IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v230y2025icp149-164.html
   My bibliography  Save this article

On numerical resolution of shape optimization bi-Laplacian eigenvalue problems

Author

Listed:
  • Chakib, Abdelkrim
  • Khalil, Ibrahim
  • Sadik, Azeddine

Abstract

In this paper, we deal with the numerical resolution of some shape optimization models for the volume-constrained buckling and clamped plate bi-Laplacian eigenvalues problems. We propose a numerical method using the Lagrangian functional, Hadamard’s shape derivative and the gradient method combined with the finite elements discretization, to determine the minimizers for the first ten eigenvalues for both problems. We investigate also numerically the maximization of some quotient functionals, which allows us to obtain the optimal possible upper bounds of these spectral quotient problems and establish numerically some conjectures. Numerical examples and illustrations are provided for different and various cost functionals. The obtained numerical results show the efficiency and practical suitability of the proposed approaches.

Suggested Citation

  • Chakib, Abdelkrim & Khalil, Ibrahim & Sadik, Azeddine, 2025. "On numerical resolution of shape optimization bi-Laplacian eigenvalue problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 230(C), pages 149-164.
    • Handle: RePEc:eee:matcom:v:230:y:2025:i:c:p:149-164
    DOI: 10.1016/j.matcom.2024.11.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475424004488
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2024.11.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    3. Julius Fergy T. Rabago & Hideyuki Azegami, 2020. "A second-order shape optimization algorithm for solving the exterior Bernoulli free boundary problem using a new boundary cost functional," Computational Optimization and Applications, Springer, vol. 77(1), pages 251-305, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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.
    3. Wei Gong & Le Liu, 2025. "On the well-posedness of tracking Dirichlet data for Bernoulli free boundary problems," Computational Optimization and Applications, Springer, vol. 91(1), pages 311-349, May.
    4. 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.
    5. Alessandro Lanza & Serena Morigi & Giuseppe Recupero, 2025. "Variational graph p-Laplacian eigendecomposition under p-orthogonality constraints," Computational Optimization and Applications, Springer, vol. 91(2), pages 787-825, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:230:y:2025:i:c:p:149-164. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.