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. Zbl1152.74381
  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.  Zbl0943.90078
  4. M.P. Bendsøe, O. Sigmund. Topology optimization, theory, methods and applications. Springer Verlag, 2003.  Zbl1059.74001

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