Seminars are held on Mondays from 2:30 - 3:30PM in CULM 611, unless otherwise noted.

For questions about the seminar schedule, please contact Thi Phong Nguyen.

September 25

Manas Rachh, Flatiron Institute

Location: CULM 611

Edge Effects at Insulator Interfaces

In this talk, we will discuss edge effects at insulator interfaces for two models: Klein-Gordon singular waveguides and the Dirac equation. In many physical regimes of interest, these setups tend to have waves that propagate along the interface of two bulk materials, even when these materials are insulating, i.e. waves in the bulk are evanescent. The interface waves present difficulties in the form of non-uniqueness for equivalent integral equation formulations. We will discuss two different methods to mediate this issue: a preconditioner based on a surface Helmholtzian, and a complex scaling approach which deforms the integral equation into the complex plane. We show that both of these approaches result in modified integral equations whose solutions are numerically compactly supported and thus can be efficiently discretized using standard numerical solvers. We demonstrate the efficiency of both these methods through several numerical examples implemented in chunkie: an easy-to-use software package in MATLAB with state-of-the-art integral equation solvers.

October 9

Arnold D. Kim, UC Merced

Location: Webex

Quantitative SAR Imaging of Dispersive Targets

We introduce a dispersive point target model and extend the synthetic aperture radar (SAR) imaging problem to (i) identify and locate these targets and (ii) recover their frequency-dependent reflectivities. We show that Kirchhoff migration (KM) is able to identify dispersive point targets in an imaging region. However, KM predicts target locations that are shifted in range from their true locations. Because of this range shift, we cannot recover the complex-valued frequency dependent reflectivity, but we can recover its absolute value and hence its radar cross-section (RCS). After showing results for an unbounded homogeneous medium, we consider dispersive targets situated below an interface separating two adjacent half spaces as a model for the buried landmine problem.

October 23

Thi-Thao-Phuong Hoang, Auburn University

Location: Webex

November 6

Montanelli Hadrien, INRIA and Institute Polytechnique de Paris (France)

Location: Webex

The Linear Sampling Method for Random Sources

We present in this talk an extension of the linear sampling method for solving the sound-soft inverse acoustic scattering problem with randomly distributed point sources. The theoretical justification of our method is based on the Helmholtz–Kirchhoff identity, the cross-correlation between measurements, and the volume and imaginary near-field operators. Implementations in MATLAB using boundary elements, the SVD, Tikhonov regularization, and Morozov’s discrepancy principle will also be discussed.