The topological sensitivity analysis consists in studying the behavior of a given shape functional when the topology of the domain is perturbed, typically by the nucleation of a small hole. This notion forms the basic ingredient of different topology optimization/reconstruction algorithms. From the theoretical viewpoint, the expression of the topological sensitivity is well-established in many situations where the governing p.d.e. system is of elliptic type. This paper focuses on the derivation of such formulas for parabolic and hyperbolic problems. Different kinds of cost functionals are considered.
Mots-clés : topological sensitivity, topology optimization, parabolic equations, hyperbolic equations
@article{COCV_2008__14_3_427_0,
author = {Vexler, Boris and Takahashi, Tak\'eo and Amstutz, Samuel},
title = {Topological sensitivity analysis for time-dependent problems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {427--455},
publisher = {EDP-Sciences},
volume = {14},
number = {3},
year = {2008},
doi = {10.1051/cocv:2007059},
mrnumber = {2434060},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv:2007059/}
}
TY - JOUR AU - Vexler, Boris AU - Takahashi, Takéo AU - Amstutz, Samuel TI - Topological sensitivity analysis for time-dependent problems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2008 SP - 427 EP - 455 VL - 14 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2007059/ DO - 10.1051/cocv:2007059 LA - en ID - COCV_2008__14_3_427_0 ER -
%0 Journal Article %A Vexler, Boris %A Takahashi, Takéo %A Amstutz, Samuel %T Topological sensitivity analysis for time-dependent problems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2008 %P 427-455 %V 14 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2007059/ %R 10.1051/cocv:2007059 %G en %F COCV_2008__14_3_427_0
Vexler, Boris; Takahashi, Takéo; Amstutz, Samuel. Topological sensitivity analysis for time-dependent problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 3, pp. 427-455. doi : 10.1051/cocv:2007059. http://www.numdam.org/articles/10.1051/cocv:2007059/
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