to validate the efficiency of the new method.

  • Keywords

eigenvalue problem, multigrid, multilevel correction, local and parallel method, finite element method.

  • AMS Subject Headings

65N30, 65N25, 65L15, 65B99

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-13-73, author = {X.-L. Han, Y. Li, H.-H. Xie and C.-G. You}, title = {Local and Parallel Finite Element Algorithm Based on Multilevel Discretization for Eigenvalue Problems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2016}, volume = {13}, number = {1}, pages = {73--89}, abstract = {

In this paper, a local and parallel algorithm based on the multilevel discretization is proposed for solving the eigenvalue problem by the finite element method. With this new scheme, the eigenvalue problem solving in the finest grid is transferred to solutions of the eigenvalue problems on the coarsest mesh and a series of solutions of boundary value problems on each level mesh. Therefore this type of multilevel local and parallel method improves the overall efficiency of solving the eigenvalue problem. Some numerical experiments are presented to validate the efficiency of the new method.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/427.html} }
TY - JOUR T1 - Local and Parallel Finite Element Algorithm Based on Multilevel Discretization for Eigenvalue Problems AU - X.-L. Han, Y. Li, H.-H. Xie & C.-G. You JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 73 EP - 89 PY - 2016 DA - 2016/01 SN - 13 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/427.html KW - eigenvalue problem, multigrid, multilevel correction, local and parallel method, finite element method. AB -

In this paper, a local and parallel algorithm based on the multilevel discretization is proposed for solving the eigenvalue problem by the finite element method. With this new scheme, the eigenvalue problem solving in the finest grid is transferred to solutions of the eigenvalue problems on the coarsest mesh and a series of solutions of boundary value problems on each level mesh. Therefore this type of multilevel local and parallel method improves the overall efficiency of solving the eigenvalue problem. Some numerical experiments are presented to validate the efficiency of the new method.

X.-L. Han, Y. Li, H.-H. Xie and C.-G. You. (2016). Local and Parallel Finite Element Algorithm Based on Multilevel Discretization for Eigenvalue Problems. International Journal of Numerical Analysis and Modeling. 13 (1). 73-89. doi:
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