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A level set method for Laplacian eigenvalue optimization subject to geometric constraints

Author

Listed:
  • Meizhi Qian

    (East China Normal University)

  • Shengfeng Zhu

    (East China Normal University)

Abstract

We consider to solve numerically the shape optimization problems of Dirichlet Laplace eigenvalues subject to volume and perimeter constraints. By combining a level set method with the relaxation approach, the algorithm can perform shape and topological changes on a fixed grid. We use the volume expressions of Eulerian derivatives in shape gradient descent algorithms. Finite element methods are used for discretizations. Two and three-dimensional numerical examples are presented to illustrate the effectiveness of the algorithms.

Suggested Citation

  • Meizhi Qian & Shengfeng Zhu, 2022. "A level set method for Laplacian eigenvalue optimization subject to geometric constraints," Computational Optimization and Applications, Springer, vol. 82(2), pages 499-524, June.
    • Handle: RePEc:spr:coopap:v:82:y:2022:i:2:d:10.1007_s10589-022-00371-1
    DOI: 10.1007/s10589-022-00371-1
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    References listed on IDEAS

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    1. Shengfeng Zhu, 2018. "Effective Shape Optimization of Laplace Eigenvalue Problems Using Domain Expressions of Eulerian Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 176(1), pages 17-34, January.
    2. Pedro R. S. Antunes & Pedro Freitas, 2012. "Numerical Optimization of Low Eigenvalues of the Dirichlet and Neumann Laplacians," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 235-257, July.
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    1. Pedro R. S. Antunes & Beniamin Bogosel, 2022. "Parametric shape optimization using the support function," Computational Optimization and Applications, Springer, vol. 82(1), pages 107-138, May.
    2. Shengfeng Zhu, 2018. "Effective Shape Optimization of Laplace Eigenvalue Problems Using Domain Expressions of Eulerian Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 176(1), pages 17-34, January.

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