Shape optimization approach for solving the Bernoulli problem by tracking the Neumann data: a Lagrangian formulation.(English)Zbl 1394.35586
Summary: The exterior Bernoulli free boundary problem is considered and reformulated into a shape optimization setting wherein the Neumann data is being tracked. The shape differentiability of the cost functional associated with the formulation is studied, and the expression for its shape derivative is established through a Lagrangian formulation coupled with the velocity method. Also, it is illustrated how the computed shape derivative can be combined with the modified \(H^1\) gradient method to obtain an efficient algorithm for the numerical solution of the shape optimization problem.
MSC:
| 35R35 | Free boundary problems for PDEs |
| 35N25 | Overdetermined boundary value problems for PDEs and systems of PDEs |
| 49K20 | Optimality conditions for problems involving partial differential equations |
| 49Q10 | Optimization of shapes other than minimal surfaces |
Keywords:
shape optimization;shape derivative;Bernoulli problem;minimax formulation;Lagrangian methodSoftware:
FreeFem++Cite
Full Text:DOI
References:
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