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Computational methods for multi-scale structural optimisation

Structural optimisation is a powerful computational methodology for finding high-performing designs for structural components or material architectures. For example, what periodic scaffold would provide the highest possible stiffness for its weight?Solving such a problem computationally requires an understanding of the relevant equations required to model the physical properties of interest, as well as efficient implementation of a range of numerical methods including finite elements, finite differences and optimisation.With recent developments in 3D printing technologies it is now becoming possible to …

Study level
PhD, Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Faculty of Science
School
School of Mathematical Sciences

Exact and approximate solutions of diffusion on evolving domains

Classical applications of mathematical analysis involve solving partial differential equation models on fixed domains, e.g. 0 < x < L. Applications in biology, however, involve studying diffusive transport on rapidly evolving domains, e.g. 0 < x < L(t), where L(t) represents the length of the evolving tissue. While many problems have been addressed for the case where L(t) increases, less attention has been paid to cases where we consider diffusion on an oscillating domain.In this project we will construct exact …

Study level
Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Faculty of Science
School
School of Mathematical Sciences

New mathematical and computational techniques for modelling with partial differential equations

Mathematical models involving partial differential equations (PDEs) are useful for simulating many important physical processes including heat and mass transfer, groundwater flow, pollutant transport and drug delivery. This project will focus on developing new mathematical and computational techniques to solve, approximate and/or analyse PDE models.Potential project topics include:developing new numerical and/or analytical methods for solving PDE modelsbuilding new reduced-order PDE models that are easier to solve, interpret or analyseextracting insight into time scales of PDE models, such as the amount …

Study level
PhD, Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Faculty of Science
School
School of Mathematical Sciences

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