A Comparison of Multiresolution and Classical One-Dimensional Homogenization Schemes

AbstractHomogenization 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