Abstract: Asymptotic methods are a very powerful tool used for solving algebraic and differential equations. While local methods provide predictions for small neighborhoods around selected points of interest, global methods give us an overview of the behavior of the system as a whole. In this presentation, we will demonstrate how to use these methods, especially homogenization and multiple scale methods, to effectively describe diffusive motion in a material with nonhomogeneous spatial dependence. This procedure is a pathway to solving many optimization problems related to filters of all kinds.