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.
Keywords: Homogenization, multiscale method, hierarchical hybrid grids
@article{M2AN_2021__55_S1_S149_0,
author = {Hannukainen, Antti and Mourrat, Jean-Christophe and Stoppels, Harmen T.},
title = {Computing homogenized coefficients \protect\emph{via} multiscale representation and hierarchical hybrid grids},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {S149--S185},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {Suppl\'ement},
doi = {10.1051/m2an/2020024},
mrnumber = {4221305},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2020024/}
}
TY - JOUR AU - Hannukainen, Antti AU - Mourrat, Jean-Christophe AU - Stoppels, Harmen T. TI - Computing homogenized coefficients via multiscale representation and hierarchical hybrid grids JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - S149 EP - S185 VL - 55 IS - Supplément PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2020024/ DO - 10.1051/m2an/2020024 LA - en ID - M2AN_2021__55_S1_S149_0 ER -
%0 Journal Article %A Hannukainen, Antti %A Mourrat, Jean-Christophe %A Stoppels, Harmen T. %T Computing homogenized coefficients via multiscale representation and hierarchical hybrid grids %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P S149-S185 %V 55 %N Supplément %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2020024/ %R 10.1051/m2an/2020024 %G en %F M2AN_2021__55_S1_S149_0
Hannukainen, Antti; Mourrat, Jean-Christophe; Stoppels, Harmen T. Computing homogenized coefficients via multiscale representation and hierarchical hybrid grids. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021), pp. S149-S185. doi: 10.1051/m2an/2020024
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