Computational Mathematics Seminar

Posted January 30, 2018

Last modified February 14, 2018

Ellya Kawecki, Oxford University

A discontinuous Galerkin finite element method for Hamilton Jacobi Bellman equations on piecewise curved domains

Abstract: We introduce a discontinuous Galerkin finite element method (DGFEM) for Hamilton Jacobi Bellman equations on piecewise curved domains, and prove that the method is consistent, stable, and produces optimal convergence rates. Upon utilising a long standing result due to N. Krylov, we may characterise the Monge Ampere equation as a HJB equation; in two dimensions, this HJB equation can be characterised further as uniformly elliptic HJB equation, allowing for the application of the DGFEM.

Applied Analysis Seminar
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Posted January 11, 2018

Last modified February 20, 2018

Wei Li, LSU

Fluorescence ultrasound modulated optical tomography in diffusive regime

Fluorescence optical tomography (FOT) is an imaging technology that localizes fluorescent targets in tissues. FOT is unstable and of poor resolution in highly scattering media, where the propagation of multiply-scattered light is governed by the smoothing diffusion equation. We study a hybrid imaging modality called fluorescent ultrasound-modulated optical tomography (fUMOT), which combines FOT with acoustic modulation to produce high-resolution images of optical properties in the diffusive regime. The principle of fUMOT is to perform multiple measurements of photon currents at the boundary as the optical properties undergo a series of perturbations by acoustic radiation, in which way internal information of the optical field is obtained. We set up a Mathematical model for ufUMOT, prove well-posedness for certain choices of parameters, and present reconstruction algorithms and numerical experiments for the well-posed cases.

Informal Topology Seminar
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Posted January 24, 2018

10:00 am - 12:00 pm Lockett 233
Federico Salmoiraghi, Department of Mathematics, LSU

TBD

Topology Seminar
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Posted November 13, 2017

3:30 pm - 4:30 pm Lockett 233
Ivan Levcovitz, CUNY Graduate Center

TBD

Applied Analysis Seminar
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Posted January 10, 2018

Last modified February 12, 2018

Masato Kimura, Kanazawa University, Japan

A phase field model for crack propagation and some applications

Algebra and Number Theory Seminar
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Posted January 15, 2018

3:10 pm - 4:00 pm
Wen-Ching Winnie Li, Pennsylvania State University

TBA

Computational Mathematics Seminar

Posted February 14, 2018

3:30 pm - 4:30 pm 1034 Digital Media Center
Yi Zhang, University of North Carolina at Greensboro

Numerical Approximations for a Singular Elliptic Variational Inequality

Abstract: The displacement obstacle problem of simply supported plates is an example of a fourth order variational inequality. As the bending rigidity tends to zero the problem degenerates to an elastic membrane obstacle problem which is a second order variational inequality. In this talk we will introduce C0 interior penalty methods for this singular perturbed problem with small parameter. Robust error estimates with respect to the parameter will be presented. We also discuss the convergence of numerical solutions to the unperturbed second order elliptic variational inequality. This is joint work with Susanne Brenner and Li-yeng Sung.

Informal Topology Seminar
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Posted January 24, 2018

10:00 am - 12:00 pm Lockett 233
Yu-Chan Chang, Louisiana State University

TBD

Topology Seminar
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Posted October 18, 2017

3:30 pm - 4:30 pm Lockett 233
Bulent Tosun, University of Alabama

TBD

Colloquium
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Posted December 17, 2017

3:30 pm - 4:20 pm TBD
Habib Ouerdiane, University of Tunis El Manar

TBD

Applied Analysis Seminar
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Posted January 16, 2018

Last modified February 20, 2018

Tadele Mengesha, The University of Tennessee, Knoxville

Sobolev regularity estimates for solutions to spectral fractional elliptic equations

Abstract: Global Calderon-Zygmund type estimates are obtained for solutions to fractional elliptic problems over smooth domains. Our approach is based on the "extension problem" where the fractional elliptic operator is realized as a Dirichlet-to-Neumann map corresponding to a degenerate elliptic PDE in one more dimension. This allows the possibility of deriving estimates for solutions to the fractional elliptic equations from that of degenerate elliptic equations. We will confirm this first by obtaining weighted estimates for the gradient of solutions to a class of linear degenerate/singular elliptic problems over a bounded, possibly non-smooth, domain. The class consists of those with coefficient matrix that symmetric, nonnegative definite, and both its smallest and largest eigenvalues are proportion to a particular weight that belongs to a Muckenhoupt class. The weighted estimates are obtained under a smallness condition on the mean oscillation of the coefficients with a weight. This is a joint work with T. Phan.

Computational Mathematics Seminar

Posted January 30, 2018

Last modified February 14, 2018

Liping Wang, Nanjing University of Aeronautics and Astronautics

A Joint Matrix Minimization Approach and the Applications in Collective Face Recognition and Seismic Wavefield Recovery

Abstract: Recently, image-set based face recognition and multi trace seismic wavefield recovery have attracted extensive attention in pattern recognition and geophysical community. Representation coding is one of popular ways for both face recognition and seismic wave reconstruction. Similar representative coding pattern among the group of samples is observed both in facial images and seismic signals. To take account of the collective correlation from a given set of testing samples as well as each individual, a matrix minimization model is presented to jointly representing all the testing samples over the coding bases simultaneously. A generalized matrix norms employed to measure the interrelation of the multiple samples and the entries of each one. For solving the involved matrix optimization problem, a unified algorithm is developed and the convergence analysis is accordingly demonstrated for the range of parameters p in (0,1]. Extensive experiments on public data of facial images and real-world seismic waves exhibit the efficient performance of the joint technique over the state-of-the-art methods in recognition or recovery accuracy and computational cost.

