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Effective Shape Optimization of Laplace Eigenvalue Problems Using Domain Expressions of Eulerian Derivatives

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  • Shengfeng Zhu

    (East China Normal University)

Abstract

We consider to solve numerically the shape optimization models with Dirichlet Laplace eigenvalues. Both volume-constrained and volume unconstrained formulations of the model problems are presented. Different from the literature using boundary-type Eulerian derivatives in shape gradient descent methods, we advocate to use the more general volume expressions of Eulerian derivatives. We present two shape gradient descent algorithms based on the volume expressions. Numerical examples are presented to show the more effectiveness of the algorithms than those based on the boundary expressions.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:176:y:2018:i:1:d:10.1007_s10957-017-1198-9
    DOI: 10.1007/s10957-017-1198-9
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    References listed on IDEAS

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    1. 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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    Cited by:

    1. 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.
    2. 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.

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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. 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.

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