In this paper, we propose a topological sensitivity analysis for the Quasi-Stokes equations. It consists in an asymptotic expansion of a cost function with respect to the creation of a small hole in the domain. The leading term of this expansion is related to the principal part of the operator. The theoretical part of this work is discussed in both two and three dimensional cases. In the numerical part, we use this approach to optimize the locations of a fixed number of air injectors in an eutrophized lake.
Mots clés : topological optimization, topological sensitivity, quasi-Stokes equations, topological gradient, shape optimization
@article{COCV_2004__10_4_478_0,
author = {Hassine, Maatoug and Masmoudi, Mohamed},
title = {The topological asymptotic expansion for the {Quasi-Stokes} problem},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {478--504},
publisher = {EDP-Sciences},
volume = {10},
number = {4},
year = {2004},
doi = {10.1051/cocv:2004016},
mrnumber = {2111076},
zbl = {1072.49027},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv:2004016/}
}
TY - JOUR AU - Hassine, Maatoug AU - Masmoudi, Mohamed TI - The topological asymptotic expansion for the Quasi-Stokes problem JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2004 SP - 478 EP - 504 VL - 10 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2004016/ DO - 10.1051/cocv:2004016 LA - en ID - COCV_2004__10_4_478_0 ER -
%0 Journal Article %A Hassine, Maatoug %A Masmoudi, Mohamed %T The topological asymptotic expansion for the Quasi-Stokes problem %J ESAIM: Control, Optimisation and Calculus of Variations %D 2004 %P 478-504 %V 10 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2004016/ %R 10.1051/cocv:2004016 %G en %F COCV_2004__10_4_478_0
Hassine, Maatoug; Masmoudi, Mohamed. The topological asymptotic expansion for the Quasi-Stokes problem. ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 4, pp. 478-504. doi : 10.1051/cocv:2004016. http://www.numdam.org/articles/10.1051/cocv:2004016/
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