Customized coarse models for highly heterogeneous materials

Abstract

Using a toy model for subsurface flow in highly heterogeneous materials, we demonstrate a methodology for building customized coarse models from generalized eigenvalue problems in overlapping subdomains. We show that this methodology allows to efficiently build accurate multiscale models with very few macroscale degrees of freedom for cases where classical computational homogenization methods break down. Such methods show great potential for modelling highly heterogeneous materials with properties that vary on small length scales. Such problems are typical in many engineering applications, for example subsurface flow or composite materials.