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Article Dans Une Revue ESAIM: Mathematical Modelling and Numerical Analysis Année : 2021

Computing homogenized coefficients via multiscale representation and hierarchical hybrid grids

Résumé

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.
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Dates et versions

hal-03154035 , version 1 (26-02-2021)

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Antti Hannukainen, Jean-Christophe Mourrat, Harmen T. Stoppels. Computing homogenized coefficients via multiscale representation and hierarchical hybrid grids. ESAIM: Mathematical Modelling and Numerical Analysis, 2021, 55, pp.S149-S185. ⟨10.1051/m2an/2020024⟩. ⟨hal-03154035⟩
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