Browsing CAAM Technical Reports by Issue Date
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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 ... 
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 ... 
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 ... 
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 ... 
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 ... 
Strong Convergence of Discrete DG Solutions of the Heat Equation
(201510)A convergence analysis to the weak solution is derived for interior penalty discontinuous Galerkin methods applied to the heat equation in two and three dimensions under general mixed boundary conditions. Strong convergence ... 
High Performance HighOrder Numerical Methods: Applications in Ocean Modeling
(201506)This thesis presents highorder numerical methods for timedependent simulations of oceanic wave propagation on modern manycore hardware architecture. Simulation of the waves such as tsunami, is challenging because of the ... 
Discontinuous Galerkin and Finite Difference Methods for the Acoustic Equations with Smooth Coefficients
(201506)This thesis analyzes the computational efficiency of two types of numerical methods: finite difference (FD) and discontinuous Galerkin (DG) methods, in the context of 2D acoustic equations in pressurevelocity form with ... 
OKL: A Unified Language for Parallel Architectures
(201506)Rapid evolution of computer processor architectures has spawned multiple programming languages and standards. This thesis strives to address the challenges caused by fast and cyclical changes in programming models. The ... 
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 ... 
Generalizations of the Alternating Direction Method of Multipliers for LargeScale and Distributed Optimization
(201506)The alternating direction method of multipliers (ADMM) has been revived in recent years due to its effectiveness at solving many largescale and distributed optimization problems, particularly arising from the areas of ... 
Block Algorithms with Augmented RayleighRitz Projections for LargeScale Eigenpair Computation
(201506)Most iterative algorithms for eigenpair computation consist of two main steps: a subspace update (SU) step that generates bases for approximate eigenspaces, followed by a RayleighRitz (RR) projection step that extracts ... 
Simulation of CO2 Sequestration in Saline Aquifers Using Discontinuous Galerkin Method
(201408)Carbon dioxide disposal into deep aquifer has been an important venue to trap excess gas emission which causes global warming. In the CO2 sequestration process, CO2 is captured from the point source and injected into the ... 
On the Approximation of the Dirichlet to Neumann Map for High Contrast Two Phase Composites and its Applications to Domain Decomposition Methods
(201408)My research is concerned with the analysis and numerical simulations of elliptic partial differential equations that model steady state flow (electric, thermal, fluid) in high contrast composite materials consisting of ... 
Block Stochastic Gradient Iteration for Convex and Noncovex Optimization
(201408)The stochastic gradient (SG) method can minimize an objective function composed of a large number of differentiable functions or solve a stochastic optimization problem, very quickly to a moderate accuracy. The block ... 
A DEIM Induced CUR Factorization
(201407)We derive a CUR matrix factorization based on the Discrete Empirical Interpolation Method (DEIM). For a given matrix A, such a factorization provides a low rank approximate decomposition of the form A ≈ CUR, where C and R are ... 
Inverse Source Problems for TimeDependent Radiative Transport
(201405)In the first part of this thesis, I develop a time reversal method for the radiative transport equation to solve two problems: an inverse problem for the recovery of an initial condition from boundary measurements, and the ... 
Numerically Stable and Statistically Efficient Algorithms for Large Scale Exponential Fitting
(201405)The exponential fitting problem appears in diverse applications such as magnetic resonance spectroscopy, mechanical resonance, chemical reactions, system identification, and radioactive decay. In each application, the ... 
An Efficient GaussNewton Algorithm for Symmetric LowRank Product Matrix Approximatins
(201405)We derive and study a GaussNewton method for computing the symmetric lowrank product (SLRP) XXT, where X / Rnkfor k<n, that is the closest approximation to a given symmetric matrix A / Rnn in Frobenius norm. When A=BTB ... 
An Alternating Direction and Projection Algorithm for Structureenforced Matrix Factorization
(201310)Structureenforced matrix factorization (SeMF) represents a large class of mathematical models ap pearing in various forms of principal component analysis, sparse coding, dictionary learning and other machine learning ...