Numerical Analysis and Scientific Computing
A numerical analyst designs, implements and analyzes algorithms for obtaining useful results from mathematical models of physical, social and financial systems. The results may be tables, visualizations or instructions for computer-driven manufacturing.
The Numerical Analysis and Scientific Computing group at NC State does research in optimization, differential and integral equations, control, uncertainty quantification, nonlinear equations, inverse problems and linear algebra. We design novel algorithms, study convergence and stability of algorithms, and implement our algorithms on state-of-the-art supercomputers.
We are deeply involved in research across disciplines and collaborate with industry and national laboratories. Our students have summer internships with our collaborators and publish papers in the mathematics literature and that of other disciplines. Currently the group’s applications include nuclear engineering, internet search, physics, chemistry, medicine, hydrology, electromagnetics, aeronautics and materials science.
Numerical analysis and scientific computing; Numerical methods for inverse problems; Optimization under uncertainty; Methods for Bayesian inversion in finite and infinite dimensions; Uncertainty quantification.
Implicit systems of ordinary differential equations, including numerical algorithms and control; applications to constrained mechanical systems, optimal control, and failure detection. Simulation and modeling.
Professor, Associate Director for CRSC, Department Head
Numerical methods for time-dependent partial differential equations, hyperbolic conservation laws, degenerate parabolic equations, numerical analysis, scientific computing.
Numerical ordinary differential equations, numerical linear algebra, dynamical systems, inverse problems.
Professor, Director of Graduate Programs
Numerical analysis, partial differential equations; applications to mechanics, fluid dynamics, and material science.
Numerical linear algebra, randomized algorithms, scientific computation, numerical analysis, matrix theory, applications to nonlinear problems, parameter estimation and statistics.
Optimal control and inverse problems for partial differential equations, control of Navier-Stokes equations, numerical partial differential equations, nonlinear semigroup theory, dynamical systems in Banach spaces, stochastic differential equations and applications, applied functional analysis.
Nonlinear equations, multilevel methods, large-scale and multi-model optimization, flow in porous media, nano-scale electronics and sensing, radiative and neutron transfer, optimal control, integral equations, partial differential equations.
Numerical analysis and scientific computing; numerical methods for partial differential equations involving free boundary and moving interface problems, and problems on irregular domains, finite difference and finite element methods; CFD, and biological flows.
Research Assistant Professor
Numerical analysis, matrix computations, Markov chains, information retrieval, data and text mining, linear algebra and its applications.
Optimization theory and algorithms. Applications in medicine, healthcare and engineering.
Arvind Krishna Saibaba
Inverse Problems, Numerical Linear Algebra, Applications to Medical Imaging and Geosciences.
Numerical analysis, financial mathematics, scientific computation, partial differential equations.
Professor, Associate Director for CRSC, Director of Multimedia Center
Scientific computation, mathematical modeling, numerical methods for the identification and control of dynamical systems.
Numerical analysis of partial differential equations and scientific computation with applications to fluid flows and wave propagation, including acoustics, electromagnetism, optics, and plasma. Inverse problems, including active control of sound and radar imaging.