Efficient numerical methods for 3D underwater acoustic wave propagation

Controlled magnetic confinement fusion offers the possibility of an inexhaustible supply of energy with zero greenhouse gas emissions.

The discontinuous Galerkin (DG) method is now an established method for computing approximate solutions of partial differential equations in many applications.

A possible application area for this project is Stellar Astronomy. The project will involve both computational and mathematics aspects, but the focus will depend on the student's interest.

Edge Localised Modes – linear stability and dynamics

Fusion energy promises baseload electricity generation with zero greenhouse gas emissions, a virtually inexhaustible supply of fuel, and significantly reduced radioactive waste, compared to fission and coal.

In ITER, broken toroidal symmetry is introduced deliberately, through the use of resonant magnetic perturbation (RMP) coils, to suppress large explosive instabilities known as edge localised modes (ELMs). It is crucial to evaluate the equilibrium and stability of magnetic field configurations with RMP for ITER scenario

As we move into exascale computing, and beyond, the chance of a fault occurring in the system increases. Traditional approaches to building resilience into the system, such as check-pointing, may become too expensive.

Approximation of High Dimensional Data Sets using Sparse Grid Techniques.

The efficient solution of the Navier Stokes equation provides many challenges. Of particular interest is the efficient description and implementation of free boundaries.

The goal of this project is to compute the particle orbits in a MRxMHD equilibrium with fully 3D field and quantify the impact of the islands and chaos to particle confinement.

In this project we rederive and implement a recently published quantum algorithm for the Vlasov-Maxwell system of equations in Q#, a quantum computation platform.

Recent development of a flowing MHD model for a rotating, collisional plasma column discovered the intriguing prediction of opposite axial acceleration of the plasma ions in the subsonic and supersonic regimes. This project would examine the regime above, below, and through the shock.

I am interested in using a multi-parameter study of invariants from algebraic topology to do statistical shape analysis. The goal is to quantitatively compare geometric objects such as a set of bones, tumours, leaves, bird beaks, etc. I have both theory and application projects.

Fusion plasmas can support a wide range of electromagnetic waves, ranging from pressure and current gradient driven modes to those driven unstable by fast particle-wave resonance. The diagnosis and control of fusion plasmas is contingent on the accurate modelling, prediction, and reliable measurement of such modes.