Scientific Computing Group

Numerical Shock Capturing Techniques

Advisor: David Gottlieb

A Parallel Multi-Domain Approximation For Parabolic Equations Using Chebyshev Polynomials And The Penalty Method

Advisor: David Gottlieb

Essentially Nonoscillatory Spectral Methods For Shock Computation

Advisor: David Gottlieb

Topics In Spectral Methods

Advisors: David Gottlieb, Jan S Hesthaven

Anti-Diffusive Flux Corrections For High Order Finite-Difference WENO Schemes

Advisor: Chi-Wang Shu

High Order Residual Distribution Conservative Finite Difference WENO Schemes For Steady State Problems On Non-Smooth Meshes

Advisor: Chi-Wang Shu

The Study Of Building Blocks For Essentially Non-Oscillatory (ENO) Schemes

Advisor: Chi-Wang Shu

Theory And Application Of Spectral Methods For The Unsteady Compressible Wake Flow Past A Two-Dimensional Circular Cylinder

Advisor: David Gottlieb

Topics In High-Order Methods For Partial Differential Equations

Advisor: David Gottlieb

Convergence To Steady State Of Weighted ENO Schemes, Norm Preserving Runge-Kutta Methods And A Modified Conjugate Gradient Method

Advisor: Chi-Wang Shu

The Local Trigonometric Transforms And Their Use In Solving Partial Differential Equations

Advisor: David Gottlieb

Numerical Methods For Hyperbolic Equations On Unstructured Meshes

Advisor: Chi-Wang Shu

Wavelets And Numerical Methods

Advisor: David Gottlieb

Algorithm Analysis And Efficient Computation Of Conservation Laws

Advisor: Chi-Wang Shu

Analysis Of The Chemical Vapor Infiltration Process

Advisor: David Gottlieb

Multi-Domain Spectral Penalty Methods For Hyperbolic Systems: Theory And Applications

Advisor: David Gottlieb

High-Order Implicit-Explicit Runge-Kutta Time Integration Schemes And Time-Consistent Filtering In Spectral Methods

Advisors: David Gottlieb, Jan S Hesthaven

High-Order Numerical Approximations Of Nonlinear Hamilton-Jacobi Equations And Approximation Of Elasticity Problems Using Stokes Problems

Advisor: Chi-Wang Shu

On Locally Divergence-Free Discontinuous Galerkin Methods

Advisor: Chi-Wang Shu

Topics In Spectral Methods: Coping With Uncertainty And The Gibbs Phenomenon

Advisor: Jan S Hesthaven

Spectral Methods For Discontinuous Problems: Applications In Electromagnetic Problem And Image Reconstruction

Advisor: David Gottlieb

Parallel ENO Schemes Applied To Shock/Cylinder Interactions And Numerical Methods By Radon Transform

Advisor: Chi-Wang Shu

Preconditioning Matrices For Spectral Derivative Operators

Advisor: David Gottlieb

Extension of a Post-Processing Technique for the Discontinuous Galerkin Finite Element Methods For Hyperbolic Equations

Advisor: Chi-Wang Shu

Multi Domain Weigthed Essentially Non Oscillatory (WENO) Method With Interpolation At Subdomain Interfaces

Advisor: Chi-Wang Shu

Advanced High-Order Numerical Methods For Shock Wave Computations

Advisor: David Gottlieb

Some Issues In High Order Numerical Schemes For Nonlinear Hyperbolic Conservation Laws

Advisor: Chi-Wang Shu

Spectral Methods For Discontinuous Problems

Advisor: David Gottlieb

Numerical Methods For Wave Problems In Complex Geometries

Advisor: David Gottlieb

High-Order Finite-Difference Simulation Of Compressible Flow Around A Circular Cylinder In An Acoustic Field

Advisor: David Gottlieb

High-Order Accurate Methods For Solving The Time-Harmonic Maxwell's Equations

Advisor: Jan S Hesthaven

Computational Algorithms For Non-Linear Discontinuous Problems

Advisor: Chi-Wang Shu

High Order Well-Balanced Numerical Schemes For Hyperbolic Systems With Source Terms

Advisor: Chi-Wang Shu

Anti-Diffusive Flux Corrections For High Order Finite Difference WENO Schemes

Advisor: Chi-Wang Shu

Discontinuous Galerkin Finite Element Methods For PDEs With Higher Order Derivatives

Advisor: Chi-Wang Shu

Spectral Methods And Absorbing Boundary Conditions For Maxwells Equations

Advisor: David Gottlieb

Discontinuous Galerkin Method Based On Non-Polynomial Approximation Spaces

Advisor: Chi-Wang Shu

Topics In Structured And Unstructured ENO Schemes

Advisor: Chi-Wang Shu