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Author:

Zheng, Bin

Title:

Finite Element Approximations of High Order Partial Differential Equations

Graduate Program:

Mathematics

Keywords:

finite element methods
high order partial differential equations
magnetohydrodynamics

File:

Download mythesis.pdf

Committee Members:

Jinchao Xu, Committee Chair/Co-Chair
Chun Liu, Committee Member
Eric M Mockensturm, Committee Member
Victor Nistor, Committee Member
Ludmil Tomov Zikatanov, Committee Member

Author:

Cho, Durkbin

Title:

MULTILEVEL METHODS FOR THE GENERALIZED FINITE ELEMENT METHOD DISCRETIZATIONS

Graduate Program:

Mathematics

Keywords:

Generalized finite element method
Subspace correction methods
Auxiliary space methods
Multilevel methods
Exact controllability technique

File:

Download mythesis.pdf

Committee Members:

Ludmil Tomov Zikatanov, Committee Chair/Co-Chair
Jinchao Xu, Committee Member
Victor Nistor, Committee Member
Virendra Puri, Committee Member

Author:

Xue, Guangri

Title:

Numerical Methods for Multiphysics, Multiphase, and Multicomponent Models for Fuel Cells

Graduate Program:

Mathematics

Keywords:

Numerical methods
multiphysics
multicomponent
fuel cell
multiphase
coupling

File:

Download thesis-GuangriXue.pdf

Committee Members:

Jinchao Xu, Committee Chair/Co-Chair
Ludmil Tomov Zikatanov, Committee Member
Chun Liu, Committee Member
Alberto Bressan, Committee Member
Chao Yang Wang, Committee Member

Author:

Li, Hengguang

Title:

ELLIPTIC EQUATIONS WITH SINGULARITIES: A PRIORI ANALYSIS AND NUMERICAL APPROACHES

Graduate Program:

Mathematics

Keywords:

the finite element method
weighted sobolev spaces
singularities
elliptic equations
a priori analysis
the multigrid method

File:

Download HengguangLiDissertation.pdf

Committee Members:

Victor Nistor, Committee Chair/Co-Chair
Ludmil Tomov Zikatanov, Committee Chair/Co-Chair
Jinchao Xu, Committee Member
Anna L Mazzucato, Committee Member
Corina Stefania Drapaca, Committee Member

Author:

Chen, Long

Title:

Robust and Accurate Algorithms for Solving Anisotropic Singularities

Graduate Program:

Mathematics

Keywords:

mesh adaptation
anisotropic error estimate
convection dominated problem
singularly perturbed problem
optimal Delaunay triangulation
nonlinear approximation

File:

Download MyThesis.pdf

Committee Members:

Jinchao Xu, Committee Chair/Co-Chair
Qiang Du, Committee Member
Chun Liu, Committee Member
James Z Wang, Committee Member
Ludmil Tomov Zikatanov, Committee Member

Author:

Lee, Young-Ju

Title:

Modelling and Simulations of non-Newtonian fluid flows

Graduate Program:

Mathematics

Keywords:

conformation tensor
non-Newtonian models
constitutive equation
positivity preserving scheme
Riccati differential equation
Lie derivative
multigrid
singular problems
falling sphere simulations
the Johnson-Segalman model

File:

Download mythesis.pdf

Committee Members:

Jinchao Xu, Committee Chair/Co-Chair
Chun Liu, Committee Member
Andrew Leonard Belmonte, Committee Member
James Spiro Vrentas, Committee Member
Nigel David Higson, Committee Member

Author:

Zhu, Yunrong

Title:

ROBUST PRECONDITIONERS FOR H(grad), H(curl) AND H(div) SYSTEMS WITH STRONGLY DISCONTINUOUS COEFFICIENTS

Graduate Program:

Mathematics

Keywords:

Jump Coefficients
Multigrid
BPX preconditioner
Domain Decomposition
Condition Number

File:

Download Zhu-thesis.pdf

Committee Members:

Jinchao Xu, Committee Chair/Co-Chair
Victor Nistor, Committee Member
Francesco Costanzo, Committee Member
Ludmil Tomov Zikatanov, Committee Member
Anna L Mazzucato, Committee Member

Author:

Chen, Yao

Title:

Algebraic Multilevel Methods for Graph Laplacians

Graduate Program:

Mathematics

Keywords:

Algebraic Multigrid Methods
Graph Laplacians
Parallel Algorithms

File:

Download main.pdf

Committee Members:

James Joseph Brannick, Committee Chair/Co-Chair
Ludmil Tomov Zikatanov, Dissertation Advisor/Co-Advisor
Jinchao Xu, Committee Member
Jesse Louis Barlow, Special Member

Author:

Urschel, John Cameron

Title:

Graph-based Topics in Applied Mathematics

Graduate Program:

Mathematics

Keywords:

Multigrid
Spectral Bisection
Fiedler Vector
Barrier Option

File:

Download UrschelThesis.pdf

Committee Members:

Victor Nistor, Thesis Advisor/Co-Advisor
Jinchao Xu, Thesis Advisor/Co-Advisor
Ludmil Tomov Zikatanov, Thesis Advisor/Co-Advisor

Author:

Wang, Lu

Title:

the auxiliary space solvers and their applications

Graduate Program:

Mathematics

Keywords:

multigrid
auxiliary space
solver

File:

Download Lu-Dissertation.pdf

Committee Members:

Jinchao Xu, Dissertation Advisor/Co-Advisor
James Joseph Brannick, Committee Member
Ludmil Tomov Zikatanov, Committee Member
Chao Yang Wang, Special Member