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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
Hongkai Zhao
UC Irvine
Title: Approximate separability of Green's functions

Abstract: Approximate separable representation of the Green's functions for differential operators is an important question in the analysis of differential equations and development of efficient numerical algorithms. It can reveal the intrinsic complexity or intrinsic degrees of freedom of the corresponding differential equation. Computationally, being able to approximate the Green's function as a sum with few separable terms is equivalent to the existence of low rank approximations of the discretized system, which can be explored for matrix compression and fast solution techniques such as in fast multiple method and direct matrix inverse solver. In this talk, we will mainly focus on the Helmholtz equation in high frequency limit based on a geometric characterization of the relation between two Green's functions and a tight dimension estimate for the best linear subspace approximating a set of almost orthogonal vectors. We derive both lower bounds and upper bounds and show their sharpness and implications for computation setups that are commonly used in practice. We will also make comparisons with other types of differential operators such as coercive elliptic differential operator with rough coefficients in divergence form. This is a joint work with Bjorn Engquist.

Date: Tuesday, March 21, 2017
Time: 4:30 pm
Location: Wean Hall 7218
Submitted by:  Ian Tice