Computational and Applied Mathematics
Recent Submissions

Bilevel Clique Interdiction and Related Problems
(201705)I introduce a formulation of the bilevel clique interdiction problem. Interdiction, a military term, describes the removal of enemy resources. The single level clique interdiction problem describes the attempt of an attacker ... 
Novel Techniques for the ZeroForcing and pMedian Graph Location Problems
(201705)This thesis presents new methods for solving two graph location problems, the pMedian problem and the zeroforcing problem. For the pmedian problem, I present a branch decomposition based method that finds the best ... 
Hermite Methods for the Simulation of Wave Propagation
(201705)Simulations of wave propagation play a crucial role in science and engineering. In applications of geophysics, they are the engine of many seismic imaging algorithms. For electrical engineers, they can be a useful tool for ... 
GPUAccelerated Discontinuous Galerkin Methods on Hybrid Meshes: Applications in Seismic Imaging
(201705)Seismic imaging is a geophysical technique assisting in the understanding of subsurface structure on a regional and global scale. With the development of computer technology, computationally intensive seismic algorithms ... 
An Inverse Free Projected Gradient Descent Method for the Generalized Eigenvalue Problem
(201705)The generalized eigenvalue problem is a fundamental numerical linear algebra problem whose applications are wide ranging. For truly largescale problems, matrices themselves are often not directly accessible, but their ... 
A ParallelInTime GradientType Method For Optimal Control Problems
(201705)This thesis proposes and analyzes a new parallelintime gradienttype method for timedependent optimal control problems. When the classical gradient method is applied to such problems, each iteration requires the forward ... 
ProjectionBased Model Reduction in the Context of Optimization with Implicit PDE Constraints
(201705)I use reduced order models (ROMs) to substantially decrease the computational cost of Newton's method for largescale timedependent optimal control problems in settings where solving the implicit constraints and their ... 
Representation and Estimation of Seismic Sources via Multipoles
(201705)Accurate representation and estimation of seismic sources are essential to the seismic inversion problem. General sources can be approximated by a truncated series of multipoles depending on the source anisotropy. Most ... 
Numerical Methods and Applications for Reduced Models of Blood Flow
(201705)The human cardiovascular system is a vastly complex collection of interacting components, including vessels, organ systems, valves, regulatory mechanisms, mi crocirculations, remodeling tissue, and electrophysiological ... 
Nonnormality in Lyapunov Equations
(201605)The singular values of the solution to a Lyapunov equation determine the potential accuracy of the lowrank approximations constructed by iterative methods. Lowrank solutions are more accurate if most of the singular ... 
Black Oil Simulation Utilizing a Central Finite Volume Scheme
(201605)Blackoil simulation is a valuable tool in predicting the multiphase multicomponent flow of fluids in reservoirs. This research validates the use of a central high resolution finite volume scheme developed by Kurganov ... 
Clique Generalizations and Related Problems
(201605)A large number of realworld problems can be model as optimization problems in graphs. The clique model was introduced to aid the study of network structure for social interaction. Each vertex represented an actor and the ... 
Accelerating Convergence by Augmented RayleighRitz Projections For LargeScale Eigenpair Computation
(201601)Iterative algorithms for largescale eigenpair computation are mostly based subspace projections consisting of two main steps: a subspace update (SU) step that generates bases for approximate eigenspaces, followed by a ... 
Born Waveform Inversion in Shot Coordinate Domain
(201605)The goal of this thesis is to integrate Born waveform inversion, variable projection algorithm and model extension concept to get a method that can improve the long scale background model updates reliably and efficiently ... 
Optimal Control of Flow and Transport Equations Using Discontinuous Galerkin Methods
(201605)This thesis analyzes the accuracy of discontinuous Galerkin methods for solving optimal control problems for flow and transport equations. The optimality conditions for each optimal control problem and error estimates for ... 
Algorithms to Find the Girth and Cogirth of a Linear Matroid
(201511)In this thesis, I present algorithms to find the cogirth and girth, the cardinality of the smallest cocircuit and circuit respectively, of a linear matroid. A set covering problem (SCP) formulation of the problems is ... 
Comparison of Reduced Models for Blood Flow Using Runge–Kutta Discontinuous Galerkin Methods
(201511)Reduced, or one–dimensional blood flow models take the general form of nonlinear hyperbolic systems, but differ greatly in their formulation. One class of models considers the physically conserved quantities of mass and ... 
Accelerated PlaneWave Discontinuous Galerkin for Heterogeneous Scattering Problems
(201511)This thesis considers algorithmic and computational acceleration of numerical wave modelling at high frequencies. Numerical propagation of linear waves at high frequencies poses a significant challenge to modern simulation ... 
Dynamics of Brain Networks During Reading
(201511)We recorded electrocorticographic (ECoG) data from 15 patients with intractable epilepsy during a word completion task to precisely describe the spatiotemporal brain dynamics underlying word reading. Using a novel technique ... 
A Spectrumbased Regularization Approach to Linear Inverse Problems: Models, Learned Parameters and Algorithms
(201506)In this thesis, we study the problem of recovering signals, in particular images, that approximately satisfy severely illconditioned or underdetermined linear systems. For example, such a linear system may represent a set ...