# Bilevel Approach of a Decomposed Topology Optimization Problem

Mathematical Modelling of Natural Phenomena (2010)

- Volume: 5, Issue: 7, page 128-131
- ISSN: 0973-5348

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topMakrizi, A., and Radi, B.. Taik, A., ed. "Bilevel Approach of a Decomposed Topology Optimization Problem." Mathematical Modelling of Natural Phenomena 5.7 (2010): 128-131. <http://eudml.org/doc/197713>.

@article{Makrizi2010,

abstract = {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},

author = {Makrizi, A., Radi, B.},

editor = {Taik, A.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {topology optimization; domain decomposition method; compliance; multilevel optimization},

language = {eng},

month = {8},

number = {7},

pages = {128-131},

publisher = {EDP Sciences},

title = {Bilevel Approach of a Decomposed Topology Optimization Problem},

url = {http://eudml.org/doc/197713},

volume = {5},

year = {2010},

}

TY - JOUR

AU - Makrizi, A.

AU - Radi, B.

AU - Taik, A.

TI - Bilevel Approach of a Decomposed Topology Optimization Problem

JO - Mathematical Modelling of Natural Phenomena

DA - 2010/8//

PB - EDP Sciences

VL - 5

IS - 7

SP - 128

EP - 131

AB - 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

LA - eng

KW - topology optimization; domain decomposition method; compliance; multilevel optimization

UR - http://eudml.org/doc/197713

ER -

## References

top- A. Makrizi, B. Radi, A. E. Hami. Solution of the topology optimization problem based subdomains method. Applied Mathematical Sciences, 2 (2008), No. 41, 2029–2045. Zbl1152.74381
- 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.
- J.F. Bard. Practical bilevel optimization: algorithms and applications. Kluwer Academic Publishers, Dordrecht, 1998. Zbl0943.90078
- M.P. Bendsøe, O. Sigmund. Topology optimization, theory, methods and applications. Springer Verlag, 2003. Zbl1059.74001

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