  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.
