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
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
Uncertainty on spheres and shells: mathematics and methods for applications. This project aims to develop new mathematics and mathematically rigorous approximation methods for physical problems on spherical geometries in the presence of uncertainty. Many physical phenomena are modelled on either a sphere or a spherical shell. Such models typically have large uncertainty in the input data, through uncertainty in model coefficients, forcing terms, geometry or boundary conditions. Yet their stochas ....Uncertainty on spheres and shells: mathematics and methods for applications. This project aims to develop new mathematics and mathematically rigorous approximation methods for physical problems on spherical geometries in the presence of uncertainty. Many physical phenomena are modelled on either a sphere or a spherical shell. Such models typically have large uncertainty in the input data, through uncertainty in model coefficients, forcing terms, geometry or boundary conditions. Yet their stochastic modelling and subsequent numerical analysis in the presence of uncertainty are still in their infancy. This project will conduct numerical analysis, stochastic analysis and approximation to address such problems.Read moreRead less
Quantifying uncertainty: innovations in high dimensional computation. High dimensional problems (problems in which there are hundreds or thousands of continuous variables) arise in many applications, from ground water flow to mathematical physics and finance. They typically present major challenges to computational resources and serious mathematical challenges in devising new and improved methods and in proving that they are effective. The aim of this project is to develop new computational meth ....Quantifying uncertainty: innovations in high dimensional computation. High dimensional problems (problems in which there are hundreds or thousands of continuous variables) arise in many applications, from ground water flow to mathematical physics and finance. They typically present major challenges to computational resources and serious mathematical challenges in devising new and improved methods and in proving that they are effective. The aim of this project is to develop new computational methods and theory for high dimensional problems, and to apply these methods to significant applications. The results are expected to allow faster and more accurate solution of problems of growing importance.Read moreRead less
Towards a science of high dimensional computation. This project aims to establish scientifically precise methods for high dimensional problems - methods that are mathematically rigorous, empirically tested, and carefully tailored to specific modern applications across physics, environment, and finance. This project expects to generate new knowledge in the area of high dimensional computation and to develop technological innovations in key areas of science and industry. Expected outcomes of this ....Towards a science of high dimensional computation. This project aims to establish scientifically precise methods for high dimensional problems - methods that are mathematically rigorous, empirically tested, and carefully tailored to specific modern applications across physics, environment, and finance. This project expects to generate new knowledge in the area of high dimensional computation and to develop technological innovations in key areas of science and industry. Expected outcomes of this project include enhanced international and interdisciplinary collaborations, and significant publications and presentations in international forums. These technological advancements will help boost Australia’s position as a world leader in creativity and innovation.Read moreRead less