Geodesic
A penalty method for topology optimization subject to a pointwise state constraint
ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 3, pp. 523-544

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This paper deals with topology optimization of domains subject to a pointwise constraint on the gradient of the state. To realize this constraint, a class of penalty functionals is introduced and the expression of the corresponding topological derivative is obtained for the Laplace equation in two space dimensions. An algorithm based on these concepts is proposed. It is illustrated by some numerical applications.

DOI : 10.1051/cocv/2009013
Classification : 49Q10, 49Q12, 49M30, 35J05
Keywords: topology optimization, topological derivative, penalty methods, pointwise state constraints 
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     author = {Amstutz, Samuel},
     title = {A penalty method for topology optimization subject to a pointwise state constraint},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {523--544},
     publisher = {EDP-Sciences},
     volume = {16},
     number = {3},
     year = {2010},
     doi = {10.1051/cocv/2009013},
     mrnumber = {2674625},
     zbl = {1201.49046},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2009013/}
}
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Amstutz, Samuel. A penalty method for topology optimization subject to a pointwise state constraint. ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 3, pp. 523-544. doi: 10.1051/cocv/2009013

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