Numerical Modeller Australia-Indonesia Facility for Disaster Reduction, AusAID March 2010 – Present (1 year 3 months) Working with Indonesian government science agencies to model risk to natural disasters.
Computational Scientist Geoscience Australia March 2003 – June 2010 (7 years 4 months) Risk Research Group, Geoscience Australia. Research and development of computational models of natural hazards such as storm surge, tsunami or flooding.
Research Fellow Australian National University Educational Institution; Research industry November 1998 – March 2003 (4 years 5 months) School of Mathematical Sciences, Australian National University. Funded by Australian Partnership for Advanced Computing. Research in computational methods for large scale enterprise data mining.
Education
Danmarks Tekniske Universitet PhD, Scientific Computing 1994 – 1998 Supervisors: Per Christian Hansen and Alan Barker Institute for Mathematical Modelling Activities and Societies: Wavelet analysis, parallel computing, partial differential equations, numerical analysis
Roskilde Universitetscenter MSc, Mathematics and Computer Science 1984 – 1993
Abstract: Wavelet analysis is a relatively new mathematical discipline which has generated much interest in both theoretical and applied mathematics over the past decade. Crucial to wavelets are their ability to analyze different parts of a function at different scales and the fact that they can represent polynomials up to a certain order exactly. As a consequence, functions with fast oscillations, or even discontinuities, in localized regions may be approximated well by a linear combination of relatively few wavelets. In comparison, a Fourier expansion must use many basis functions to approximate such a function well. These properties of wavelets have lead to some very successful applications within the field of signal processing. This dissertation revolves around the role of wavelets in scientific computing and it falls into three parts:
Part I gives an exposition of the theory of orthogonal, compactly supported wavelets in the context of multiresolution analysis. These wavelets are particularly attractive because they lead to a stable and very efficient algorithm, namely the fast wavelet transform (FWT). We give estimates for the approximation characteristics of wavelets and demonstrate how and why the FWT can be used as a front-end for efficient image compression schemes.
Part II deals with vector-parallel implementations of several variants of the Fast Wavelet Transform. We develop an efficient and scalable parallel algorithm for the FWT and derive a model for its performance.
Part III is an investigation of the potential for using the special properties of wavelets for solving partial differential equations numerically. Several approaches are identified and two of them are described in detail. The algorithms developed are applied to the nonlinear Schrödinger equation and Burgers' equation. Numerical results reveal that good performance can be achieved provided that problems are large, solutions are highly localized, and numerical parameters are chosen appropriately, depending on the problem in question.
