On the penalization by the perimeter in shape optimization applied to Dirichlet inverse obstacle problem
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916193362771968 |
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| author | Caubet, Fabien Dambrine, Marc Dardé, Jérémi |
| author_facet | Caubet, Fabien Dambrine, Marc Dardé, Jérémi |
| contents | This paper is devoted to the understanding of regularisation process in the shape optimization approach to the so-called Dirichlet inverse obstacle problem for elliptic operators. More precisely, we study two different regularisations of the very classical shape optimization approach consisting in minimizing a mismatched functional. The first one is an implicit regularisation when working in the class of inclusion having a uniform $\varepsilon$-cone property, a natural class in shape optimization. As this regularity is not trivial to guarantee numerically, we discuss the regularisation by perimeter penalization. We show that this second regularisation provides a stability gain in the minimization process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03536 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the penalization by the perimeter in shape optimization applied to Dirichlet inverse obstacle problem Caubet, Fabien Dambrine, Marc Dardé, Jérémi Optimization and Control 35R30 35B35 49Q10 This paper is devoted to the understanding of regularisation process in the shape optimization approach to the so-called Dirichlet inverse obstacle problem for elliptic operators. More precisely, we study two different regularisations of the very classical shape optimization approach consisting in minimizing a mismatched functional. The first one is an implicit regularisation when working in the class of inclusion having a uniform $\varepsilon$-cone property, a natural class in shape optimization. As this regularity is not trivial to guarantee numerically, we discuss the regularisation by perimeter penalization. We show that this second regularisation provides a stability gain in the minimization process. |
| title | On the penalization by the perimeter in shape optimization applied to Dirichlet inverse obstacle problem |
| topic | Optimization and Control 35R30 35B35 49Q10 |
| url | https://arxiv.org/abs/2404.03536 |