Computing homogenized coefficients via multiscale representation and hierarchical hybrid grids
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Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Date
2021-02-26
Major/Subject
Mcode
Degree programme
Language
en
Pages
S149-S185
Series
ESAIM: Mathematical Modelling and Numerical Analysis, Volume 55
Abstract
We present an efficient method for the computation of homogenized coefficients of divergence-form operators with random coefficients. The approach is based on a multiscale representation of the homogenized coefficients. We then implement the method numerically using a finite-element method with hierarchical hybrid grids, which is a semi-implicit method allowing for significant gains in memory usage and execution time. Finally, we demonstrate the efficiency of our approach on two- and three-dimensional examples, for piecewise-constant coefficients with corner discontinuities. For moderate ellipticity contrast and for a precision of a few percentage points, our method allows to compute the homogenized coefficients on a laptop computer in a few seconds, in two dimensions, or in a few minutes, in three dimensions.Description
Publisher Copyright: © 2021 The authors, published by EDP Sciences, SMAI. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.
Keywords
Hierarchical hybrid grids, Homogenization, Multiscale method
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Citation
Hannukainen , A , Mourrat , J C & Stoppels , H T 2021 , ' Computing homogenized coefficients via multiscale representation and hierarchical hybrid grids ' , ESAIM: Mathematical Modelling and Numerical Analysis , vol. 55 , pp. S149-S185 . https://doi.org/10.1051/m2an/2020024
