Time and Location: Friday, 1:002:00PM, POB 6.304 Special time and locations are indicated in red.
If you are interested in meeting a speaker, please contact Kui Ren (ren@math.utexas.edu)
Here are the links to the past seminars: Fall 2017 Spring 2017 Fall 2016 Spring 2016 Fall 2015 Spring 2015 Fall 2014 Spring 2014 Spring 2013 Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009
Dates 
Spekers and Hosts 
Title and Abstract 



01/26/2018 
Li Wang SUNY Buffalo 
Front capturing schemes for nonlinear PDEs with a free boundary limit Evolution in physical or biological systems often involves interplay between nonlinear interaction among the constituent “particles”, and convective or diffusive transport, which is driven by density dependent pressure. When pressuredensity relationship becomes highly nonlinear, the evolution equation converges to a free boundary problem as a stiff limit. In terms of numerics, the nonlinearity and degeneracy bring great challenges, and there is lack of standard mechanism to capture the propagation of the front in the limit. In this talk, I will introduce a numerical scheme for tumor growth models based on a predictioncorrection reformulation, which naturally connects to the free boundary problem in the discrete sense. As an alternative, I will present a variational method for a class of continuity equations (such as KellerSegel model) using the gradient flow structure, which has builtin stability, positivity preservation and energy decreasing property, and serves as a good candidate in capturing the stiff pressure limit. 



02/02/2018 





02/05/2018 4:005:00PM RLM 5.104 (Mathematics Colloqium) 
Liliana Borcea University of Michigan 
Untangling the nonlinearity in inverse scattering using datadriven reduced order models We discuss an inverse problem for the wave equation, where an array of sensors probes an unknown, heterogeneous medium with pulses and measures the scattered waves. The goal in inversion is to determine from these measurements scattering structures in the medium, modeled mathematically by a reflectivity function. Most imaging methods assume a linear mapping between the unknown reflectivity and the array data. The linearization, known as the Born (single scattering) approximation is not accurate in strongly scattering media, so the reconstruction of the reflectivity may be poor. We show that it is possible to remove the multiple scattering (nonlinear) effects from the data using a reduced order model (ROM). The ROM is defined by an orthogonal projection of the wave propagator operator on the subspace spanned by the time snapshots of the solution of the wave equation. The snapshots are known only at the sensor locations, which is enough information to construct the ROM. The main result discussed in the talk is a novel, linearalgebraic algorithm that uses the ROM to map the data to its Born approximation. 



02/06/2018 1:002:00PM RLM 10.176 
Liliana Borcea University of Michigan 
Pulse Reflection in a Random Waveguide with a Turning Point Guided waves arise in a variety of applications like underwater acoustics, optics, the design of musical instruments, and so on. We present an analysis of wave propagation and reflection in an acoustic waveguide with random sound soft boundary and a turning point. The waveguide has slowly bending axis and variable cross section. The variation consists of a slow and monotone change of the width of the waveguide and small and rapid fluctuations of the boundary, on the scale of the wavelength. These fluctuations are modeled as random. The turning point is many wavelengths away from the source, which emits a pulse that propagates toward the turning point, where it is reflected. We consider a regime where scattering at the random boundary has a significant effect on the reflected pulse. We determine from first principles when this effects amounts to a deterministic pulse deformation. This is known as a pulse stabilization result. The reflected pulse shape is not the same as the emitted one. It is damped, due to scattering at the boundary, and is deformed by dispersion in the waveguide. An example of an application of this result is in inverse problems, where the travel time of reflected pulses at the turning points can be used to determine the geometry of the waveguide. 



02/16/2018 
Alexander Mamonov University of Houston 
TBA 



02/23/2018 





03/02/2018 





03/06/2018 
Alexei Novikov Penn State University 
TBA 



03/16/2018 

SPRING BREAK 



03/23/2018 





03/30/2018 

NO SEMINAR 



04/06/2018 
Braxton Osting University of Utah 
TBA 



04/13/2018 





04/20/2018 





04/27/2018 





05/04/2018 

