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Shape Optimization of an Imperfect Interface: Steady-State Heat Diffusion

Author

Listed:
  • Grégoire Allaire

    (Institut Polytechnique de Paris)

  • Beniamin Bogosel

    (Institut Polytechnique de Paris)

  • Matías Godoy

    (Institut Polytechnique de Paris)

Abstract

In the context of a diffusion equation, this work is devoted to a two-phase optimal design problem where the interface, separating the phases, is imperfect, meaning that the solution is discontinuous, while the normal flux is continuous and proportional to the jump of the solution. The shape derivative of an objective function with respect to the interface position is computed by the adjoint method. Numerical experiments are performed with the level set method and an exact remeshing algorithm so that the interface is captured by the mesh at each optimization iteration. Comparisons with a perfect interface are discussed in the setting of optimal design or inverse problems.

Suggested Citation

  • Grégoire Allaire & Beniamin Bogosel & Matías Godoy, 2021. "Shape Optimization of an Imperfect Interface: Steady-State Heat Diffusion," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 169-201, October.
    • Handle: RePEc:spr:joptap:v:191:y:2021:i:1:d:10.1007_s10957-021-01928-6
    DOI: 10.1007/s10957-021-01928-6
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