Browsing by Author "Popov, Bojan"
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AdjointBased Sensitivity for Radiation Transport Using an Eddington Tensor Formulation
Halvic, Ian William (20180504)Adjoint methods can provide a firstorder approximation of the response a physical system experiences due to a perturbation in the system’s parameters. However, when applying the method to time dependent transport, memory ... 
Anonymous, authentic, and accountable resource management based on the Ecash paradigm
Lam, Tak Cheung (20090515)The prevalence of digital information management in an open network has driven the need to maintain balance between anonymity, authenticity and accountability (AAA). Anonymity allows a principal to hide its identity from ... 
Application of L1 Minimization Technique to Image SuperResolution and Surface Reconstruction
Talavatifard, Habiballah (20130506)A surface reconstruction and image enhancement nonlinear finite element technique based on minimization of L1 norm of the total variation of the gradient is introduced. Since minimization in the L1 norm is computationally ... 
Approximation Techniques for Incompressible Flows with Heterogeneous Properties
Salgado Gonzalez, Abner Jonatan (20111021)We study approximation techniques for incompressible flows with heterogeneous properties. Speci cally, we study two types of phenomena. The first is the flow of a viscous incompressible fluid through a rigid porous ... 
A Conformal Mapping Grid Generation Method for Modeling HighFidelity Aeroelastic Simulations
Worley, Gregory (20100714)This work presents a method for building a threedimensional mesh from two dimensional topologically identical layers, for use in aeroelastic simulations. The method allows modeling of large deformations of the wing in ... 
Continuous Finite Element Approximation of Hyperbolic Systems
Yang, Yong (20160613)The main purpose of this work is to study continuous finite element methods for hyperbolic problems. In scalar case, it is shown that using consistent mass matrix is not compatible with the maximum principle. Moreover, we ... 
Convergence Analysis of Wavelet Schemes for ConvectionReaction Equations under Minimal Regularity Assumptions
Liu, Jiangguo; Popov, Bojan; Wang, Hong; Ewing, Richard E. (SIAM Journal on Numerical Analysis, 2005) 
Entropy Viscosity Method for Lagrangian Hydrodynamics and Central Schemes for Mean Field Games
Tomov, Vladimir (20140418)In this dissertation we consider two major subjects. The primary topic is the Entropy Viscosity method for Lagrangian hydrodynamics, the goal of which is to solve numerically the Euler equations of compressible gas dynamics. ... 
Error Estimates of a Firstorder Lagrange Finite Element Technique for Nonlinear Scalar Conservation Equations
Guermond, JeanLuc; Popov, Bojan (SIAM Journal on Numerical Analysis, 2016) 
Generalized Discontinuous Multiscale Methods for Flows in Highly Heterogeneous Porous Media
Moon, Minam (20150605)This dissertation is devoted to the development, study and testing of numerical methods for elliptic and parabolic equations with heterogeneous coefficients. The motivation for this study is to meet the need for fast and ... 
High Order Invariant Domain Preserving Finite Volume Schemes for Nonlinear Hyperbolic Conservation Laws
Hua, Yuchen (20190524)In this dissertation we develop high order invariant domain preserving schemes for general hyperbolic systems. The schemes are based on the general central schemes of formally second, third and fourth order accuracy. The ... 
HighOrder Maximum Principle Preserving (MPP) Techniques for Solving Conservation Laws with Applications on Multiphase Flow
Quezada De Luna, Manuel (20160727)We develop numerical methods to solve the linear scalar conservation law fulfilling the maximum principle. To do this we use continuous and discontinuous Galerkin finite elements and achieve the preservation on the maximum ... 
Improved QuasiStatic Methods for TimeDependent Neutron Diffusion and Implementation in Rattlesnake
Prince, Zachary Merritt (20170420)Transient reactor simulations are a chronically formidable challenge due to the computational rigor of evaluating the neutron transport equation, as well as its coupling with other physical phenomena. The goal of this ... 
Invariant Domains and FirstOrder Continuous Finite Element Approximation for Hyperbolic Systems
Guermond, JeanLuc; Popov, Bojan (SIAM Journal on Numerical Analysis, 2016) 
$L^1$Approximation of Stationary Hamilton–Jacobi Equations
Guermond, JeanLuc; Popov, Bojan (SIAM Journal on Numerical Analysis, 2009) 
Load Balancing Unstructured Meshes for Massively Parallel Transport Sweeps
Ghaddar, Tarek Habib (20160426)When running any massively parallel code, load balancing is a priority in order to achieve the best possible parallel efﬁciency. A load balanced problem has an equal number of degrees of freedom per processor. Load balancing ... 
A Local Minimax Method Using the Generalized Nehari Manifold for Finding Differential Saddles
Ji, Bingbing (20171130)In order to find the first few unconstrained saddles of functionals with different types of variational structures, a new local minimax method (LMM), based on a dynamics of points on virtual geometric objects such as curves, ... 
Mesh independent convergence of modified inexact Newton methods for second order nonlinear problems
Kim, Taejong (Texas A&M University, 20060816)In this dissertation, we consider modified inexact Newton methods applied to second order nonlinear problems. In the implementation of Newton's method applied to problems with a large number of degrees of freedom, it is ... 
Multiscale numerical methods for some types of parabolic equations
Nam, Dukjin (20090515)In this dissertation we study multiscale numerical methods for nonlinear parabolic equations, turbulent diffusion problems, and high contrast parabolic equations. We focus on designing and analysis of multiscale methods ... 
NonLinear Spatial Multigrid Method For NonLinear S2 Acceleration
Kliewer, John David (20180424)A nonlinear spatial multigrid algorithm was developed and explored as a technique to efficiently solve the nonlinear S2 acceleration equations for SN neutron transport calculations in 1D slabs. Acceleration of the basic ...