

August 28, 2015
Junshan Lin
Department of Mathematics and Statistics, Auburn University
Location and Time: Parker Hall 328, 2pm3pm
Title: Inverse Source Problems for the Acoustic and Electromagnetic Waves
Abstract: This talk seeks to give an introduction to inverse problems. I will focus on the inverse source problem (ISP), which is a typical type of inverse problem for its important practical applications, clear math, and close relations to other inverse scattering problems.
In the first half of the talk, I will give an overview of the ISP and explain in details about the illposedness, which is a common issue for most inverse problems, based upon the mathematical structure behind the ISP. This part is intended for graduate students and those who do not have any background in inverse problems. The second half of the talk will consist of more recent developments for this topic. More precisely, I will illustrate how the illposedness of the ISP can be alleviated with multiple frequency data or when some a priori information about the source is given. Both the theory and numerics will be covered.

September 11, 2015 (special applied math seminar)
Hongkai Zhao
Department of Mathematics, University of California, Irvine
Location and Time: Parker Hall 250, 4pm5pm
Title: Approximate separability of Green's function and intrinsic complexity of differential operators
Abstract: Approximate separable representation of the Green's functions for differential operators is a fundamental question in the analysis of differential equations and development of efficient numerical algorithms. It can reveal intrinsic complexity, e.g., Kolmogorov nwidth or degrees of freedom of the corresponding differential equation. Computationally, being able to approximate a Green's function as a sum with few separable terms is equivalent to the existence of low rank approximation 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 Helmholtz equation in the high frequency limit for which we developed a new approach to study the approximate separability of Green's function based on an 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 and hyperbolic differential operator. This is a joint work with Bjorn Engquist.

September 18, 2014 (special applied math seminar)
Paul Martin
Department of Mathematics and Statistics, Colorado School of Mines
Location and Time: Parker Hall 250, 2pm3pm
Title: Acoustic and Electric Faraday Cages
Abstract: A Faraday cage is used for shielding from external fields. We consider
simple twodimensional mathematical models of cages, using many
identical small circles to represent the crosssections of many parallel
wires. The main emphasis of the talk will be on periodic configurations
of N small circles distributed evenly around a large circle (a ring). We
calculate the fields around the wires due to an ambient (or incident)
field, and then we investigate what happens when N gets large so that
the gaps between the wires shrinks. We expect that, in the limit, the
cage will behave as a ring (with no gaps), and this expectation is
confirmed. However, we will see that the limiting problem is approached
very slowly.

September 25, 2015
TinYau Tam
Department of Mathematics and Statistics, Auburn University
Location and Time: Parker Hall 328, 2pm3pm
Title: TBA
Abstract: TBA

October 2, 2015
HansWerner van Wyk
Department of Mathematics and Statistics, Auburn University
Location and Time: Parker Hall 328, 2pm3pm
Title: Computing with Surface Roughness
Abstract: The importance of surface texture/roughness in the modeling of various physical processes involving heat transfer, diffusion, and flow, has been widely established experimentally. However, the precise variations in surface height are rarely directly observable. We discuss some statistical models that are commonly used to describe surface roughness and outline some methods to account for such statistical variations in numerical solutions of associated partial differential equations.

October 23, 2015
Todd Burwell
Boeing Research Center, Huntsville, AL
Location and Time: Parker Hall 352, 10am11am
(special time!!)
Title: An Overview of Applied Mathematics at Boeing

November 6, 2015
Yanzhao Cao
Department of Mathematics and Statistics, Auburn University
Location and Time: Parker Hall 328, 2pm3pm
Title: TBA
Abstract: TBA
