North Carolina State
University Numerical Analysis

Research

Numerical Linear Algebra

M. T. (Moody) Chu:: Eigenvalue and eigenvector computation via homotopy methods.
R. E. (Bob) Funderlic:: Lanczos and conjugate gradient methods as well as the generalized singular value decomposition.
I. C. F. (Ilse) Ipsen:: Eigenvalue and eigenvector computation, inverse iteration,perturbation theory.
C. T. (Tim) Kelley:: Krylov methods.
C. D. (Carl) Meyer: (Professor of Mathematics): Numerical linear algebra and matrix computations, applied linear algebra, discrete Markov chains, aggregation/disaggregation algorithms.
W. J. (Billy) Stewart: (Professor of Computer Science): Numerical Linear algebra; computational Markov chains; queueing networks; performance analysis of computer and communication systems.
R. E. (Bob) White:: Iterative methods and the numerical solution of the equilibrium equations.

Numerical PDEs

Alina Chertock:: Free boundary problems for nonlinear PDEs, focusing on both analytic asymptotic methods and high-resolution numerical methods. Numerical methods for time dependent PDEs, hyperbolic conservation laws, degenerate parabolic equations.
P. (Pierre) Gremaud:: Variational methods in continuum mechanics and numerical methods for conservation Laws.
M. Haider:: Mathematical modeling, PDEs, integral equations, boundary element methods.
K. (Kazi) Ito:: Numerical methods for solutions to PDEs; feedback synthesis for systems governed by nonlinear PDEs and boundary control as well as mathematical analysis and numerical methods in control of Navier-Stokes equation.
C. T. (Tim) Kelley:: Nonlinear equations, multilevel methods, flow in porous media, radiative transfer, and integral equations.
Zhilin Li:: Numerical methods for differential equations, especially for moving bounday/interface problems and applications.
J. S. (Jeff) Scroggs:: Development of parallel numerical methods for the approximation of solutions to partial differential equations with application to fluid dynamics.
S. (Seymon) Tsynkov: (Associate Professor of Mathematics): Artificial Boundary Conditions (ABCs) for External Aerodynamics, combined Implementation of Non-Local ABCs with the New Generation of Advanced Multigrid Flow Solvers Based on Factorizable Schemes, Long-Term Numerical Integration of Wave-Type Solutions, Active Shielding and Control of Environmental Noise, Numerical Solution of the Nonlinear Helmholtz Equation.
R. E. (Bob) White:: Numerical solution of Richards' equation for the fluid flow in unsaturated porous media.

Numerical ODEs

S. L. (Steve) Campbell:: Numerical methods for implicit systems of differential equations and their applications in mechanics and control. Numerical solution of DAEs.
M. T. (Moody) Chu:: Numerical analysis of implicit systems of differential equations.

Numerical Control & Optimization

H. T. (Tom) Banks:: Parameter identification and estimation.
S. L. (Steve) Campbell:: Numerical methods in mechanics and control.
K. (Kazi) Ito:: Optimal control and inverse problems in systems governed by PDEs, feedback synthesis for systems governed by nonlinear PDEs, and boundary control.
C. T. (Tim) Kelley:: Numerical methods for large scale optimization.
Kartik K. Sivaramakrishnan: (Assistant Professor of Mathematics): Theory, algorithms, and applications of convex optimization including linear, second order, and semidefinite programming; interior point methods; and decomposition and nonsmooth approaches for large scale optimization.
H. T. (Hien) Tran:: Numerical methods for identification and control of infinite-dimensional systems; mathematical modeling and control of gas flow dynamics in a rapid thermal chemical vapor epitaxy reactor.

Numerical Modeling

M. Haider:: Mathematical modeling, PDEs, integral equations, boundary element methods.
C. T. (Tim) Kelley:: Numerical models for flow in porous media, and radiative transfer.

C. D. (Carl) Meyer:: Numerical aspects of Markov chain models, nearly uncoupled models, and aggregation/disaggregation techniques.
J. F. (John) Monahan:: Statistical computing, time series analysis, and Bayesian analysis. Current work concerns random integration rules for Bayesian problems and applications to meteorology of complex principal components analysis of variables in time and space.
M. S. (Mette) Olufsen:: Biofluid dynamics, computational neuroscience, scientific computation, and interdisciplinary research in areas of mathematical biology.
J. S. (Jeff) Scroggs:: Computational fluid dynamics.
C. E. (Chuck) Siewert:: Neutron-transport theory and radiative transfer, polarization problems in radiative transfer and combined mode, radiation-conduction, heat transfer.
W. J. (Billy) Stewart:: Computational Markov chains; queueing networks; performance analysis of computer and communication systems.
P. J. (Paul) Turinsky:: Computational reactor physics; nuclear fuel management optimization and parallel solution of diffusion and transport equations; multilevel acceleration of the nodal solution form of the neutron diffusion equation; parallel solution utilizing domain decomposition of the integral form of the neutron transport equation; stochastic optimization of the in-core nuclear fuel management optimization problem.