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

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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.

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Acknowledgements

The authors thank M. Boissier, A. Ferrer and F. Feppon for their useful comments and fruitful discussion. This work was supported by the SOFIA project and funded by BPI (Banque Publique d’Investissement).

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  1. CMAP, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, 91128, Palaiseau, France

    Grégoire Allaire, Beniamin Bogosel & Matías Godoy

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  1. Grégoire Allaire
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  2. Beniamin Bogosel
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  3. Matías Godoy
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Correspondence to Matías Godoy.

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Communicated by Yannick Privat.

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Allaire, G., Bogosel, B. & Godoy, M. Shape Optimization of an Imperfect Interface: Steady-State Heat Diffusion. J Optim Theory Appl 191, 169–201 (2021). https://doi.org/10.1007/s10957-021-01928-6

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