The numerical analysis group consists of Stephen Brill, Jodi Mead, and Barbara Zubik-Kowal.
Stephen Brill's research is in the area of numerical solution of ordinary and partial differential equations, particularly those which model single- and multi-phase flow and contaminant transport in porous media. He is presently working on obtaining analytical formulas for collocation discretizations of convection-diffusion equations and studying these formulas to choose the value of free parameters so as to obtain highly accurate numerical solutions.
Jodi Mead's work relates mathematical theory with problems from the natural and engineering sciences, including their computer solutions. This involves ordinary and partial differential equations, inverse theory, and parallel algorithms. Some specific applications she has worked on are in computational aeroacoustics and ocean modeling. In the former, the work is concerned with approximating the noise from an aircraft for long time periods and over large distances. In the latter, she studies nonlinear differential equations and the blending of their solutions with data from the ocean.
Barbara Zubik-Kowal is currently investigating several problems. One is to obtain new parallelizable numerical methods for the wave equation. The goal is to enlarge the step-size for time integration methods without any instability effects. Another investigation concerns a numerical implementation of algorithms for inverse problems which arise in a model in oceanography. A third line of inquiry is to analyze stability of numerical schemes for computing the current induced on the surface of a thin wire by an incident time-dependent electromagnetic field. The current can be computed as a numerical solution of a certain complicated integral equation coupled with a pair of first order partial differential equations for the potentials on the wire.