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
A Robust Optimization Technique for Identifying Geomechanical Parameters Using In-situ Measurements. The aim of this project is to develop a robust optimisation technique for identifying geomechanical parameters for subsequent stability analysis of rock structures in particular open pits. The development involves a novel solution method based on current work in finite element method and large-scale optimisation with partial differential equation constraints. The outcomes of the project will prov ....A Robust Optimization Technique for Identifying Geomechanical Parameters Using In-situ Measurements. The aim of this project is to develop a robust optimisation technique for identifying geomechanical parameters for subsequent stability analysis of rock structures in particular open pits. The development involves a novel solution method based on current work in finite element method and large-scale optimisation with partial differential equation constraints. The outcomes of the project will provide a sophisticated numerical technique for geotechnical engineers/scientists to determine geomechanical parameters accurately from in-situ observation and displacement measurements, leading to the optimal design of rock structures in subsequent analysis.Read moreRead less
Regularisation methods of inverse problems: theory and computation. This project aims to investigate regularisation methods for inverse problems which are ill-posed in the sense that their solutions depend discontinuously on the data. When only noisy data is available, regularisation methods define stable approximate solutions by replacing the original inverse problem with a family of well-posed neighbouring problems monitored by a so-called regularisation parameter. The project expects to devel ....Regularisation methods of inverse problems: theory and computation. This project aims to investigate regularisation methods for inverse problems which are ill-posed in the sense that their solutions depend discontinuously on the data. When only noisy data is available, regularisation methods define stable approximate solutions by replacing the original inverse problem with a family of well-posed neighbouring problems monitored by a so-called regularisation parameter. The project expects to develop purely data-driven rules to choose the regularisation parameter and show how they work in theory, and in practice. It will also develop convex framework, acceleration strategies as well as preconditioning and splitting ideas to design efficient regularisation solvers.Read moreRead less
A new perturbation method for solving singular operator equations with applications to complex systems. This project will develop new methods for analysis of web-based search routines such as Google PageRank, a new algorithm for optimal estimation of random signals, more accurate error analysis in the approximate solution of singular systems of equations and enhanced understanding of models for the simulated management of urban stormwater. The project will involve collaboration between two Aus ....A new perturbation method for solving singular operator equations with applications to complex systems. This project will develop new methods for analysis of web-based search routines such as Google PageRank, a new algorithm for optimal estimation of random signals, more accurate error analysis in the approximate solution of singular systems of equations and enhanced understanding of models for the simulated management of urban stormwater. The project will involve collaboration between two Australian universities and a leading European Research Institute. It will provide employment and vital training for two postdoctoral Research fellows and research projects for three postgraduate students and two honours students.Read moreRead less
The design and development of a novel high power-to-weight actuator. Powerful and compact actuators are becoming increasingly in demand due to the sophistication in a range of uses varying from aerospace to automotive accessories. The aim of this project is to develop an actuator with high performance and power-to-weight ratio, suitable for use in cutting-edge applications. In the first instance, the focus will be on developing an automotive mirror actuator in close collaboration with the indust ....The design and development of a novel high power-to-weight actuator. Powerful and compact actuators are becoming increasingly in demand due to the sophistication in a range of uses varying from aerospace to automotive accessories. The aim of this project is to develop an actuator with high performance and power-to-weight ratio, suitable for use in cutting-edge applications. In the first instance, the focus will be on developing an automotive mirror actuator in close collaboration with the industrial partner, but the generic research outcomes will be applicable to development of actuators for other purposes. The new generation actuators will contribute to Australian manufacturing exports to become internationally competitive.Read moreRead less