Research Areas and Projects

Sparse Grids

A class of functions which allow approximation of high dimensional function

Smoluchowski Equation

The Smoluchowski equation describes stochastic processes in physics, chemistry and biology. In many applications, the state vectors are high-dimensional.

Datamining

Data mining is a new area of research, applying methods from statistics, machine learning and computational mathematics to the analysis of very large data sets.

Adaptive Optics

Adaptive optics is an emerging field with applications in areas as diverse as astronomy, opthalmology, 3D imaging, retinal imaging, laser material processing and military imaging. Light is distorted by the medium through which it travels, adaptive optics attempts to compensate for that distortion to produce more clear and detailed images.

Thin Plate Splines

Thin Plate splines are functions which balance the effect of fitting a set of data points against the overall smoothness oft he function. We have been investigating ways to use finite element techniques to approximate the thin plate spline in 2 and 3 dimensions.

Shallow Water Wave Equation

The Shallow water wave equation is used to model inundation processes such as dam breaks, tidal inundation, and tsunamis. We are investigating the properties of this equation for flows over discontinuities in the terrain.

Free Surface Navier-Stokes Solver

We are investigating methods for solving the Navier Stokes equation.

Simulation of Tsunamis

Impacts to the built environment from a hazard such tsunami are critical in understanding the economic and social effects of such events on our communities. In order to better understand these effects, Geoscience Australia and the Australian National University are developing a software modelling tool for the simulation of inundation of coastal areas by tsunamis.