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 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 
02/03/2017 
Fernando GuevaraVasquez University of Utah 
Wave manipulation of particles in a fluid Consider a compressible fluid that is subject to a standing acoustic wave. Particles within the fluid are subject to an acoustic radiation force and tend to move to minima of the associated potential. In many cases, these minima coincide with the nodal sets of the standing wave, which are solutions to the Helmholtz equation. We present two methods for solving the control problem of finding the settings for transducers lining a reservoir (i.e. boundary conditions), necessary to best approximate a desired particle pattern within the reservoir. In the first method, a discretized version of the control problem is reduced to finding the smallest eigenvalue of a matrix. In the second method, we use an approximation result of functions by entire solutions to the Helmholtz equation to give an efficient and explicit solution to the control problem. An application of this principle is to fabricate selectively reinforced composite materials, where the matrix is a photocured polymer and the inclusions are carbon nanotubes. 
02/10/2017 

02/17/2017 
NO SEMINAR 

02/24/2017 
NO SEMINAR 

03/03/2017 
NO SEMINAR 




03/07/2017 
Jose Morales Escalante Technical University of Vienna, Austria 
DG Schemes for Collisional Electron Transport with Insulating Conditions on Rough Boundaries

03/10/2017 
Yunan Yang UT Austin 
Optimal Transport for Seismic Inversion Optimal transport has become a well developed topic in analysis since it was first proposed by Monge in 1781. Due to their ability to incorporate differences in both intensity and spatial information, the related Wasserstein metrics have been adopted in a variety of applications, including seismic inversion. Quadratic Wasserstein metric (W2) has ideal properties like convexity and insensitivity to noise, while conventional L2 norm is known to suffer from local minima. We propose two ways of using W2 in seismic inversion, a tracebytrace comparison solved by sorting, and the global comparison which requires numerical solution to MongeAmpere equation. 
03/17/2017 
SPRING BREAK 

03/24/2017 
Samuel Cole University of Illinois at Chicago 
A simple algorithm for spectral clustering of random graphs A basic problem in data science is to partition a data set into “clusters" of similar data. When the data are represented in a matrix, the spectrum of the matrix can be used to capture this similarity. This talk will consider how this spectral clustering performs on random matrices. Specifically, we consider the planted partition model, in which $n = ks$ vertices of a random graph are partitioned into $k$ clusters, each of size $s$. Edges between vertices in the same cluster and different clusters are included with constant probability $p$ and $q$, respectively (where $0 \le q < p \le 1$). We present a simple, efficient algorithm that, with high probability, recovers the clustering as long as the cluster sizes are are least $\Omega(\sqrt{n})$. 
03/31/2017 

04/07/2017 
Peijun Li Purdue University 
Inverse Source Problems for Wave Propagation The inverse source problems, as an important research subject in inverse scattering theory, have significant applications in diverse scientific and industrial areas such as antenna design and synthesis, medical imaging, optical tomography, and fluorescence microscopy. Although they have been extensively studied by many researchers, some of the fundamental questions, such as uniqueness, stability, and uncertainty quantification, still remain to be answered. In this talk, our recent progress will be discussed on the inverse source problems for acoustic, elastic, and electromagnetic waves. I will present a new approach to solve the stochastic inverse source problem. The source is assumed to be a random function driven by the additive white noise. The inverse problem is to determine the statistical properties of the random source. The stability will be addressed for the deterministic counterparts of the inverse source problems. We show that the increasing stability can be achieved by using the Dirichlet boundary data at multiple frequencies. I will also highlight ongoing projects in random medium and timedomain inverse problems. 
04/14/2017 
Luis Chacon LANL 
A Multiscale, Conservative, Implicit 1D2V Multispecies VlasovFokkerPlanck Solver for ICF Capsule Implosion Simulations Plasma collisionality conditions during the implosion of an ICF
capsule vary widely. Early in the implosion process, the plasma is
cold and very collisional. Later in the implosion, however, the
plasma becomes very hot, and the collisional mean free path
becomes a large fraction of the system size. In this regime,
kinetic phenomena may become important, and a fully kinetic
treatment is needed to assess their impact on compression and
yield in 


04/21/2017 
Mike O'Neil Courant Institute 
Integral equation methods for the LaplaceBeltrami problem The reformulation of many of the classical constantcoefficient PDEs of mathematical physics (e.g. Laplace, Helmholtz, Maxwell, etc.) as boundary integral equations is a standard mathematical tool, which, when coupled with iterative solvers and fast algorithms such as fast multipole methods (FMMs), allows for the nearly optimaltime solution of these PDEs. Extending these methods to variable coefficient PDEs, especially those defined along surfaces, is not straightforward and ongoing research. In this talk, we will address the problem of solving the LaplaceBeltrami problem along surfaces in three dimensions. The LaplaceBeltrami problem is a variable coefficient PDE, with applications in electromagnetics, fluidstructure interactions, and surface diffusions. Our resulting integral equation is ready for acceleration using standard FMMs for Laplace potentials; several numerical examples will be provided. 
04/28/2017 
Jean Ragusa Texas A&M 
TBA 
05/05/2017 
Carlos Borges ICES, UT Austin 
High Resolution Solution of Inverse Scattering Problems I describe a fast, stable framework for the solution of the inverse acoustic scattering problem. Given full aperture far field measurements of the scattered field for multiple angles of incidence, the recursive linearization is used to obtain high resolution reconstructions of properties of the scatterer. Despite the fact that the underlying optimization problem is formally illposed and nonconvex, recursive linearization requires only the solution of a sequence of linear least squares problems at successively higher frequencies. By seeking a suitably bandlimited approximation of the sound speed prole, each least squares calculation is wellconditioned and involves the solution of a large number of forward scattering problems. For two dimension problems we employ spectrally accurate, fast direct solvers. For the largest problems considered, approximately one million partial differential equations were solved, requiring approximately two days to compute using a parallel MATLAB implementation on a multicore workstation. 