Discovery Early Career Researcher Award - Grant ID: DE130100333
Funder
Australian Research Council
Funding Amount
$315,640.00
Summary
A new class of fast and reliable spectral methods for partial differential equations. The project will develop novel fast and reliable spectral methods for computing solutions to general partial differential equations. These methods will be applied to solve important equations that arise in mathematical physics and other areas where high accuracy is essential.
Novel mathematics and numerical methods for ferromagnetic problems. This project aims to develop novel mathematical theories and numerical methods for ferromagnetic problems. These problems arise from many real-life applications, for example in storage devices and magnetic sensors, which are often affected by random (thermal) noise. Since thermal noise limits the data-retention time of the devices, analysing the effect of noise is highly significant. Expected outcomes will be novel computational ....Novel mathematics and numerical methods for ferromagnetic problems. This project aims to develop novel mathematical theories and numerical methods for ferromagnetic problems. These problems arise from many real-life applications, for example in storage devices and magnetic sensors, which are often affected by random (thermal) noise. Since thermal noise limits the data-retention time of the devices, analysing the effect of noise is highly significant. Expected outcomes will be novel computational techniques to solve the underlying equations and deal with randomness. The project aims to put Australia in the forefront of international research in numerical methods in micromagnetism. The new computational methods are expected to be used to advance technology in magnetic memory devices.Read moreRead less
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
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
Discovery Early Career Researcher Award - Grant ID: DE170100222
Funder
Australian Research Council
Funding Amount
$313,964.00
Summary
Optimal adaptivity for uncertainty quantification. This project aims to use an adaptive mesh refinement algorithm to improve the ratio of approximation accuracy versus computational time. Partial differential equations with random coefficients are crucial in simulating groundwater flow, structural stability and composite materials, but their numerical approximation is difficult and time consuming. Advances in adaptive mesh refinement theory allow full analysis and mathematical understanding of t ....Optimal adaptivity for uncertainty quantification. This project aims to use an adaptive mesh refinement algorithm to improve the ratio of approximation accuracy versus computational time. Partial differential equations with random coefficients are crucial in simulating groundwater flow, structural stability and composite materials, but their numerical approximation is difficult and time consuming. Advances in adaptive mesh refinement theory allow full analysis and mathematical understanding of the convergence behaviour of the proposed algorithm. The project intends to develop a theory of adaptive algorithms and freely available software for their reliable (and mathematically underpinned) simulation which could solve problems beyond the capabilities of even the most powerful computers.Read moreRead less
Novel Mathematics and Efficient Computational Techniques for Human Vision. This project aims to develop a new mathematical framework to understand elastic properties of human corneas. The project expects to generate new knowledge in understanding bio-mechanical models for human corneas, as well as other engineering applications involving materials with random fluctuations of elasticity. Expected outcomes of this project include new mathematics and computational algorithms for solving complex mat ....Novel Mathematics and Efficient Computational Techniques for Human Vision. This project aims to develop a new mathematical framework to understand elastic properties of human corneas. The project expects to generate new knowledge in understanding bio-mechanical models for human corneas, as well as other engineering applications involving materials with random fluctuations of elasticity. Expected outcomes of this project include new mathematics and computational algorithms for solving complex mathematical equations which describe elastic and hyper-elastic materials such as human corneas. This project will benefit Australia by enhancing the standing in cutting edge research trends in computational mathematics such as uncertainty quantification and machine learning.Read moreRead less
The mathematics of novel magnetic memory materials. Magnetic memories are the world’s principal device for storing information. The next generation will have greatly increased access speed and data-storage capacity. This project will develop the mathematical theory of these new magnetic memory materials, a crucial first step in understanding and being able to fine-tune their properties.
Novel Approaches for Problems with Uncertainties. This project aims to develop novel mathematical theories and numerical methods for problems affected by uncertainty in input data. This type of uncertainty exists in most mathematical models of real life applications. For these problems, a single deterministic simulation with one set of input data is of limited use. Therefore, novel techniques to deal with randomness are essential. The problems in this project are driven by specific applications ....Novel Approaches for Problems with Uncertainties. This project aims to develop novel mathematical theories and numerical methods for problems affected by uncertainty in input data. This type of uncertainty exists in most mathematical models of real life applications. For these problems, a single deterministic simulation with one set of input data is of limited use. Therefore, novel techniques to deal with randomness are essential. The problems in this project are driven by specific applications from ferromagnetism, structural acoustics and vibration. The new theories may lay the foundation for understanding ferromagnetic materials and structural acoustics. The novel approaches to be developed in this project may form the basis for the study of stochastic liquid crystal theory and other interface problems.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
Mathematical and Numerical Models of Piezoelectric Wave Energy Converters. The project will investigate piezoelectric wave energy converters. We will derive the equations of motion in a form suitable for use in marine engineering paradigms using variational methods and then solve these analytically and with smoothed particle hydrodynamics. Using these innovative techniques, this project will generate new knowledge capable of elucidating the multifaceted physical phenomena that occur when comple .... Mathematical and Numerical Models of Piezoelectric Wave Energy Converters. The project will investigate piezoelectric wave energy converters. We will derive the equations of motion in a form suitable for use in marine engineering paradigms using variational methods and then solve these analytically and with smoothed particle hydrodynamics. Using these innovative techniques, this project will generate new knowledge capable of elucidating the multifaceted physical phenomena that occur when complex fluid motion and deformable structures interact. The project outcomes include the development of mathematical and computation methods to handle intricate behaviours of piezoelectric elastic-fluids systems. These groundbreaking methods will allow these wave energy systems to be analysed and their effectiveness assessed.Read moreRead less