# overview
My research focuses on large scale serial and parallel scientific computation, numerical and iterative methods for partial differential equations, multigrid and domain decomposition methods, electromagnetic problems and mixed finite element methods, and perfectly matched layer far field approximation for scattering problems.

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

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4012 Fluid Mechanics And Thermal Engineering

# keywords[]
Combined Mixed And Standard Galerkin Discretization Methods

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Mixed Approximation Of Elliptic Boundary Value Problems

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4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# educationAndTraining[].organization.label
Northeastern University - (Shenyang, China)

# educationAndTraining[].organization.label
Cornell University - (Ithaca, New York, United States)

# awardsAndHonors[].label
Association of Former Students University-Level Distinguished Achievement Award, The

# publications[].label
AN EFFICIENT NUMERICAL PROCEDURE FOR THE COMPUTATION OF STEADY-STATE HARMONIC CURRENTS IN FLAT PLATES

# publications[].publisher
Institute of Electrical and Electronics Engineers (IEEE)

# publications[].label
Analysis of a finite PML approximation for the three dimensional time-harmonic Maxwell and acoustic scattering problems

# publications[].label
On the stability of the L-2 projection in H-1(Omega)

# publications[].label
Iterative solution of a coupled mixed and standard Galerkin discretization method for elliptic problems

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Least-squares for second-order elliptic problems

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Almost optimal interior penalty discontinuous approximations of symmetric elliptic problems on non-matching grids

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A least-squares approximation method for the time-harmonic Maxwell equations

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A NEW COMPUTATIONAL APPROACH FOR THE LINEARIZED SCALAR POTENTIAL FORMULATION OF THE MAGNETOSTATIC FIELD PROBLEM

# publications[].publisher
Institute of Electrical and Electronics Engineers (IEEE)

# publications[].label
Computational scales of Sobolev norms with application to preconditioning

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Overlapping Schwarz preconditioners for indefinite time harmonic Maxwell equations

# publications[].label
Overlapping Schwarz preconditioners for indefinite time harmonic Maxwell equations

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NUMERICAL APPROXIMATION OF FRACTIONAL POWERS OF ELLIPTIC OPERATORS

# publications[].label
Overlapping Schwarz preconditioners for indefinite time harmonic maxwell equations

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Two-level preconditioners for 2m'th order elliptic finite element problems

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Thermal blooming of a rapidly moving laser beam.

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Chapter 7 Preconditioned Iterative Methods for Nonselfadjoint or Indefinite Elliptic Boundary Value Problems

# publications[].label
Multigrid convergence for second order elliptic problems with smooth complex coefficients

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ANALYSIS OF A CARTESIAN PML APPROXIMATION TO THE THREE DIMENSIONAL ELECTROMAGNETIC WAVE SCATTERING PROBLEM

# publications[].label
DOMAIN DECOMPOSITION TYPE ITERATIVE TECHNIQUES FOR PARABOLIC PROBLEMS ON LOCALLY REFINED GRIDS

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
ANALYSIS OF V-CYCLE MULTIGRID ALGORITHMS FOR FORMS DEFINED BY NUMERICAL QUADRATURE

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
A least-squares approximation method for the time-harmonic Maxwell equations

# publications[].label
DOMAIN DECOMPOSITION METHODS FOR PROBLEMS WITH PARTIAL REFINEMENT

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
The approximation of the Maxwell eigenvalue problem using a least-squares method

# publications[].label
THE H-GRADIENT METHOD FOR MAGNETOSTATIC FIELD COMPUTATIONS

# publications[].publisher
Institute of Electrical and Electronics Engineers (IEEE)

# publications[].label
Analysis of non-overlapping domain decomposition algorithms with inexact solves

# publications[].label
Multiplier spaces for the mortar finite element method in three dimensions

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
Iterative solution of a coupled mixed and standard Galerkin discretization method for elliptic problems

# publications[].label
Least-squares methods for linear elasticity based on a discrete minus one inner product

# publications[].label
ERROR ANALYSIS OF A FINITE ELEMENT METHOD FOR THE SPACE-FRACTIONAL PARABOLIC EQUATION

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
On the occasion of the sixtieth birthday of Richard E. Ewing

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Uzawa type algorithms for nonsymmetric saddle point problems

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A mixed method for axisymmetric div-curl systems

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Galerkin FEM for Fractional Order Parabolic Equations with Initial Data in H-s, 0 <= s <= 1

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MULTILEVEL ITERATION FOR MIXED FINITE-ELEMENT SYSTEMS WITH PENALTY

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
A new approximation technique for div-curl systems

# publications[].label
VARIATIONAL FORMULATION OF PROBLEMS INVOLVING FRACTIONAL ORDER DIFFERENTIAL OPERATORS

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A Multigrid Algorithm for an Elliptic Problem with a Perturbed Boundary Condition

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A least-squares approach based on a discrete minus one inner product for first order systems

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Compensating for thermal blooming of repetitively pulsed lasers

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Stability of Discrete Stokes Operators in Fractional Sobolev Spaces

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Numerical well model for non-Darcy flow through isotropic porous media

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Closed form for the second order born lineshift integral

# publications[].label
Iterative techniques for time dependent Stokes problems

# publications[].label
The Mathematical Theory of Finite Element Methods (Susanne C. Brenner and L. Ridgway Scott)

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
The convergence of V-cycle multigrid algorithms for axisymmetric Laplace and Maxwell equations

# publications[].label
Analysis of a finite element PML approximation for the three dimensional time-harmonic maxwell problem

# researcherOn[].label
The Development and Anlysis of Sweeping Preconditioners for Scattering Problems

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# streetAddress
Texas A&M University; Mathematics; 3368 TAMU