Browsing Rice University Electronic Theses and Dissertations by Subject "Applied Mathematics"
Now showing items 143 of 43

A coupled finite volume and discontinuous Galerkin method for convectiondiffusion problems
(2012)This work formulates and analyzes a new coupled finite volume (FV) and discontinuous Galerkin (DG) method for convectiondiffusion problems. DG methods, though costly, have proved to be accurate for solving convectiondiffusion ... 
A minimumcostneighbor multicast routing protocol for mobile wireless ad hoc networks
(2010)MiCoN (MinimumCost Neighbor) is a new ondemand multicast routing protocol for mobile wireless ad hoc networks. Multicast routing in MiCoN is based on a new multiroute unicast routing protocol for maintaining routes ... 
A numerical study of an adjoint based method for reservoir optimization
(2010)A numerical reservoir simulator that uses a finite volume spatial discretization and two time discretization schemes is developed and tested. First and second order derivatives for the numerical simulator are derived, using ... 
Accelerated Discontinuous Galerkin Solvers with the Chebyshev Iterative Method on the Graphics Processing Unit
(2011)This work demonstrates implementations of the discontinuous Galerkin (DG) method on graphics processing units (GPU), which deliver improved computational time compared to the conventional central processing unit (CPU). The ... 
Accelerated HighPerformance Compressive Sensing using the Graphics Processing Unit
(2011)This thesis demonstrates the advantages of new practical implementations of compressive sensing (CS) algorithms tailored for the graphics processing unit (CPU) using a software platform called Jacket. There exist many ... 
Adaptive finite element methods for linearquadratic convection dominated elliptic optimal control problems
(2010)The numerical solution of linearquadratic elliptic optimal control problems requires the solution of a coupled system of elliptic partial differential equations (PDEs), consisting of the socalled state PDE, the adjoint ... 
An alternative approach to differential semblance velocity analysis via normal moveout correction
(2010)This thesis develops a new computation of the objective function and gradient for normal moveoutbased differential semblance (DS). The DS principle underlies a class of algorithms for seismic velocity analysis. The simplest ... 
An Approach for the Adaptive Solution of Optimization Problems Governed by Partial Diﬀerential Equations with Uncertain Coeﬃcients
(20120905)Using derivative based numerical optimization routines to solve optimization problems governed by partial differential equations (PDEs) with uncertain coefficients is computationally expensive due to the large number of ... 
An asymptotic minimax analysis of nonlocal means on edges
(2012)This thesis analyzes the nonlocal means denoising algorithm using the criterion of minimax optimality from statistical decision theory. We show that nonlocal means is minimax suboptimal on images with smooth discontinuities ... 
An efficient algorithm for total variation regularization with applications to the single pixel camera and compressive sensing
(2010)In this thesis, I propose and study an efficient algorithm for solving a class of compressive sensing problems with total variation regularization. This research is motivated by the need for efficient solvers capable of ... 
Application of harmonic coordinates to 2D interface problems on regular grids
(2012)Finite difference and finite element methods exhibit first order convergence when applied to static interface problems where the grid and interface are not aligned. Although modified and unstructured grid methods would ... 
Approximate MultiParameter Inverse Scattering Using Pseudodifferential Scaling
(2011)I propose a computationally efficient method to approximate the inverse of the normal operator arising in the multiparameter linearized inverse problem for reflection seismology in two and three spatial dimensions. Solving ... 
Branchdecomposition heuristics for linear matroids
(2010)This thesis present two new heuristics which utilize classification and maxflow algorithm respectively to derive nearoptimal branchdecompositions for linear matroids. In the literature, there are already excellent ... 
Cocircuits of vector matroids
(2012)In this thesis, I present a set covering problem (SCP) formulation of the matroid cogirth problem, finding the cardinality of the smallest cocircuit of a matroid. Addressing the matroid cogirth problem can lead to significantly ... 
Complex flow and transport phenomena in porous media
(2010)This thesis analyzes partial differential equations related to the coupled surface and subsurface flows and develops efficient high order discontinuous Galerkin (DG) methods to solve them numerically. Specifically, the ... 
Compressive Sensing for 3D Data Processing Tasks: Applications, Models and Algorithms
(2012)Compressive sensing (CS) is a novel sampling methodology representing a paradigm shift from conventional data acquisition schemes. The theory of compressive sensing ensures that under suitable conditions compressible signals ... 
Compressive sensing for signal ensembles
(2010)Compressive sensing (CS) is a new approach to simultaneous sensing and compression that enables a potentially large reduction in the sampling and computation costs for acquisition of signals having a sparse or compressible ... 
Coupling surface flow with porous media flow
(2010)This thesis proposes a model for the interaction between ground flow and surface flow using a coupled system of the NavierStokes and Darcy equations. The coupling of surface flow with porous media flow has important ... 
Discontinuous Galerkin formulation for multicomponent multiphase flow
(2010)The understanding of multiphase multicomponent transport in capillary porous media plays an important role in scientific and engineering disciplines such as the petroleum and environmental industries. The two most commonly ... 
Discontinuous Galerkin Methods for Elliptic Partial Differential Equations with Random Coefficients
(2011)This thesis proposes and analyses two numerical methods for solving elliptic partial differential equations with random coefficients. The stochastic problem is first transformed into a parametrized one by the use of the ... 
Discontinuous Galerkin time domain methods for acoustics and comparison with finite difference time domain methods
(2010)This thesis describes an implementation of the discontinuous Galerkin finite element time domain (DGTD) method on unstructured meshes to solve acoustic wave equations in heterogeneous media. In oil industry people use ... 
