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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.
|ESAIM: Mathematical Modelling and Numerical Analysis
|Published - 26 Feb 2021
|MoE publication type
|A1 Journal article-refereed
- Hierarchical hybrid grids
- Multiscale method
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- 1 Finished
01/01/2018 → 31/12/2020
Project: Academy of Finland: Other research funding