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。第一个目标是对所有最新一代的加速和预处理算法进行全面的调查，并选择那些在与中子扩散和输运方程的高阶离散化一起使用时性能最好的算法。这可能涉及改变这些算法，以便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伸缩和计算有效的解(即，大于二次多项式的阶数，其中最近观察到计算性能下降)。第二个目标是研究具有离散纵坐标(SN)角离散的中子输运方程(NTE)的一阶和二阶形式的并行化策略。第三个目标是了解HPC加速、预条件和并行化算法如何与空间自适应性和能量群相关网格相结合。如果时间允许，这将扩展到研究如何将这些算法与空间角度自适应相结合。

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.