Interface-aware numerical methods for stochastic inverse problems. This project aims to design novel high-performance numerical tools for solving large-scale forward and inverse problems dominated by stochastic interfaces and quantifying associated uncertainties. In real-world applications such as groundwater, these tools are instrumental for assimilating big datasets into mathematical models for providing reliable predictions. By advancing and integrating high-order polytopal schemes, multileve ....Interface-aware numerical methods for stochastic inverse problems. This project aims to design novel high-performance numerical tools for solving large-scale forward and inverse problems dominated by stochastic interfaces and quantifying associated uncertainties. In real-world applications such as groundwater, these tools are instrumental for assimilating big datasets into mathematical models for providing reliable predictions. By advancing and integrating high-order polytopal schemes, multilevel methods, transport maps, and dimension reduction, this project's anticipated outcomes are highly accurate and cost-efficient numerical schemes, certified by rigorous mathematical analysis. This should provide data-centric simulation tools with enhanced reliability, for engineering and scientific applications.Read moreRead less
Towards predictive 4D computational models for the heart. This project aims to develop novel high-performance numerical algorithms for multiscale and multiphysics PDEs with dynamic interfaces, the development and analysis of a novel PDE system modelling the electromechanics of heart and torso, and the combination of these numerical techniques and models to deliver predictive tools for patient-specific simulations of the cardiac function. It involves the design and mathematical analysis of space- ....Towards predictive 4D computational models for the heart. This project aims to develop novel high-performance numerical algorithms for multiscale and multiphysics PDEs with dynamic interfaces, the development and analysis of a novel PDE system modelling the electromechanics of heart and torso, and the combination of these numerical techniques and models to deliver predictive tools for patient-specific simulations of the cardiac function. It involves the design and mathematical analysis of space-time variational discretisations on embedded meshes, 4D computational geometry algorithms for numerical integration and multilevel solvers. By combining scientific computing and machine learning, one anticipated outcome of this research is a new generation of nonlinear PDE approximations and solvers.Read moreRead less
New Approaches to Modelling and Analysing Long-Memory Random Processes. The project aims to develop new approaches using infinite-dimensional Markov processes to solving important long-standing problems from the theory of long memory random processes and their applications. It aims to: construct a class of new representations of random processes; derive inequalities for the key numerical characteristics; and, devise and investigate numerical methods for computing the characteristics and for perf ....New Approaches to Modelling and Analysing Long-Memory Random Processes. The project aims to develop new approaches using infinite-dimensional Markov processes to solving important long-standing problems from the theory of long memory random processes and their applications. It aims to: construct a class of new representations of random processes; derive inequalities for the key numerical characteristics; and, devise and investigate numerical methods for computing the characteristics and for performing statistical inference on the long memory models. The accuracy of numerical approximations will be analysed using simulations on supercomputers. Expected outcomes include models and results of practical importance with applications such as intrusion detection problems, cell motility for biological data and telecommunication.Read moreRead less
Advanced simulation methods for the coupled solar interior and atmosphere. This project aims to develop numerical methods for complex magnetohydrodynamic simulations able to handle sharp and dynamically evolving inhomogeneities, spherical geometries, and dramatic variations in density and wave speed across the simulation domain. The project plans to develop these methods within the context of solar wave processes, which are fundamental to the transfer of energy from the sun’s interior to its out ....Advanced simulation methods for the coupled solar interior and atmosphere. This project aims to develop numerical methods for complex magnetohydrodynamic simulations able to handle sharp and dynamically evolving inhomogeneities, spherical geometries, and dramatic variations in density and wave speed across the simulation domain. The project plans to develop these methods within the context of solar wave processes, which are fundamental to the transfer of energy from the sun’s interior to its outer atmosphere, to the acceleration of the solar wind that rushes past the Earth continually, and to solar activity in general. This would provide the best available modelling of how the sun's atmosphere works, with direct implications for how the Earth's space environment is determined by solar storms and eruptions.Read moreRead less
Mathematics for breaking limits of speed and density in magnetic memories. The aim of this project is to develop a mathematical theory and numerical models of stochastic partial differential equations for magnetic nano-structures. Such materials will yield next-generation magnetic memories with up to three orders of magnitude faster switching speeds and dramatically increased data storage density. New mathematical theories will help understand their sensitivity to small random fluctuations that ....Mathematics for breaking limits of speed and density in magnetic memories. The aim of this project is to develop a mathematical theory and numerical models of stochastic partial differential equations for magnetic nano-structures. Such materials will yield next-generation magnetic memories with up to three orders of magnitude faster switching speeds and dramatically increased data storage density. New mathematical theories will help understand their sensitivity to small random fluctuations that can destroy stored information. This project aims to revolutionise mathematical modelling of magnetic memories and put Australia at the forefront of international research. Technological advances to create much smaller and faster memory devices are expected to enable groundbreaking ways of managing and mining big data.Read moreRead less
Numerical modelling of the solar atmosphere. This project will develop a complete and realistic model of the magnetic solar activity using computer simulations of the interconnected solar interior and atmosphere. The results of this project will provide a deeper insight into the physical processes behind solar activity phenomena and will help in the development of methods of solar activity prediction.
