Plenary Speaker

Yalchin Efendiev, Department of Mathematics, Texas A&M University

Numerical Homogenization and Multiscale Methods for Heterogeneous Problems

In this talk, I will discuss multiscale model reduction techniques for problems in heterogeneous media. I will discuss homogenization-based multiscale methods and their relation to multiscale finite element methods. I will describe a general multiscale framework for constructing local (space-time) reduced order models for problems with multiple scales and high contrast. I will focus on a recently proposed method, Generalized Multiscale Finite Element Method, that systematically constructs local multiscale finite element basis functions on a coarse grid. I will discuss the issues related to the construction of multiscale basis functions, main ingredients of the method, and a number of applications. These methods are intended for multiscale problems without scale separation and high contrast.