Geodesic
Topology optimization methods with gradient-free perimeter approximation
Samuel Amstutz1 ; Nicolas Van Goethem2
1Université d'Avignon, France
2Universidade de Lisboa, Portugal
Interfaces and free boundaries, Tome 14 (2012) no. 3, pp. 401-430

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DOI

In this paper we introduce a family of smooth perimeter approximating functionals designed to be incorporated within topology optimization algorithms. The required mathematical properties, namely the Γ-convergence and the compactness of sequences of minimizers, are first established. Then we propose several methods for the solution of topology optimization problems with perimeter penalization showing different features. We conclude by some numerical illustrations in the contexts of least square problems and compliance minimization.
DOI : 10.4171/ifb/286
Classification : 49-XX, 35-XX, 00-XX
Mots-clés : Topology optimization, perimeter, Γ-convergence, homogenization

Samuel Amstutz  1   ; Nicolas Van Goethem  2

1 Université d'Avignon, France
2 Universidade de Lisboa, Portugal 
Samuel Amstutz; Nicolas Van Goethem. Topology optimization methods with gradient-free perimeter approximation. Interfaces and free boundaries, Tome 14 (2012) no. 3, pp. 401-430. doi: 10.4171/ifb/286
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     year = {2012},
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     number = {3},
     doi = {10.4171/ifb/286},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/286/}
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