Volume 55, 2021Regular 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
|Page(s)||S149 - S185|
|Published online||26 February 2021|
Computing homogenized coefficients via multiscale representation and hierarchical hybrid grids
Department of Mathematics and Systems Analysis, Aalto University, Espoo, Finland
2 DMA, Ecole normale supérieure, CNRS, PSL University, Paris, France
* Corresponding author: firstname.lastname@example.org
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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