Computing homogenized coefficients via multiscale representation and hierarchical hybrid grids

A. Hannukainen , Jean-Christophe Mourrat (1) , H. T Stoppels

1 DMA - Département de Mathématiques et Applications - ENS Paris

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.

Domaines: Analyse numérique [math.NA]

A. Hannukainen, Jean-Christophe Mourrat, H. T Stoppels. Computing homogenized coefficients via multiscale representation and hierarchical hybrid grids. ESAIM: Mathematical Modelling and Numerical Analysis, 2021, ⟨10.1051/m2an/2020024⟩. ⟨hal-02144903⟩