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

这个博士项目的目的是多方面的。第一个目标是进行全面调查的所有最新一代的加速和预处理算法，并选择这些算法，将执行最佳的时候，与高阶离散的中子扩散和输运方程。这可以涉及改变这些算法，使得它们能够产生中子输运方程的一阶和二阶形式的高阶离散化的可缩放和计算有效的解（即，大于二次多项式阶，其中最近已经观察到计算性能下降）。第二个目标是调查的并行化策略的一阶和二阶形式的中子输运方程（NTE）与离散纵坐标（SN）角离散。第三个目的是了解HPC加速，预处理和并行化算法可以结合空间自适应，能源集团相关的网格。如果时间允许，这将扩展到研究如何联合收割机这些算法与空间角度自适应。

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.