A Multiresolution Strategy for Numerical Homogenization

Abstract

Homogenization may be defined as an analysis in which we construct equations describing coarse-scale behavior of the solution while ignoring fine-scale detail. This work concerns a multiresolution strategy for homogenization of differential equations. As the first step towards a more general treatment of nonlinear ODEs and PDEs, we consider the homogenization via multiresolution analysis (MRA) of systems of linear ODEs with variable coefficients and forcing terms. We develop an efficient numerical approach which generates the coefficients of the homogenized equation. As one of the examples we treat wave propagation in a stratified medium.