A comparison of multiresolution and classical one-dimensional homogenization schemes

Abstract

Homogenization is a collection of methods for extracting or constructing equations for the coarse-scale behavior of solutions to equations which incorporate many scales. This paper compares the classical method of homogenization with the recently developed multiresolution strategy for a particular class of one-dimensional second-order elliptic equations. We also examine several physical examples which highlight the distinctions between the two methods. © 1998 Academic Press.