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.
Accepté le :
DOI : 10.1051/cocv/2017014
Mots-clés : Shape optimization, shape derivative, second order method, level-set method
@article{COCV_2019__25__A3_0,
author = {Fehrenbach, J\'er\^ome and de Gournay, Fr\'ed\'eric},
title = {Shape optimization via a levelset and a {Gauss-Newton} method},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {25},
year = {2019},
doi = {10.1051/cocv/2017014},
mrnumber = {3943357},
zbl = {1437.49058},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2017014/}
}
TY - JOUR AU - Fehrenbach, Jérôme AU - de Gournay, Frédéric TI - Shape optimization via a levelset and a Gauss-Newton method JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2019 VL - 25 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2017014/ DO - 10.1051/cocv/2017014 LA - en ID - COCV_2019__25__A3_0 ER -
%0 Journal Article %A Fehrenbach, Jérôme %A de Gournay, Frédéric %T Shape optimization via a levelset and a Gauss-Newton method %J ESAIM: Control, Optimisation and Calculus of Variations %D 2019 %V 25 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2017014/ %R 10.1051/cocv/2017014 %G en %F COCV_2019__25__A3_0
Fehrenbach, Jérôme; de Gournay, Frédéric. Shape optimization via a levelset and a Gauss-Newton method. ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 3. doi : 10.1051/cocv/2017014. http://www.numdam.org/articles/10.1051/cocv/2017014/
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