The gradient based topological optimization tools introduced during the last ten years tend naturally to modify the topology of a domain by creating small holes inside the domain. Once these holes have been created, they usually remain unchanged, at least during the topological phase of the optimization algorithm. In this paper, a new asymptotic expansion is introduced which allows to decide whether an existing hole must be removed or not for improving the cost function. Then, two numerical examples are presented: the first one compares topological optimization with standard shape optimization, and the second one, issued from a lake oxygenation problem, illustrates the use of the new asymptotic expansion.
Classification : 49Q10, 49Q12, 74P05, 74P10, 74P15
Mots clés : topological optimization, topological sensitivity, topological gradient, shape optimization, Stokes equations
@article{COCV_2008__14_1_160_0,
author = {Hassine, Maatoug and Guillaume, Philippe},
title = {Removing holes in topological shape optimization},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {160--191},
publisher = {EDP-Sciences},
volume = {14},
number = {1},
year = {2008},
doi = {10.1051/cocv:2007045},
zbl = {1140.49029},
mrnumber = {2375755},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv:2007045/}
}
TY - JOUR AU - Hassine, Maatoug AU - Guillaume, Philippe TI - Removing holes in topological shape optimization JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2008 DA - 2008/// SP - 160 EP - 191 VL - 14 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2007045/ UR - https://zbmath.org/?q=an%3A1140.49029 UR - https://www.ams.org/mathscinet-getitem?mr=2375755 UR - https://doi.org/10.1051/cocv:2007045 DO - 10.1051/cocv:2007045 LA - en ID - COCV_2008__14_1_160_0 ER -
Hassine, Maatoug; Guillaume, Philippe. Removing holes in topological shape optimization. ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 1, pp. 160-191. doi : 10.1051/cocv:2007045. http://www.numdam.org/articles/10.1051/cocv:2007045/
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