Reduction of the resonance error. Part 1: Approximation of homogenized coefficients

Gloria, Antoine

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1142/S0218202511005507

Title :

Reduction of the resonance error. Part 1: Approximation of homogenized coefficients

Author(s) :

Gloria, Antoine [Auteur]
SImulations and Modeling for PArticles and Fluids [SIMPAF]

Journal title :

Mathematical Models and Methods in Applied Sciences

Pages :

1601-1630

Publisher :

World Scientific Publishing

Publication date :

2011

ISSN :

0218-2025

HAL domain(s) :

Mathématiques [math]/Analyse numérique [math.NA]

English abstract : [en]

This paper is concerned with the approximation of effective coefficients in homogenization of linear elliptic equations. One common drawback among numerical homogenization methods is the presence of the so-called resonance ...
Show more >This paper is concerned with the approximation of effective coefficients in homogenization of linear elliptic equations. One common drawback among numerical homogenization methods is the presence of the so-called resonance error, which roughly speaking is a function of the ratio $\epsilon/\eta$, where $\eta$ is a typical macroscopic lengthscale and $\epsilon$ is the typical size of the heterogeneities. In the present work, we propose an alternative for the computation of homogenized coefficients (or more generally a modified cell-problem), which is a first brick in the design of effective numerical homogenization methods. We show that this approach drastically reduces the resonance error in some standard cases.Show less >

Language :

Anglais

Popular science :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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