Time and Location: Friday, 1:00-2:00PM, 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 Guevara-Vasquez 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 photo-cured polymer and the inclusions are carbon nanotubes. |
02/10/2017 |
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02/17/2017 |
NO SEMINAR |
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02/24/2017 |
NO SEMINAR |
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03/03/2017 |
NO SEMINAR |
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03/07/2017 |
Jose Morales Escalante Technical University of Vienna, Austria |
DG Schemes for Collisional Electron Transport with Insulating Conditions on Rough Boundaries
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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 trace-by-trace comparison solved by sorting, and the global comparison which requires numerical solution to Monge-Ampere equation. |
03/17/2017 |
SPRING BREAK |
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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 |
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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 time-domain inverse problems. |
04/14/2017 |
Luis Chacon LANL |
A Multiscale, Conservative, Implicit 1D-2V Multispecies Vlasov-Fokker-Planck 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 |
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04/21/2017 |
Mike O'Neil Courant Institute |
Integral equation methods for the Laplace-Beltrami problem The reformulation of many of the classical constant-coefficient 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 optimal-time 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 Laplace-Beltrami problem along surfaces in three dimensions. The Laplace-Beltrami problem is a variable coefficient PDE, with applications in electromagnetics, fluid-structure 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 |
Massively Parallel Radiation Transport Simulations: Current Status and Challenges Ahead In this talk, I will provide an overview of solution techniques and iterative techniques employed to solve the first-order form of the radiation transport equation on massively parallel machines. A review of scaling efficiency for transport sweeps (up to order 1-million processes) will be provided for logically Cartesian grids. Challenges posed by the need to move to unstructured (load-unbalanced) grids and ongoing research will be discussed. Diffusion-based synthetic accelerators for the one-speed (within-group) and multigroup transport equations will be presented and issues related to massively parallel diffusion-accelerated transport sweeps be analyzed. |
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 ill-posed and non-convex, recursive linearization requires only the solution of a sequence of linear least squares problems at successively higher frequencies. By seeking a suitably band-limited approximation of the sound speed prole, each least squares calculation is well-conditioned 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 multi-core workstation. |