Geodesic
Bilevel Approach of a Decomposed Topology Optimization Problem
A. Makrizi1 ; B. Radi2
1 GGDA, F.S. Ben M’sik, Boulevard Cdt Driss Harti, BP: 7955, Casablanca, Morocco
2 FST Errachidia, BP: 509, Boutalamine, Errachidia, Morocco
Mathematical modelling of natural phenomena, Tome 5 (2010) no. 7 Supplement, pp. 128-131.

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In topology optimization problems, we are often forced to deal with large-scale numerical problems, so that the domain decomposition method occurs naturally. Consider a typical topology optimization problem, the minimum compliance problem of a linear isotropic elastic continuum structure, in which the constraints are the partial differential equations of linear elasticity. We subdivide the partial differential equations into two subproblems posed on non-overlapping sub-domains. In this paper, we consider the resulting problem as multilevel one and show that it can be written as one level problem
DOI : 10.1051/mmnp/20105721

A. Makrizi 1 ; B. Radi 2

1 GGDA, F.S. Ben M’sik, Boulevard Cdt Driss Harti, BP: 7955, Casablanca, Morocco
2 FST Errachidia, BP: 509, Boutalamine, Errachidia, Morocco 
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A. Makrizi; B. Radi. Bilevel Approach of a Decomposed Topology Optimization Problem. Mathematical modelling of natural phenomena, Tome 5 (2010) no. 7 Supplement, pp. 128-131. doi : 10.1051/mmnp/20105721. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20105721/

[1] A. Makrizi, B. Radi, A. E. Hami Solution of the topology optimization problem based subdomains method Applied Mathematical Sciences 2008 2029 2045

[2] A. Makrizi, B. Radi and A. El Hami. Approche multiniveaux pour la résolution de l’optimisation topologique décomposée. Proceedings du premier congrès de la société marocaine de mathématiques appliquées, ENIM, Rabat, 06-08 Février 2008.

[3] J.F. Bard. Practical bilevel optimization: algorithms and applications. Kluwer Academic Publishers, Dordrecht, 1998.

[4] M.P. Bendsøe, O. Sigmund. Topology optimization, theory, methods and applications. Springer Verlag, 2003.

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