New structures in geometric numerical integration. Many scientific phenomena in physics, astronomy, chemistry, and geoscience, are modelled by differential equations (DEs). Generally DEs have no closed form solutions, and one must rely on numerical integration. Traditionally this is done using, for example, Runge-Kutta methods or linear multistep methods, respectively finite difference or finite element methods. Recently, however, novel so-called ‘geometric’ integration methods that preserve qua ....New structures in geometric numerical integration. Many scientific phenomena in physics, astronomy, chemistry, and geoscience, are modelled by differential equations (DEs). Generally DEs have no closed form solutions, and one must rely on numerical integration. Traditionally this is done using, for example, Runge-Kutta methods or linear multistep methods, respectively finite difference or finite element methods. Recently, however, novel so-called ‘geometric’ integration methods that preserve qualitative features of many DEs exactly (as opposed to traditional methods) have been discovered, leading to crucial stability improvements. Combining aspects of dynamical systems theory and traditional numerical DEs, this project will improve, extend, and systematise this new field of geometric integration.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE140101398
Funder
Australian Research Council
Funding Amount
$355,744.00
Summary
Quantifying the risk of groundwater contamination from hydraulic fracturing in coal seam gas operations in Australia. Concern for impacts to groundwater resources due to coal seam gas operations has led to heated debate in the community. This project will assess the risk to groundwater contamination from fracking in coal seam gas operations. It is critical that naturally occurring compounds in the coal seam and injected compounds are not mobilised to aquifers topped by water bores. This project ....Quantifying the risk of groundwater contamination from hydraulic fracturing in coal seam gas operations in Australia. Concern for impacts to groundwater resources due to coal seam gas operations has led to heated debate in the community. This project will assess the risk to groundwater contamination from fracking in coal seam gas operations. It is critical that naturally occurring compounds in the coal seam and injected compounds are not mobilised to aquifers topped by water bores. This project will build accurate, site-specific, dynamic numerical models of the hydraulic-fracturing process in coal seam gas operations. This will enable prediction of the maximum vertical extent of stimulated fractures in specific coal seams and will help establish criteria for when and where fracking in coal seam gas wells is safe in relation to groundwater contamination.Read moreRead less
Algorithms for multi-scale problems in science and engineering. This project aims to develop theoretical formulations and algorithms for modelling fundamental problems in molecular electrostatics, dispersion force theory, acoustics and electromagnetic scattering in applications where current approaches may be useless. Many engineering applications, from microelectronics to bioengineering devices, need to operate across dimensions from a few millimetres down to a million times smaller. This large ....Algorithms for multi-scale problems in science and engineering. This project aims to develop theoretical formulations and algorithms for modelling fundamental problems in molecular electrostatics, dispersion force theory, acoustics and electromagnetic scattering in applications where current approaches may be useless. Many engineering applications, from microelectronics to bioengineering devices, need to operate across dimensions from a few millimetres down to a million times smaller. This large range of length scales means traditional modelling tools and computational techniques will rapidly become intractable. This project will meet this need to strengthen the Australian technological skill base and contribute to innovations in areas ranging from bioengineering to nanotechnology.Read moreRead less
Modelling of soft multi-scale systems. This project develops realistic physical models and efficient computational methods as the platform technology for giving highly accurate predictions of the complex behaviour of soft deformable systems. The outcomes will add to our understanding of the mechano-biology of living cells and artificial soft body tissues, the cellular uptake of nutrients and drugs, the energy-efficient processing of high value pharmaceutical emulsions and the design of functiona ....Modelling of soft multi-scale systems. This project develops realistic physical models and efficient computational methods as the platform technology for giving highly accurate predictions of the complex behaviour of soft deformable systems. The outcomes will add to our understanding of the mechano-biology of living cells and artificial soft body tissues, the cellular uptake of nutrients and drugs, the energy-efficient processing of high value pharmaceutical emulsions and the design of functional polymers and proteins using molecular models. The new knowledge will advance the frontier of material design and characterisation of soft complex materials.Read moreRead less