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

Antoine Gloria 1
1 SIMPAF - SImulations and Modeling for PArticles and Fluids
Inria Lille - Nord Europe, LPP - Laboratoire Paul Painlevé - UMR 8524
Abstract : 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.
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Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2011, 21 (8), pp.1601-1630. 〈10.1142/S0218202511005507〉
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Antoine Gloria. Reduction of the resonance error. Part 1: Approximation of homogenized coefficients. Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2011, 21 (8), pp.1601-1630. 〈10.1142/S0218202511005507〉. 〈inria-00457159〉

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