An Embedded Corrector Problem for Homogenization. Part I: Theory
| Autor: | Virginie Ehrlacher, Frédéric Legoll, Eric Cancès, Benjamin Stamm, Shuyang Xiang |
|---|---|
| Přispěvatelé: | MATHematics for MatERIALS (MATHERIALS), Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), École des Ponts ParisTech (ENPC)-École des Ponts ParisTech (ENPC)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), École des Ponts ParisTech (ENPC), Laboratoire Navier (NAVIER UMR 8205), École des Ponts ParisTech (ENPC)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel, Rheinisch-Westfälische Technische Hochschule Aachen University (RWTH), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), École des Ponts ParisTech (ENPC)-École des Ponts ParisTech (ENPC), Rheinisch-Westfälische Technische Hochschule Aachen (RWTH) |
| Rok vydání: | 2020 |
| Předmět: |
Efficient algorithm
Ecological Modeling General Physics and Astronomy Numerical Analysis (math.NA) 010103 numerical & computational mathematics General Chemistry 01 natural sciences Homogenization (chemistry) Computer Science Applications 010101 applied mathematics Homogeneous Modeling and Simulation FOS: Mathematics Applied mathematics Mathematics - Numerical Analysis 0101 mathematics [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] Mathematics |
| Zdroj: | Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2020, 18 (3), pp.1179-1209. ⟨10.1137/18M120035X⟩ Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Society for Industrial and Applied Mathematics, 2020, 18 (3), pp.1179-1209. ⟨10.1137/18M120035X⟩ |
| ISSN: | 1540-3467 1540-3459 |
| Popis: | International audience; This article is the first part of a two-fold study, the objective of which is the theoretical analysis and numerical investigation of new approximate corrector problems in the context of stochastic homogenization. We present here three new alternatives for the approximation of the homogenized matrix for diffusion problems with highly-oscillatory coefficients. These different approximations all rely on the use of an embedded corrector problem (that we previously introduced in [Cances, Ehrlacher, Legoll and Stamm, C. R. Acad. Sci. Paris, 2015]), where a finite-size domain made of the highly oscillatory material is embedded in a homogeneous infinite medium whose diffusion coefficients have to be appropriately determined. The motivation for considering such embedded corrector problems is made clear in the companion article [Cances, Ehrlacher, Legoll, Stamm and Xiang, J. Comput. Phys 2020], where a very efficient algorithm is presented for the resolution of such problems for particular heterogeneous materials. In the present article, we prove that the three different approximations we introduce converge to the homogenized matrix of the medium when the size of the embedded domain goes to infinity. |
| Databáze: | OpenAIRE |
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