One area of my research is in
numerical methods for partial
differential equations with Dr. Catherine Mavriplis, Dr. Louis Wicker,
and Dustin Williams. We have done comparisons of Finite
Differences, Discontinuous Galerkin, and Spectral Difference
methodologies for various model problems, including 1D constant
advection, Burgers (inviscid and viscous), linear acoustic-advection
system, and 2D Quasilinear Advection (Smolarkiewicz). In the
future I plan to apply the SD discretization to a shallow water
equation set on the sphere in order to compare the performance of DG
and SD for global shallow water test cases. A recent talk and paper are on the documents page.
I worked on another research project in the fall of 2008 with Dr.
Lakshmivarahan of the School of Computer Science on detecting errors in
model forecasts due to parameter and initial condition errors using a
variational approach. The paper and talk are on the documents page.
Currently I am working on estimating a parameter in the
ADCIRC storm surge model that
governs the wave propagation properties of the finite element solver
for the shallow water equation with my advisor, Dr. Luther White.
In addition, I am working with
Dr.
Mary Lou Zeeman of Bowdoin College to increase awareness amongst
mathematicians of the mathematical challenges present in the field of
climate prediction, climate modeling, and climate change.
Here's a good website (and a good book) which is an introduction to climate modeling:
