Research Interests for Timothy Lucas

I am studying a three-dimensional system of reaction-diffusion equations with stochastic source terms that arises from an immunology model. I have shown convergence of a first order splitting method for this system. This allows us to take advantage of known numerical methods for the diffusion, reaction and stochastic differential equations. In particular, I have implemented a parallel multigrid scheme for the diffusion.

I am currently working with Dr. William K. Allard in the Mathematics department and Dr. Thomas B. Kepler in the Center for Computational Immunology.

Keywords:

Numerical Analysis, Partial Differential Equations, Multigrid, Stochastic Differential Equations, Parallel Computing

Recent Publications

1. T.A. Lucas, Operator Splitting for an Immunology Model Using Reaction-Diffusion Equations with Stochastic Source Terms (Submitted, Fall, 2007) (Submitted.) [abs] [author's comments]
2. F. Mitha, T.A. Lucas, F. Feng, T.B. Kepler and C. Chan, The multiscale systems immunology project: Software forcell-based immunological simulation, Source Code for Biology and Medicine (Submitted, Fall, 2007) (Submitted.) [abs]