Optimal design in small amplitude homogenization

Grégoire Allaire; Sergio Gutiérrez

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

  • Volume: 41, Issue: 3, page 543-574
  • ISSN: 0764-583X

Abstract

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This paper is concerned with optimal design problems with a special assumption on the coefficients of the state equation. Namely we assume that the variations of these coefficients have a small amplitude. Then, making an asymptotic expansion up to second order with respect to the aspect ratio of the coefficients allows us to greatly simplify the optimal design problem. By using the notion of H-measures we are able to prove general existence theorems for small amplitude optimal design and to provide simple and efficient numerical algorithms for their computation. A key feature of this type of problems is that the optimal microstructures are always simple laminates.

How to cite

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Allaire, Grégoire, and Gutiérrez, Sergio. "Optimal design in small amplitude homogenization." ESAIM: Mathematical Modelling and Numerical Analysis 41.3 (2007): 543-574. <http://eudml.org/doc/250029>.

@article{Allaire2007,
abstract = { This paper is concerned with optimal design problems with a special assumption on the coefficients of the state equation. Namely we assume that the variations of these coefficients have a small amplitude. Then, making an asymptotic expansion up to second order with respect to the aspect ratio of the coefficients allows us to greatly simplify the optimal design problem. By using the notion of H-measures we are able to prove general existence theorems for small amplitude optimal design and to provide simple and efficient numerical algorithms for their computation. A key feature of this type of problems is that the optimal microstructures are always simple laminates. },
author = {Allaire, Grégoire, Gutiérrez, Sergio},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Optimal design; H-measures; homogenization.; small amplitude homogenization; -measures; shape optimization},
language = {eng},
month = {8},
number = {3},
pages = {543-574},
publisher = {EDP Sciences},
title = {Optimal design in small amplitude homogenization},
url = {http://eudml.org/doc/250029},
volume = {41},
year = {2007},
}

TY - JOUR
AU - Allaire, Grégoire
AU - Gutiérrez, Sergio
TI - Optimal design in small amplitude homogenization
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2007/8//
PB - EDP Sciences
VL - 41
IS - 3
SP - 543
EP - 574
AB - This paper is concerned with optimal design problems with a special assumption on the coefficients of the state equation. Namely we assume that the variations of these coefficients have a small amplitude. Then, making an asymptotic expansion up to second order with respect to the aspect ratio of the coefficients allows us to greatly simplify the optimal design problem. By using the notion of H-measures we are able to prove general existence theorems for small amplitude optimal design and to provide simple and efficient numerical algorithms for their computation. A key feature of this type of problems is that the optimal microstructures are always simple laminates.
LA - eng
KW - Optimal design; H-measures; homogenization.; small amplitude homogenization; -measures; shape optimization
UR - http://eudml.org/doc/250029
ER -

References

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