Math/ICES Center of Numerical Analysis Seminar (Spring 2017)

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






02/17/2017


NO SEMINAR




02/24/2017


NO SEMINAR




03/03/2017


NO SEMINAR




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




03/24/2017






03/31/2017






04/07/2017

Peijun Li

Purdue University

TBA




04/14/2017






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

TBA




05/05/2017