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Pré-Publication, Document De Travail Année : 2024

On the penalization by the perimeter in shape optimization applied to Dirichlet inverse obstacle problem

Résumé

This paper is devoted to the understanding of regularization process in the shape optimization approach to the so-called Dirichlet inverse obstacle problem for elliptic operators. More precisely, we study two different regularization of the very classical shape optimization approach consisting in minimizing a mismatched functional. The first one is an implicit regularization when working in the class of inclusion having a uniform ε-cone property, a natural class in shape optimization. As this regularity is not trivial to guarantee numerically, we discuss the regularization by perimeter penalization. We show that this second regularization provides a stability gain in the minimization process.
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Dates et versions

hal-04529274 , version 1 (02-04-2024)

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  • HAL Id : hal-04529274 , version 1

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Fabien Caubet, Marc Dambrine, Jérémi Dardé. On the penalization by the perimeter in shape optimization applied to Dirichlet inverse obstacle problem. 2024. ⟨hal-04529274⟩
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