In this paper we introduce a numerical approach adapted to the minimization of the eigenmodes of a membrane with respect to the domain. This method is based on the combination of the Level Set method of S. Osher and J.A. Sethian with the relaxed approach. This algorithm enables both changing the topology and working on a fixed regular grid.
Keywords: shape optimization, eigenvalue, level set, relaxation
@article{COCV_2004__10_3_315_0, author = {Oudet, \'Edouard}, title = {Numerical minimization of eigenmodes of a membrane with respect to the domain}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {315--330}, publisher = {EDP-Sciences}, volume = {10}, number = {3}, year = {2004}, doi = {10.1051/cocv:2004011}, mrnumber = {2084326}, zbl = {1076.74045}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv:2004011/} }
TY - JOUR AU - Oudet, Édouard TI - Numerical minimization of eigenmodes of a membrane with respect to the domain JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2004 SP - 315 EP - 330 VL - 10 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv:2004011/ DO - 10.1051/cocv:2004011 LA - en ID - COCV_2004__10_3_315_0 ER -
%0 Journal Article %A Oudet, Édouard %T Numerical minimization of eigenmodes of a membrane with respect to the domain %J ESAIM: Control, Optimisation and Calculus of Variations %D 2004 %P 315-330 %V 10 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv:2004011/ %R 10.1051/cocv:2004011 %G en %F COCV_2004__10_3_315_0
Oudet, Édouard. Numerical minimization of eigenmodes of a membrane with respect to the domain. ESAIM: Control, Optimisation and Calculus of Variations, Volume 10 (2004) no. 3, pp. 315-330. doi : 10.1051/cocv:2004011. http://archive.numdam.org/articles/10.1051/cocv:2004011/
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