Time: Tuesday, November 3, 2015
2:00pm
MTH1311

Speaker: Dr. Christina Frederick (Georgia Tech)

Title: Nonuniform sampling and multiscale computation

Abstract: The Heterogeneous Multiscale Method (HMM) is a framework for efficiently solving problems that couple physical models on different scales, for example, determining the effective properties of composite materials. Simulations often involve discretizations by means of sampling. We discuss an interesting connection between HMM for numerical homogenization problems and nonuniform sampling strategies for bandlimited functions. The sampling and reconstruction problem is formulated by viewing typical functions in homogenization theory as structured multiband signals. Our main result is a stable reconstruction algorithm for this class of signals using $d-$dimensional periodic nonuniform sampling. The proposed sampling sets are of optimal rate according to the minimal sampling requirements of Landau.