Computing homogenized coefficients via multiscale representation and hierarchical hybrid grids
For researchers in computational homogenization, this method reduces memory and time requirements, enabling desktop computation of homogenized coefficients.
The paper presents an efficient method for computing homogenized coefficients of divergence-form operators with random coefficients, achieving computation in seconds (2D) or minutes (3D) on a laptop with a few percent precision.
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.