Shared and Distributed Memory Parallel Pre-Conditioning and Acceleration Algorithms for "Spline- Enhanced" Spatial Discretisations

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The aim of this PhD project is manifold. The first aim is to conduct a comprehensive survey of all the latest generation acceleration and preconditioning algorithms and select those algorithms that will perform optimally when used in conjunction with high order discretisations of the neutron diffusion and transport equations. This may involve altering these algorithms so that they are able to produce scaleable and computationally efficient solutions of high order discretisations of the first and second order forms of the neutron transport equation (i.e., greater than quadratic polynomial order where computational performance degradation has been observed recently). The second aim is to investigate parallelisation strategies for both first and second order forms of the neutron transport equation (NTE) with discrete ordinate (SN) angular discretisations. The third aim is to understand how HPC acceleration, preconditioning and parallelisation algorithms can be combined with spatial adaptivity, and energy group dependent meshes. If time permits this would be extended to investigating how to combine these algorithms with space-angle adaptivity.