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Shape optimization for interface identification in nonlocal models

Author

Listed:
  • Matthias Schuster

    (Universitaet Trier)

  • Christian Vollmann

    (Universitaet Trier)

  • Volker Schulz

    (Universitaet Trier)

Abstract

Shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations. Here we consider a class of shape optimization problems constrained by nonlocal equations which involve interface–dependent kernels. We derive a novel shape derivative associated to the nonlocal system model and solve the problem by established numerical techniques. The code for obtaining the results in this paper is published at ( https://github.com/schustermatthias/nlshape ).

Suggested Citation

  • Matthias Schuster & Christian Vollmann & Volker Schulz, 2024. "Shape optimization for interface identification in nonlocal models," Computational Optimization and Applications, Springer, vol. 88(3), pages 963-997, July.
    • Handle: RePEc:spr:coopap:v:88:y:2024:i:3:d:10.1007_s10589-024-00575-7
    DOI: 10.1007/s10589-024-00575-7
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    References listed on IDEAS

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    1. S. Z. Levendorskiǐ, 2004. "Pricing Of The American Put Under Lévy Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(03), pages 303-335.
    2. Martin Siebenborn, 2018. "A Shape Optimization Algorithm for Interface Identification Allowing Topological Changes," Journal of Optimization Theory and Applications, Springer, vol. 177(2), pages 306-328, May.
    3. Nicole Cusimano & Alfonso Bueno-Orovio & Ian Turner & Kevin Burrage, 2015. "On the Order of the Fractional Laplacian in Determining the Spatio-Temporal Evolution of a Space-Fractional Model of Cardiac Electrophysiology," PLOS ONE, Public Library of Science, vol. 10(12), pages 1-16, December.
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