Volume 28, 2022
|Number of page(s)||47|
|Published online||01 July 2022|
Mathematical analysis of a coupling method for the practical computation of homogenized coefficients
École Nationale des Ponts et Chaussées and Inria Paris, 6 et 8 avenue Blaise Pascal, 77455 Marne-La-Vallée Cedex 2, France
* Corresponding author: email@example.com
Accepted: 26 April 2022
We present the mathematical study of a computational approach originally introduced by R. Cottereau [Int. J. Numer. Meth. Eng. 95 (2013) 71-90]. The approach aims at evaluating the effective (a.k.a. homogenized) coefficient of a medium with some fine-scale structure. It combines, using the Arlequin coupling method, the original fine-scale description of the medium with an effective description and optimizes upon the coefficient of the effective medium to best fit the response of an equivalent purely homogeneous medium. We prove here that the approach is mathematically well-posed and that it provides, under suitable assumptions, the actual value of the homogenized coefficient of the original medium in the limit of asymptotically infinitely fine structures. The theory presented here therefore usefully complements our numerical developments of Gorynina et al. [SIAM J. Sci. Comput. 43 (2021) A1273-A1304].
Mathematics Subject Classification: 35J / 35B27 / 74Q15
Key words: Elliptic PDEs / oscillatory coefficients / homogenization / coarse-graining
© The authors. Published by EDP Sciences, SMAI 2022
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