This project is motivated by the GEMS research in summer 2008, when
I first got exposed to the meshfree method under the supervision of
Dr. Tobin Driscoll. A treecode algorithm is developed for the fast evaluation of multiquadric
radial basis
function (RBF) approximations with varying shape parameters. The code is able to evaluate an approximation
on N centers at M points in O((N + M ) log M) time in the ideal case. When applied to adaptive schemes, the computation time using iterative
solver such as GMRES scales favorably with the treecode.
Tear Film Projects
After joining the
tear film group, I have been involved in several
projects modeling the dynamics of tear film in different moving domains, while considering different factors that interplay with the film evolution. All the work are supervised by Dr. Richard Braun and Dr. Tobin Driscoll.
In this project, we considered heat-affected evaporation in a 1-D moving domain representing eye blinking. Numerical results reveal a similarity to quantitative in vivo observations of the film dynamics
and temperature at geometric center of cornea.
In this project, we consider the Marangoni force exerted by
evolution of lipid concentraion on film dynamics on a 2-D rectangular
domain.
We try to explore the dynamics of film on a eye-shaped domain,
where conformal mapping plays a big role in problem setup.
