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

Grégoire Allaire (1) , Beniamin Bogosel (1) , Matias Godoy (1, 2)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 CNRS - Centre National de la Recherche Scientifique

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.

Mots clés: imperfect interfaces; shape optimization; level set method

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]

Grégoire Allaire, Beniamin Bogosel, Matias Godoy. Shape optimization of an imperfect interface: steady-state heat diffusion. 2021. ⟨hal-03102760v1⟩