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We examine shape optimization problems in the context of inexact sequential quadratic programming. Inexactness is a consequence of using adaptive finite element methods (AFEM) to approximate the state and adjoint equations (via the dual weighted residual method), update the boundary, and compute the geometric functional. We present a novel algorithm that equidistributes the errors due to shape optimization and discretization, thereby leading to coarse resolution in the early stages and fine resolution upon convergence, and thus optimizing the computational effort. We discuss the ability of the algorithm to detect whether or not geometric singularities such as corners are genuine to the problem or simply due to lack of resolution - a new paradigm in adaptivity.
@article{COCV_2012__18_4_1122_0,
author = {Morin, Pedro and Nochetto, Ricardo H. and Pauletti, Miguel S. and Verani, Marco},
title = {Adaptive finite element method for shape optimization},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1122--1149},
publisher = {EDP-Sciences},
volume = {18},
number = {4},
year = {2012},
doi = {10.1051/cocv/2011192},
mrnumber = {3019475},
zbl = {1259.49046},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2011192/}
}
TY - JOUR AU - Morin, Pedro AU - Nochetto, Ricardo H. AU - Pauletti, Miguel S. AU - Verani, Marco TI - Adaptive finite element method for shape optimization JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2012 SP - 1122 EP - 1149 VL - 18 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2011192/ DO - 10.1051/cocv/2011192 LA - en ID - COCV_2012__18_4_1122_0 ER -
%0 Journal Article %A Morin, Pedro %A Nochetto, Ricardo H. %A Pauletti, Miguel S. %A Verani, Marco %T Adaptive finite element method for shape optimization %J ESAIM: Control, Optimisation and Calculus of Variations %D 2012 %P 1122-1149 %V 18 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2011192/ %R 10.1051/cocv/2011192 %G en %F COCV_2012__18_4_1122_0
Morin, Pedro; Nochetto, Ricardo H.; Pauletti, Miguel S.; Verani, Marco. Adaptive finite element method for shape optimization. ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 4, pp. 1122-1149. doi: 10.1051/cocv/2011192
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