| Issue |
ESAIM: M2AN
Volume 55, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
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|---|---|---|
| Page(s) | S149 - S185 | |
| DOI | https://doi.org/10.1051/m2an/2020024 | |
| Published online | 26 February 2021 | |
Computing homogenized coefficients via multiscale representation and hierarchical hybrid grids
1
Department of Mathematics and Systems Analysis, Aalto University, Espoo, Finland
2
DMA, Ecole normale supérieure, CNRS, PSL University, Paris, France
* Corresponding author: mourrat@dma.ens.fr
Received:
19
June
2019
Accepted:
5
April
2020
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.
Mathematics Subject Classification: 65N55 / 35B27
Key words: Homogenization / multiscale method / hierarchical hybrid grids
© The authors, published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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