# 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

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topAllaire, 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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