A coupled finite volume method for viscoelastic flow problems on highly-skewed unstructured meshes: a computational rheology revolution. Commercial tools are unavailable for 21st century industry to analyse complex flow processes involving viscoelastic materials. Using fabrication of microstructured polymer optical fibre as a key case study, a coupled finite volume methodology holds the key for the next generation of computational rheology simulators.
Geometric Methods in Geophysical Fluid Dynamics. The need for a reliable weather forecast has never been more evident. This project addresses fundamental problems which are obstacles to more accurate weather forecasts. The dynamics of the atmosphere and the oceans is inherently complex. The complexity of the flow is confined though by conservation laws. This observation has not yet been used in current weather models. These conservation laws will be the guiding principle for the design of a stab ....Geometric Methods in Geophysical Fluid Dynamics. The need for a reliable weather forecast has never been more evident. This project addresses fundamental problems which are obstacles to more accurate weather forecasts. The dynamics of the atmosphere and the oceans is inherently complex. The complexity of the flow is confined though by conservation laws. This observation has not yet been used in current weather models. These conservation laws will be the guiding principle for the design of a stable numerical integration scheme.
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Advanced computational algorithms for three-dimensional systems. This project deals with the development, analysis and implementation of efficient computer algorithms for a range of complex three dimensional systems. Major areas of focus are forward and inverse acoustic and electromagnetic scattering; dynamical and evolution processes in water waves and tumour growth; and the solution of mathematical models on spheres (earth). Potential application areas of the project include defence science ....Advanced computational algorithms for three-dimensional systems. This project deals with the development, analysis and implementation of efficient computer algorithms for a range of complex three dimensional systems. Major areas of focus are forward and inverse acoustic and electromagnetic scattering; dynamical and evolution processes in water waves and tumour growth; and the solution of mathematical models on spheres (earth). Potential application areas of the project include defence science; ocean engineering; medical research; meteorology and global environmental sciences.Read moreRead less
Lifting the curse of dimensionality - bringing together the quasi Monte Carlo and sparse grid methods. This project is expected to lead to improved methods for handling high-dimensional problems (i.e. problems with many variables) that arise in finance, statistics, commerce, physics, and many other fields. In turn this could lead to significant economic benefit, especially to high-value service industries such as the finance industry. By strengthening international collaboration, it will also ....Lifting the curse of dimensionality - bringing together the quasi Monte Carlo and sparse grid methods. This project is expected to lead to improved methods for handling high-dimensional problems (i.e. problems with many variables) that arise in finance, statistics, commerce, physics, and many other fields. In turn this could lead to significant economic benefit, especially to high-value service industries such as the finance industry. By strengthening international collaboration, it will also help to maintain Australia's strong position in international research in the mathematical sciences.Read moreRead less
A multi-scale approach for modelling coupled transport in heterogeneous and anisotropic porous media. Mathematical Sciences foster interdisciplinary collaboration and underpin fundamental understanding of significant national/international research priorities in science and technology. This world-class team will advance knowledge in modelling complex systems ensuring the competitiveness of Australian research in this important field. A key outcome is a multi-scale computational strategy that can ....A multi-scale approach for modelling coupled transport in heterogeneous and anisotropic porous media. Mathematical Sciences foster interdisciplinary collaboration and underpin fundamental understanding of significant national/international research priorities in science and technology. This world-class team will advance knowledge in modelling complex systems ensuring the competitiveness of Australian research in this important field. A key outcome is a multi-scale computational strategy that can be used by engineers in Australia and France to simulate transport phenomena in porous media, which have significant environmental impact. The research will lead to publications in scientific journals and communications at national/international conferences. Research training of postdocs and PhD students is another excellent outcome of the project.Read moreRead less
Novel Mathematical Technologies for Financial Valuation and Risk. The finance industry is a key industry sector in Australia, with a highly qualified and well-paid work force. The profitability and stability of financial institutions rests in part on their ability to accurately and rapidly value innovative financial products and to quantify risk, yet many contemporary financial products are difficult to value quickly and accurately. This project will bring innovative mathematical technologies ....Novel Mathematical Technologies for Financial Valuation and Risk. The finance industry is a key industry sector in Australia, with a highly qualified and well-paid work force. The profitability and stability of financial institutions rests in part on their ability to accurately and rapidly value innovative financial products and to quantify risk, yet many contemporary financial products are difficult to value quickly and accurately. This project will bring innovative mathematical technologies to bear on complex financial problems. It has the potential to improve both the profitability and stability of Australian financial institutions, and to enhance their role regionally and internationally.Read moreRead less
Constrained and Stable Solutions of Nonlinear and Semismooth Equations. In this project, comprehensive models for designing safe power system parameters will be proposed, efficient algorthms for solving these models will be constructed. The new models and algorithms in this project will provide efficient tools to prevent catastrophic events in power systems, which is related with national security. This project will also strengthen collaboration of Australian applied
mathematians with inter ....Constrained and Stable Solutions of Nonlinear and Semismooth Equations. In this project, comprehensive models for designing safe power system parameters will be proposed, efficient algorthms for solving these models will be constructed. The new models and algorithms in this project will provide efficient tools to prevent catastrophic events in power systems, which is related with national security. This project will also strengthen collaboration of Australian applied
mathematians with international researchers and engineering scientists. This is important for the advance of science and technology in
Australia.Read moreRead less
Approximation, Cubature and Point Designs on Spheres. The sphere is important in fields ranging from geophysics to global climate modelling to chemistry to codes for modern communications. This project aims to strengthen and unify key areas of mathematics on the sphere and at the same time provide methods and constructiions of practical significance. The areas of focus are constructive approximation of functions on the sphere, numerical integration on the sphere, and well distributed sets of poi ....Approximation, Cubature and Point Designs on Spheres. The sphere is important in fields ranging from geophysics to global climate modelling to chemistry to codes for modern communications. This project aims to strengthen and unify key areas of mathematics on the sphere and at the same time provide methods and constructiions of practical significance. The areas of focus are constructive approximation of functions on the sphere, numerical integration on the sphere, and well distributed sets of points on the sphere, including spherical designs.Read moreRead less
Nonsmooth Optimization in Constrained Spline Interpolation. Traditional methods based on standard calculus may not work for optimization problems with constraints; however, such problems can be reformulated as nonsmooth problems that need special treatment. The project aims to approach several important problems in constrained spline interpolation and approximation, from the perspective of nonsmooth optimization. The research, which builds upon a recent breakthrough in the approach to the convex ....Nonsmooth Optimization in Constrained Spline Interpolation. Traditional methods based on standard calculus may not work for optimization problems with constraints; however, such problems can be reformulated as nonsmooth problems that need special treatment. The project aims to approach several important problems in constrained spline interpolation and approximation, from the perspective of nonsmooth optimization. The research, which builds upon a recent breakthrough in the approach to the convex best interpolation by the applicant and his collaborators, is expected to provide fundamental theory for Newton-type methods being used for these problems with a vast number of applications in data fitting and curve and surface design.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE120101707
Funder
Australian Research Council
Funding Amount
$375,000.00
Summary
Regularisation methods for solving nonlinear ill-posed inverse problems. Nonlinear inverse problems arise in numerous applications and their stable resolutions require regularisation methods. This project will develop various efficient solvers by using optimisation tools and Newton type procedures and consider their convergence properties. The methods will be applied to practical problems including the tomography techniques.