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A Nonnested Augmented Subspace Method for Elliptic Eigenvalue Problems with Curved Interfaces

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Abstract

In this paper, we present a nonnested augmented subspace algorithm and its multilevel correction method for solving elliptic eigenvalue problems with curved interfaces. The augmented subspace algorithm and the corresponding multilevel correction method are designed based on a coarse finite element space which is not the subset of the finer finite element space. The nonnested augmented subspace method can transform the eigenvalue problem-solving on the finest mesh to the solving linear equation on the same mesh and small scale eigenvalue problem on the low dimensional augmented subspace. The corresponding theoretical analysis and numerical experiments are provided to demonstrate the efficiency of the proposed algorithms.

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Acknowledgements

The authors would like to thank the editor and two anonymous referees for their valuable comments which improve this manuscript a lot. Additionally, we are very grateful to Prof. Pierre Jolivet for his kind discussion and help to implement numerical examples with FreeFEM++. Especially, Prof. Pierre Jolivet helps us to do the efficient interpolation between two nonnested meshes which is very important to implement the proposed method in this paper. Here, we express our thanks for all the developers of FreeFEM++.

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Authors and Affiliations

  1. China Electronics Technology Group Corporation No. 15 Research Institute, Beijing, 100083, China

    Haikun Dang

  2. ICMSEC, LSEC, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Haikun Dang, Hehu Xie & Gang Zhao

  3. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Haikun Dang, Hehu Xie & Gang Zhao

  4. Faculty of Science, Beijing University of Technology, Beijing, 100124, China

    Chenguang Zhou

  5. LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Chenguang Zhou

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  1. Haikun Dang
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  2. Hehu Xie
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Correspondence to Chenguang Zhou.

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This work was supported by Beijing Natural Science Foundation (Z200003), the Research Foundation for Beijing University of Technology New Faculty (006000514122516), the National Center for Mathematics and Interdisciplinary Science, CAS.

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Dang, H., Xie, H., Zhao, G. et al. A Nonnested Augmented Subspace Method for Elliptic Eigenvalue Problems with Curved Interfaces. J Sci Comput 94, 34 (2023). https://doi.org/10.1007/s10915-022-02089-y

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  • DOI: https://doi.org/10.1007/s10915-022-02089-y

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