Computing homogenized coefficients via multiscale representation and hierarchical hybrid grids
Abstract
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.
Cite
@article{arxiv.1905.06751,
title = {Computing homogenized coefficients via multiscale representation and hierarchical hybrid grids},
author = {A. Hannukainen and J. -C. Mourrat and H. Stoppels},
journal= {arXiv preprint arXiv:1905.06751},
year = {2019}
}
Comments
33 pages, 13 figures