Computational Schemes for Initial-Boundary Value Problems. Many physical phenomena can be modelled as initial-boundary value problems described by partial differential equations. Simulations of such models require efficient and robust computational algorithms. The main aim of this project is to propose numerical algorithms for two dimensional spatial problems and three dimensional time-space models. A major focus of the project is to investigate methods that require about half the computation ....Computational Schemes for Initial-Boundary Value Problems. Many physical phenomena can be modelled as initial-boundary value problems described by partial differential equations. Simulations of such models require efficient and robust computational algorithms. The main aim of this project is to propose numerical algorithms for two dimensional spatial problems and three dimensional time-space models. A major focus of the project is to investigate methods that require about half the computational resources over celebrated schemes for solving boundary value problems.Read moreRead less
GEOMETRIC NUMERICAL INTEGRATION. Many scientific phenomena in physics, astronomy, and chemistry, are modelled by ordinary differential equations (ODEs). Often these equations have no solution in closed form, and one relies on numerical integration. Traditionally this is done using Runge-Kutta methods or linear multistep methods. In the last decade, however, we (and others) have discovered novel classes of so-called "geometric" numerical integration methods that preserve qualititative featur ....GEOMETRIC NUMERICAL INTEGRATION. Many scientific phenomena in physics, astronomy, and chemistry, are modelled by ordinary differential equations (ODEs). Often these equations have no solution in closed form, and one relies on numerical integration. Traditionally this is done using Runge-Kutta methods or linear multistep methods. In the last decade, however, we (and others) have discovered novel classes of so-called "geometric" numerical integration methods that preserve qualititative features of certain ODE's exactly (in contrast to traditional methods), leading to crucial stability improvements. Extending concepts from dynamical systems theory and traditional numerical ODEs, this project will improve, extend and systematize this new field of geometric integration.Read moreRead less
Geometric Integration. This project gives an important boost to Australia's strength in the niche area of geometric numerical integration,in the face of strong international competition. It gathers 7 world experts from 5 countries to create new computer programs to improve calculations in dynamics, with applications ranging from astronomy, physics, chemistry, biology, and meteorology to finance. It strengthens Australia's links with the mathematical software industry, and will lead to world-clas ....Geometric Integration. This project gives an important boost to Australia's strength in the niche area of geometric numerical integration,in the face of strong international competition. It gathers 7 world experts from 5 countries to create new computer programs to improve calculations in dynamics, with applications ranging from astronomy, physics, chemistry, biology, and meteorology to finance. It strengthens Australia's links with the mathematical software industry, and will lead to world-class graduates and research training.Read moreRead less
Geometric numerical integration of differential equations. Differential equations (DEs) play a central role in modelling scientific phenomena in physics, biology, chemistry, astronomy, meteorology, and geoscience. We have developed new ways of solving DEs, using geometric integration, which have significant advantages over traditional methods because of the crucial nonlinear stability they provide.
This project, combining 7 world experts from 6 countries and 1 early career researcher, will pl ....Geometric numerical integration of differential equations. Differential equations (DEs) play a central role in modelling scientific phenomena in physics, biology, chemistry, astronomy, meteorology, and geoscience. We have developed new ways of solving DEs, using geometric integration, which have significant advantages over traditional methods because of the crucial nonlinear stability they provide.
This project, combining 7 world experts from 6 countries and 1 early career researcher, will place Australia at the forefront of this intensive international activity.
It will significantly strengthen Australia's links with the mathematical software industry (e.g. Wolfram Research, Inc), and will lead to world class graduates and research training.
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