no. 6
Local defect-correction method based on multilevel discretization for Steklov eigenvalue problem
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 6, pp. 2899-2920

In this paper, we propose a local defect-correction method for solving the Steklov eigenvalue problem arising from the scalar second order positive definite partial differential equations based on the multilevel discretization. The objective is to avoid solving large-scale equations especially the large-scale Steklov eigenvalue problem whose computational cost increases exponentially. The proposed algorithm transforms the Steklov eigenvalue problem into a series of linear boundary value problems, which are defined in a multigrid space sequence, and a series of small-scale Steklov eigenvalue problems in a coarse correction space. Furthermore, we use the local defect-correction technique to divide the large-scale boundary value problems into small-scale subproblems. Through our proposed algorithm, we avoid solving large-scale Steklov eigenvalue problems. As a result, our proposed algorithm demonstrates significantly improved the solving efficiency. Additionally, we conduct numerical experiments and a rigorous theoretical analysis to verify the effectiveness of our proposed approach.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1051/m2an/2021076
Classification : 65N30, 65N25, 65L15, 65B99
Keywords: Steklov eigenvalue problem, local defect-correction, multilevel correction 
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     author = {Xu, Fei and Chen, Liu and Huang, Qiumei},
     title = {Local defect-correction method based on multilevel discretization for {Steklov} eigenvalue problem},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {2899--2920},
     year = {2021},
     publisher = {EDP-Sciences},
     volume = {55},
     number = {6},
     doi = {10.1051/m2an/2021076},
     mrnumber = {4347304},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/m2an/2021076/}
}
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Xu, Fei; Chen, Liu; Huang, Qiumei. Local defect-correction method based on multilevel discretization for Steklov eigenvalue problem. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 6, pp. 2899-2920. doi: 10.1051/m2an/2021076

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