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Shape optimization of an imperfect interface: steady-state heat diffusion

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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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03102760
Contributor : Matías Godoy Connect in order to contact the contributor
Submitted on : Friday, August 13, 2021 - 5:23:38 PM
Last modification on : Saturday, August 21, 2021 - 3:26:51 AM

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  • HAL Id : hal-03102760, version 2

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Grégoire Allaire, Beniamin Bogosel, Matias Godoy. Shape optimization of an imperfect interface: steady-state heat diffusion. 2021. ⟨hal-03102760v2⟩

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