Computing homogenized coefficients<i>via</i>multiscale representation and hierarchical hybrid grids

We present an efficient method for the computation of homogenized coefficients divergence-form operators with random coefficients. The approach is based on a multiscale representation then implement numerically using finite-element hierarchical hybrid grids, which semi-implicit allowing significant gains in memory usage and execution time. Finally, we demonstrate efficiency our two- three-dimensional examples, piecewise-constant corner discontinuities. For moderate ellipticity contrast precision few percentage points, allows to compute laptop computer seconds, two dimensions, or minutes, three dimensions.