Geodesic
A bilevel shape optimization problem for the exterior Bernoulli free boundary value problem
Henry Kasumba1 ; Karl Kunisch2 ; Antoine Laurain3
1for Computational and Applied Mathematics, Linz, Austria
2Karl-Franzens-Universität Graz, Austria
3TU Berlin, Germany
Interfaces and free boundaries, Tome 16 (2014) no. 4, pp. 459-487

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DOI

A bilevel shape optimization problem with the exterior Bernoulli free boundary problem as lower-level problem and the control of the free boundary as the upper-level problem is considered. Using the shape of the inner boundary as the control, we aim at reaching a specific shape for the free boundary. A rigorous sensitivity analysis of the bilevel shape optimization in the infinite-dimensional setting is performed. The numerical realization using two different cost functionals presented in this paper demonstrate the efficiency of the approach.
DOI : 10.4171/ifb/326
Classification : 35-XX, 49-XX
Mots-clés : Bernoulli free boundary problem, shape optimization, multilevel optimization

Henry Kasumba  1   ; Karl Kunisch  2   ; Antoine Laurain  3

1 for Computational and Applied Mathematics, Linz, Austria
2 Karl-Franzens-Universität Graz, Austria
3 TU Berlin, Germany 
Henry Kasumba; Karl Kunisch; Antoine Laurain. A bilevel shape optimization problem for the exterior Bernoulli free boundary value problem. Interfaces and free boundaries, Tome 16 (2014) no. 4, pp. 459-487. doi: 10.4171/ifb/326
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     title = {A bilevel shape optimization problem for the exterior {Bernoulli} free boundary value problem},
     journal = {Interfaces and free boundaries},
     pages = {459--487},
     year = {2014},
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     number = {4},
     doi = {10.4171/ifb/326},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/326/}
}
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