Development of time-parallel numerical integration algorithms using probabilistic methods with applications to magnetic fusion plasma.

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The context of the research - In many branches of science, from astrophysics to epidemiology, mathematical and computational modelling is vital and often involves the numerical integration of large systems of differential equations. Many simulations are limited by bottlenecks that arise when attempting to numerically integrate over long time periods sequentially, causing them to become computationally intractable in real time. By distributing a calculation across the many processors present in modern supercomputers, the computational load can be reduced drastically. Whilst spatially-parallel integration methods have been well explored in the literature, much less attention has been devoted to parallelisation in the time dimension.The aims and objectives of the research - The purpose of this PhD project will be to develop new (or improve existing) time-parallel integration algorithms, using stochastic and statistical methods, in order to reduce simulation times for large-scale systems of differential equations. The interplay between numerics and statistics (known as uncertainty quantification) is currently a very open field and the algorithm(s) being developed will need to be general enough to adapt to the complexity of the problems being solved.The novelty of the research methodology - The majority of currently known time-parallel algorithms have been formulated, studied and analysed using deterministic methods. The algorithm(s) developed in this project will incorporate a measure of stochasticity in order to exploit the statistical differences between deterministically generated solutions. In doing this, statistical and machine learning approaches may be exploited for numerical gain.The potential impact, applications, and benefits - A successfully designed algorithm could be used by UKAEA in order to significantly reduce simulation run times and hence integrate over previously (computationally) intractable ranges of time for magnetic fusion plasmas. These methods are not strictly limited to numerical fusion problems either. The same benefits could be realised in applications to other large-scale integration problems in climate modelling, astrophysics, drug research and many more.How the research relates to the remit - By developing statistically-based time-parallel algorithms with applications to magnetic fusion plasma, the proposed area of research contributes to multiple themes under the EPSRC remit. Namely the 'Numerical analysis' and 'UK Magnetic Fusion Research Programme' themes.Research area; Energy, Mathematical SciencesExternal Partner - Culham Centre for Fusion Energy (part of the UK Atomic Energy Authority)