| Issue |
ESAIM: COCV
Volume 25, 2019
|
|
|---|---|---|
| Article Number | 3 | |
| Number of page(s) | 23 | |
| DOI | https://doi.org/10.1051/cocv/2017014 | |
| Published online | 05 April 2019 | |
Shape optimization via a levelset and a Gauss-Newton method
1
Institut de Mathématiques de Toulouse, UMR CNRS 5219, Université de Toulouse, France
2
INSA de Toulouse, Institut de Mathématiques de Toulouse, UMR CNRS 5219, Université de Toulouse, France.
* Corresponding author: frederic@degournay.fr
Received:
20
June
2016
Accepted:
18
February
2017
In the context of shape optimization via level-set methods, we propose a general framework for a Gauss-Newton method to optimize quadratic functionals. Our approach provides a natural extension of the shape derivative as a vector field defined in the whole working domain. We implement and discuss this method in two cases: first a least-square error minimization reminiscent of the Electrical Impedance Tomography problem, and second the compliance problem with volume constraints.
Mathematics Subject Classification: 49Q10 / 49M15 / 49M29 / 74P05 / 74P10 / 74P20
Key words: Shape optimization / shape derivative / second order method / level-set method
© EDP Sciences, SMAI 2019
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