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Applied and Computational Mathematics

DMS Applied Mathematics Seminar
Sep 21, 2018 02:00 PM
Parker Hall 328

Speaker: Thi Thao Phuong Hoang  Auburn University

Title:Conservative explicit local time-stepping schemes for the shallow water equations

Abstract: We present explicit local time-stepping (LTS) schemes of second and third order accuracy for the shallow water equations. The system is discretized in space by a C-grid staggering method, namely the TRiSK scheme adopted in MPAS-Ocean, a global ocean model with the capability of resolving multiple resolutions within a single simulation. The time integration is designed based on the strong stability preserving Runge-Kutta (SSP-RK) methods, but different time step sizes can be used in different regions of the domain and are only restricted by respective local CFL conditions. The proposed schemes preserve some important physical quantities in the discrete sense, such as exact conservation of the mass and potential vorticity and conservation of the total energy within time truncation errors. Moreover, they inherit the natural parallelism of the original explicit global time-stepping schemes. Extensive numerical tests are presented to illustrate the performance of the proposed algorithms.

DMS Applied Mathematics Seminar
Aug 31, 2018 02:00 PM
Parker Hall 328

Speaker: Junshan Lin (Auburn University)


Title: Mathematical Theories and Computational Approaches for Resonances Through Nanoholes


Abstract: In this talk, I will focus on certain resonance phenomena that occur in nano-optics, which leads to the so-called extraordinary optical transmission (EOT) phenomenon widely used in bio-sensing, near-field imaging, etc.


Mathematical theories will be presented to understand such resonance phenomena and quantify the EOT rigorously. Computational approaches will also be discussed to obtain those resonances in an effective manner. I will try to make the talk accessible to graduate students with some PDE background.

DMS Applied Math Seminar
Apr 13, 2018 02:00 PM
Parker Hall 328

Speaker: Prof. William Rundell, Texas A&M University

Title: Inverse Problems for Anomalous Diffusion Models

DMS Applied Mathematics Seminar
Apr 06, 2018 02:00 PM
Parker Hall 328

Speaker: Prof. Tian-Xiao He, Department of Mathematics at Illinois Wesleyan University. 

Title: Generalization of Stirling Numbers and Stirling Functions

Abstract:  Here we present a unified approach to Stirling numbers and their generalizations, as well as generalized Stirling functions by using generalized factorial functions, k-Gamma functions, and generalized divided difference. Previous well-known extensions of Stirling numbers due to Riordan, Carlitz, Howard, Charalambides-Koutras, Gould-Hopper, Hsu-Shiue, Tsylova Todorov, Ahuja-Enneking, and Stirling functions introduced by Butzer and Hauss, Butzer, Kilbas, Trujilloet, and others are included as particular cases of our generalization. Some basic properties related to our general pattern such as their recursive relations and generating functions are discussed. Three algorithms for calculating the Stirling numbers based on our generalization are also given, which include a comprehensive algorithm using the characterization of Riordan arrays.
DMS Applied Mathematics Seminar
Mar 23, 2018 02:00 PM
Parker Hall 328

Speaker: Professor Jianliang Qian, Michigan State University.

Title: Babich-like ansatz for point-source Maxwell's equations

Abstract: We propose a novel Babich-like ansatz consisting of an infinite series of dyadic coefficients (three-by-three matrices) and spherical Hankel functions for solving point-source Maxwell's equations in an inhomogeneous medium so as to produce the so-called dyadic Green's function. Using properties of spherical Hankel functions, we derive governing equations for the unknown asymptotics of the ansatz including the traveltime function and dyadic coefficients. By proposing matching conditions at the point source, we rigorously derive asymptotic behaviors of these geometrical-optics ingredients near the source so that their initial data at the source point are well defined. To verify the feasibility of the proposed ansatz, we truncate the ansatz to keep only the first two terms, and we further develop partial-differential-equation based Eulerian approaches to compute the resulting asymptotic solutions. Numerical examples demonstrate that our new ansatz yields a uniform asymptotic solution in the region of space containing a point source but no other caustics.

Graduate students are especially urged to attend.
DMS Applied Mathematics Seminar
Feb 23, 2018 02:00 PM
Parker Hall 328

Speaker: Martin Short from Georgia Tech

Title: Modeling and predicting urban crime – How data assimilation helps bridge the gap between stochastic and continuous models

Abstract: Data assimilation is a powerful tool for combining mathematical models with real-world data to make better predictions and estimate the state and/or parameters of dynamical systems. In this talk I will give an overview of some work on models for predicting urban crime patterns, ranging from stochastic models to differential equations. I will then present some work on data assimilation techniques that have been developed and applied for this problem, so that these models can be joined with real data for purposes of model fitting and crime forecasting.

DMS Applied Mathematics Seminar
Feb 02, 2018 02:00 PM
Parker Hall 328

Speaker: Lianzhang Bao, Jilin University

Title: Traveling wave solutions in backward forward parabolic equation and others

Abstract:  In the talk I will first derive backward forward parabolic equations from population dynamics via a biased random walk, then some properties and the existence of the traveling wave solutions to these equations will be discussed. Finally, some results related to partial differential equation control and inverse problems will be presented.

DMS Applied Mathematics Seminar
Dec 01, 2017 02:00 PM
Parker Hall 328

Speaker: Prof. Peter Monk, University of Delaware

Title: Inverse Scattering in a Waveguide

Abstract: I shall present a study of the inverse problem of determining the shape of inclusions in a sound hard waveguide using either frequency or time domain data. Mostly I will focus on the time domain problem and start by proving existence and uniqueness for the forward problem. Then I will derive a numerical method using time domain integral equations. For the inverse problem I will use the Linear Sampling Method due to Colton and Kirsch. After analysis of the time domain inversion scheme, I will provide a few numerical examples.

DMS Applied Mathematics Seminar
Nov 17, 2017 12:30 PM
Parker Hall 246


Speaker: Dr. Bo Liu, Computer Science Department, AU

Title: Gradient, Semi-gradient and Pseudo-gradient Reinforcement Learning

Abstract: In this talk, I will present the establishment of a unified general framework for stochastic-gradient-based temporal-difference learning algorithms that use proximal gradient methods. The primal-dual saddle-point formulation is introduced, and state-of-the-art stochastic gradient solvers, such as mirror descent and extragradient are used to design several novel reinforcement learning algorithms. The finite-sample analysis is given along with detailed empirical experiments to demonstrate the effectiveness of the proposed algorithms. Several important extensions, such as control learning, variance reduction, acceleration, and regularization will also be discussed in detail.

DMS Applied Mathematics Seminar
Nov 10, 2017 02:00 PM
Parker Hall 328

Speaker: Hyesuk Lee (Clemson University)

Title: Finite element approximation and analysis for non-Newtonian fluid-structure interaction

Abstract:  Numerical study of non-Newtonian fluid-structure interaction (FSI) provides significant challenges not only due to the strong coupling between the solid and fluid substructures, but also the complexity of fluid model in a moving domain. As a result, advances in numerical study for non-Newtonian FSI have been limited and there are still many open problems in the area.

In this talk both monolithic and decoupling approaches are considered for analytical and numerical studies of fluid-structure interaction problems, where the fluid is governed by a quasi-Newtonian or a viscoelastic fluid model. We will present finite element error estimates for a quasi-Newtonian FSI system and numerical results that show comparisons with a Newtonian FSI system. For a viscoelastic FSI problem we will discuss some issues with the stress boundary condition on the interface and present simulation results with/without interface stress boundary conditions.

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Last Updated: 09/25/2015