Topology Seminar
Seminar website

Posted October 18, 2017

3:30 pm - 4:30 pm
Ina Petkova, Dartmouth College

TBD

Applied Analysis Seminar
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Posted January 10, 2018

Last modified February 5, 2018

Prashant Kumar Jha, LSU

Numerical analysis of finite element approximation of nonlocal fracture models

We discuss nonlocal fracture model and present numerical analysis of finite element approximation. The peridynamic potential considered in this work is the regularized version of the bond-based potential generally considered in peridynamic literature (Silling 2000). In the limit of vanishing nonlocality, peridynamic model behaves like a elastodynamic model away from a crack zone and has a finite fracture energy associate to crack set (Lipton 2014, 2016).Using this property we relate the parameters in a peridynamic potential with given elastic constant and fracture toughness. Before we consider finite element approximation, we show that the problem is well posed. We show the existence of evolutions in H^2 space. We consider finite element discretization in space and central difference in time to approximate the problem. Approximation is shown to converge in L^2 norm at the rate Cttriangle t+C_sh^2/s^2. Here triangle t is the size of time step, h is the mesh size, and is the size of horizon (nonlocal scale). Constants C_t and C_s are independent of h and triangle t. In the absence of nonlinearity, stability of approximation is shown. Numerical results are presented to verify the convergence rate. This is a joint work with Robert Lipton.

Algebra and Number Theory Seminar
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Posted January 16, 2018

3:10 pm - 4:00 pm
Rina Anno, Kansas State University

TBA

Informal Topology Seminar
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Posted January 24, 2018

10:00 am - 12:00 pm Lockett 233
Nurdin Takenov, Louisiana State University

TBD

Topology Seminar
Seminar website

Posted January 10, 2018

Last modified January 12, 2018

Adam Levine, Duke University

TBD

Colloquium
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Posted December 17, 2017

3:30 pm - 4:20 pm TBD
Guozhen Lu, University of Connecticut

TBD

Informal Topology Seminar
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Posted January 24, 2018

10:00 am - 12:00 pm Lockett 233
Sudipta Ghosh, Louisiana State University

TBD

Pasquale Porcelli Lecture Series
Special Lecture Series

Posted November 7, 2017

Last modified January 29, 2018

Irene Fonseca, Carnegie Mellon University

Porcelli Lecture 1: The Mathematics of Inpainting

(The talk is intended to be accessible to High School Students.) In this talk we will illustrate how mathematical techniques can be used in image processing. These play an important role in the creation of digital inpainting methods with a wide spectrum of applications, such as in the process of image restoration of ancient frescoes where missing parts of damaged images are filled in based on the information collected from neighboring areas.

Pasquale Porcelli Lecture Series
Special Lecture Series

Posted November 7, 2017

Last modified January 29, 2018

Irene Fonseca, Carnegie Mellon University

Porcelli Lecture 2: Variational Problems in Materials Science

(Intended to be accessible to Undergraduate Students.) Abstract: Quantum dots are man-made nanocrystals of semiconducting materials. Their formation and assembly patterns play a central role in nanotechnology, and in particular in the optoelectronic properties of semiconductors. Changing the dots' size and shape gives rise to many

applications that permeate our daily lives, such as the new Samsung QLED TV monitor that uses quantum dots to turn "light into perfect color"!

Quantum dots are obtained via the deposition of a crystalline overlayer (epitaxial film) on a crystalline substrate. When the thickness of the film reaches a critical value, the profile of the film becomes corrugated and islands (quantum dots) form. As the creation of quantum dots evolves with time, materials defects appear. Their modeling is of great interest in materials science since material properties, including rigidity and conductivity, can be strongly influenced by the presence of defects such as dislocations.

In this talk we will use methods from the calculus of variations and partial differential equations to model and mathematically analyze the onset of quantum dots, the regularity and evolution of their shapes, and the nucleation and motion of dislocations.

Pasquale Porcelli Lecture Series
Special Lecture Series

Posted November 7, 2017

Last modified January 29, 2018

Irene Fonseca, Carnegie Mellon University

Porcelli Lecture 3: Variational Problems in Imaging Science

(The talk is intended to be accessible to Graduate Students.) Abstract: The mathematical treatment of image processing is strongly hinged on variational methods, partial differential equations, and machine learning. The bilevel scheme combines the principles of machine learning to adapt the model to a given data, while variational methods provide model-based approaches which are mathematically rigorous, yield stable solutions and error estimates. The combination of both leads to the study of weighted Ambrosio-Tortorelli and Mumford-Shah variational models for image processing.

Algebra and Number Theory Seminar
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Posted January 15, 2018

3:10 pm - 4:00 pm
Li Guo, Rutgers University at Newark

TBA

Colloquium
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Posted December 26, 2017

3:30 pm - 4:20 pm TBD
Stefan Kolb, Newcastle University

TBD

Algebra and Number Theory Seminar
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Posted January 16, 2018

3:10 pm - 4:00 pmTBA

Colloquium
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Posted January 12, 2018

3:30 pm - 4:20 pm TBD
Birge Huisgen-Zimmermann, University of California, Santa Barbara

TBD

Topology Seminar
Seminar website

Posted November 12, 2017

Last modified January 8, 2018

Miriam Kuzbary, Rice University

TBD

Colloquium
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Posted January 30, 2018

3:30 pm - 4:20 pm TBD
Luis Silvestre, University of Chicago

TBD