Bilevel Approach of a Decomposed Topology Optimization Problem

A. Makrizi; B. Radi

Mathematical Modelling of Natural Phenomena (2010)

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

Abstract

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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

How to cite

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Makrizi, 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

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  1. 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. 
  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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