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High-dimensional approximation using equilibrium measures
Date: 2016/4/25             Browse: 255

High-dimensional approximation using equilibrium measures

Speaker: Akil Narayan

Time: Apr 25, 3:30pm - 4:30pm.

Location: Room 405, Administration Center

Abstract:

We consider the problem of approximating solutions to parameter-dependent partial differential equations. Standard approaches frequently involve collecting PDE solutions computed at a judiciously-chosen finite set of parametric samples, and using these to predict the solution manifold behavior for all parameter values. In this talk we consider choosing parameter samples according to the pluripotential equilibrium measure. We also show that such an approach typically yields very stable, high-order computational procedures for parametrized PDE approximation, including discrete least-squares and compressive sampling.

Bio:

Dr. Narayan received his Bachelor's Degree from Northwestern University, and his Master's and PhD degrees from Brown University. He served as a postdoctoral researcher at Purdue University until starting an Assistant Professorship in the Mathematical Department at the University of Massachusetts Dartmouth. Dr. Narayan is receipient of a 2015 Young Investigator Program Award from the Air Force Office of Scientific Research. Dr. Narayan joined University of Utah in July 2015.

Research Interests:

Dr. Narayan's primary research interests lie in approximation theory and methods, sparse and regularized representations, mathematical shape analysis, high-order numerical methods, and data assimilation. He applies these methods to parameterized systems, high-dimensional approximation, and hierarchical model simulations.

SIST-Seminar 16027