Endogenous Sparse Recovery
(2012)Sparsity has proven to be an essential ingredient in the development of efficient solutions to a number of problems in signal processing and machine learning. In all of these settings, sparse recovery methods are employed ... 
Finite Element Nonlocal Technique Based on Superconvergent Patch Second Derivative Recovery
(2012)This dissertation proposes a finite element procedure for evaluating the high order strain derivatives in nonlocal computational mechanics. The superconvergent second derivative recovery methods used are proven to be ... 
Implicitly Restarted DEIM_Arnoldi: An inner product free Krylov method for eigenproblems
(2010)This thesis proposes an inner product free Krylov method called Implicitly Restarted DEIM_Arnoldi (IRD) to solve large scale eigenvalue problems. This algorithm is based on the Implicitly Restarted Arnoldi (IRA) scheme, ... 
Interval exchange transformations: Applications of Keane's construction and disjointness
(2010)This thesis is divided into two parts. The first part uses a family of Interval Exchange Transformations constructed by Michael Keane to show that IETs can have some particular behavior including: (1) IETs can be topologically ... 
Model reduction of large spiking neurons
(2010)This thesis introduces and applies model reduction techniques to problems associated with simulation of realistic single neurons. Neurons have complicated dendritic structures and spatiallydistributed ionic kinetics that ... 
Modeling price dynamics on electronic stock exchanges with applications in developing automated trading strategies
(2009)This thesis develops models for accurate prediction of price changes on electronic stock exchanges by utilizing autoregressive and logistic methods. Prices on these electronic stock exchanges, also called ECNs, are solely ... 
Modeling Systems from Measurements of their Frequency Response
(2012)The problem of modeling systems from frequency response measurements is of interest to many engineers. In electronics, we wish to construct a macromodel from tabulated impedance, admittance or scattering parameters to ... 
NOOP: A mathematical model of objectoriented programming
(2012)Computer software is ubiquitous. More than 35 × 10 18 computer instructions are executed around the globe each second. As computers dominate more aspects of our lives, there is a growing need to reason more accurately about ... 
On the Integrality Gap of the Subtour Relaxation of the Traveling Salesman Problem for Certain Fractional 2matching Costs
(20140411)This thesis provides new bounds on the strength of the subtour relaxation of the Traveling Salesman Problem (TSP) for fractional 2matching cost instances whose support graphs have no fractional cycles larger than five ... 
Optimization governed by stochastic partial differential equations
(2010)This thesis provides a rigorous framework for the solution of stochastic elliptic partial differential equation (SPDE) constrained optimization problems. In modeling physical processes with differential equations, much of ... 
Optimization of shell structure acoustics
(2010)This thesis analyzes a mathematical model for shell structure acoustics, and develops and implements the adjoint equations for this model. The adjoint equations allow the computation of derivatives with respect to large ... 
PenaltyFree Discontinuous Galerkin Methods for the Stokes and NavierStokes Equations
(2012)This thesis formulates and analyzes loworder penaltyfree discontinuous Galerkin methods for solving the incompressible Stokes and NavierStokes equations. Some symmetric and nonsymmetric discontinuous Galerkin methods ... 
Preconditioned iterative methods for inhomogeneous acoustic scattering applications
(2010)This thesis develops and analyzes efficient iterative methods for solving discretizations of the LippmannSchwinger integral equation for inhomogeneous acoustic scattering. Analysis and numerical illustrations of the ... 
Recovery of neuronal channel densities from calcium fluorescence
(2011)Neurons have the ability to dynamically adjust their own membrane channel densities to modulate the strength of communication with other neurons. This process is integral to such neuronal functions as spatial recognition ... 
Refined Spectral Asymptotics for the Telegrapher's Equation
(2011)In this research, I derive a refined asymptotic expression for the eigenvalues, [Special characters omitted.] , of the operator matrix from the telegrapher's equation to accuracy O (1/ n 2). First, the expression for the ... 
Regime Change: Sampling Rate vs. BitDepth in Compressive Sensing
(2012)The compressive sensing (CS) framework aims to ease the burden on analogtodigital converters (ADCs) by exploiting inherent structure in natural and manmade signals. It has been demonstrated that structured signals can ... 
Resistor networks and optimal grids for the numerical solution of electrical impedance tomography with partial boundary measurements
(2010)The problem of Electrical Impedance Tomography (EIT) with partial boundary measurements is to determine the electric conductivity inside a body from the simultaneous measurements of direct currents and voltages on a subset ... 
Ritz values and Arnoldi convergence for nonHermitian matrices
(2012)This thesis develops ways of localizing the Ritz values of nonHermitian matrices. The restarted Arnoldi method with exact shifts, useful for determining a few desired eigenvalues of a matrix, employs Ritz values to refine ... 
Source localization in cluttered acoustic waveguides
(2010)Mode coupling due to scattering by weak random inhomogeneities leads to the loss of coherence in the wave field measured a long distances of propagation. This in turn leads to the deterioration of coherent source localization ... 
Spectral Properties of LimitPeriodic Schrodinger Operators
(2012)We investigate spectral properties of limitperiodic SchrÃ¶dinger operators in [cursive l] 2 ([Special characters omitted.] ). Our goal is to exhibit as rich a spectral picture as possible. We regard limitperiodic potentials ... 
Techniques for Realtime Viewing and Manipulation of Volumetric Data
(2011)Visualizing and manipulating volumetric data is a major component in many areas including anatomical registration in biomedical fields, seismic data analysis in the oil industry, machine part design in computeraided ... 
Young tableaux with applications to representation theory and flag manifolds
(2010)We outline the use of Young tableaux to describe geometric and algebraic objects using combinatorial methods. In particular, we discuss applications to representations of the symmetric group and the general linear group, ...