Innovations in spherical approximation - construction, analysis and applications. The motivating problems for this project come from geophysics, including climate, weather forecasting, planetary gravitation and magnetism, and from coding theory and molecular chemistry. National benefit is expected to arise both from an improved ability to handle problems of key economic importance, and from an enhanced position in the international scientific world, through public presentation in leading journa ....Innovations in spherical approximation - construction, analysis and applications. The motivating problems for this project come from geophysics, including climate, weather forecasting, planetary gravitation and magnetism, and from coding theory and molecular chemistry. National benefit is expected to arise both from an improved ability to handle problems of key economic importance, and from an enhanced position in the international scientific world, through public presentation in leading journals and international conferences, and from direct collaboration with internationally leading scientists from USA, UK and Germany. The project will also increase the pool of trained mathematicians with expertise in areas important for applications.
Read moreRead less
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
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
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
Algebraic methods for Markov Chain Monte Carlo and quasi-Monte Carlo. In an increasingly complex world, the requirements on computational methods for solving real world problems from areas like statistics, finance, economics, physics and others are also constantly increasing. The results from this project will significantly improve existing computational methods, thereby helping to solve existing computational challenges and further strengthening Australia's reputation as a leading scientific lo ....Algebraic methods for Markov Chain Monte Carlo and quasi-Monte Carlo. In an increasingly complex world, the requirements on computational methods for solving real world problems from areas like statistics, finance, economics, physics and others are also constantly increasing. The results from this project will significantly improve existing computational methods, thereby helping to solve existing computational challenges and further strengthening Australia's reputation as a leading scientific location. The research carried out will be in collaboration with international experts, creating and strengthening existing ties of Australian research institutions with other world class research institutes overseas.Read moreRead less
High dimensional problems of integration and approximation. In many applications, notably financial mathematics, problems of
integration and approximation of functions in very high dimensions
are of great interest. By finding modern mathematical solutions to
these problems, we will therefore contribute to Australia's future
success in developing innovative technologies for industrial and
economic applications. By researching at an internationally
competitive level and by cooperating with i ....High dimensional problems of integration and approximation. In many applications, notably financial mathematics, problems of
integration and approximation of functions in very high dimensions
are of great interest. By finding modern mathematical solutions to
these problems, we will therefore contribute to Australia's future
success in developing innovative technologies for industrial and
economic applications. By researching at an internationally
competitive level and by cooperating with international experts, we
will have a share in further strengthening the excellent role of
Australian research institutions within the international scientific
community in mathematics and scientific computing.Read moreRead less
Advanced Bayesian Inversion Algorithms for Wave Propagation. This project aims to improve algorithms for detecting hidden items by developing new computational mathematical techniques capable of reconstructing the shape and location of objects using electromagnetic waves. This project expects to generate new knowledge in the areas of Bayesian Inversion and computational wave propagation. Expected outcomes of this project are algorithms that can be developed for use in nonintrusive radio wave sec ....Advanced Bayesian Inversion Algorithms for Wave Propagation. This project aims to improve algorithms for detecting hidden items by developing new computational mathematical techniques capable of reconstructing the shape and location of objects using electromagnetic waves. This project expects to generate new knowledge in the areas of Bayesian Inversion and computational wave propagation. Expected outcomes of this project are algorithms that can be developed for use in nonintrusive radio wave security scanners. This should provide benefits such as the capability to scan a crowd without a checkpoint, which will have the potential to improve security in public places.Read moreRead less
Innovative Methods for Very High Dimensional Problems. Real world problems tend to involve an enormous number of variables. This "curse of dimensionality" poses great difficulty in application areas such as statistics, finance, economics, and physics. These high dimensional problems are not confined to Australia, and there is great demand worldwide for effective and efficient methods to tackle these problems. The novel methods developed here will lead to improvements in prevailing computational ....Innovative Methods for Very High Dimensional Problems. Real world problems tend to involve an enormous number of variables. This "curse of dimensionality" poses great difficulty in application areas such as statistics, finance, economics, and physics. These high dimensional problems are not confined to Australia, and there is great demand worldwide for effective and efficient methods to tackle these problems. The novel methods developed here will lead to improvements in prevailing computational technologies, which will help to enhance Australia's reputation as a leading scientific innovator. The international collaborations will increase the research output of the country, build up the knowledge base in the discipline, draw international interest, and initiate linkages.Read moreRead less