Self-Adaptive, Unstructured Mesh, NURBS Enhanced, Polyhedral Schemes, with Hybrid Multicore CPU and Manycore GPU Solution Algorithms, for Nuclear Reac

(a)发展计算效率高、数值准确、空间自适应的二维和三维nurbs增强VE方法。这将建立在伦敦帝国理工学院核工程小组先前进行的研发工作的基础上。(b)利用中子输运方程的原解（正解）和伴随解以及相关的规定泛函，发展数学上严格的、双加权残差的、基于目标的或面向目标的误差测量。这将适用于特征值（核临界的Keff）问题以及固定（或规定）中子源问题。在这种情况下，典型的“目标”将是感兴趣的全局量，如临界度（或Keff），计算域规定区域内的局部裂变/捕获反应速率，或局部量，如计算域规定点上的标量/角中子通量、中子/伽马射线光子通量、辐射剂量或辐射损伤（每原子位移或DPA）。(c)在nurbs增强的非结构化多边形/多面体网格上开发计算效率高、大规模并行、混合多核CPU/多核GPU离散坐标（SN）扫描的中子输运求解器。这将利用混合OpenMP（共享），MPI（分布式）和CUDA/OpenCL （GPU）并行软件库的优势。一个关键的方面将是研究基于离散坐标（SN）扫描的中子输运求解器算法在使用多核CPU和使用多核GPU方面更优的具体方面，以及如何有效地在这两种不同类型的计算单元之间有效地传递数据。(d)该项目的最后一个方面将是将所制订的方法应用于标准多维和多尺度核反应堆物理和反应堆屏蔽基准核查试验案例。这些基准验证测试用例将用于研究使用混合多核CPU和多核GPU工作站和HPC系统的自适应、大规模并行、nurbs增强的虚拟元素方法的计算效率、可扩展性和数值精度。这些将包括OECD/NEA 3D C5G7 UOX/MOX彩色核反应堆物理基准验证测试用例和扩展的OECD/NEA KAIST轻水反应堆（LWR）核反应堆物理基准测试用例。对于反应堆屏蔽，OECD/NEA SINBAD耦合中子和伽马射线光子输运ASPIS和曲柄导管基准验证测试案例将进行研究。

(a) Development of computationally efficient, numerically accurate, spatially self-adaptive NURBS-enhanced VE methods in 2D and 3D. This will build upon prior R&D work performed by the nuclear engineering group at Imperial College London.(b) Development of mathematically rigorous, dual-weighted-residual, goal-based or goal-oriented error measures using the primal (forward) and adjoint solutions of the neutron transport equation with an associated prescribed functional. This will be applied to both eigenvalue (Keff of nuclear criticality) problems as well as fixed (or prescribed) neutron source problems. In this case typical "goals" will be global quantities of interest, such as the degree of criticality (or Keff), the local fission/capture reaction rate within prescribed regions of the computational domain, or local quantities such as scalar/angular neutron flux, neutron/gamma-ray photon fluence, radiation dose or radiation damage (displacement per atom or DPA) at prescribed points within the computational domain.(c) Development of computationally efficient, massively parallel, hybrid multicore CPU/manycore GPU discrete ordinate (SN) sweep based neutron transport solvers on NURBS-enhanced unstructured polygonal/polyhedral meshes. This will take advantage of hybrid OpenMP (shared), MPI (distributed) and CUDA/OpenCL (GPU) parallel software libraries. A key aspect will be investigating what specific aspect of the discrete ordinate (SN) sweep based neutron transport solver algorithm will be more optimal in terms of the use of the multicore CPU versus use of the manycore GPU and how data can be effectively passed between these two different types of compute units as efficiently as possible for sweep algorithms.(d) A final aspect of the project will be applying the methods developed to standard multidimensional and multiscale nuclear reactor physics and reactor shielding benchmark verification test cases. These benchmark verification test cases will be used to investigate the computational efficiency, scalability and numerical accuracy of the self-adaptive, massively parallel, NURBS-enhanced virtual element methods using hybrid multicore CPU and manycore GPU workstation and HPC systems. These will include the OECD/NEA 3D C5G7 UOX/MOX colour-set nuclear reactor physics benchmark verification test case and the extended quarter-core OECD/NEA KAIST Light Water Reactor (LWR) nuclear reactor physics benchmark test case. For reactor shielding the OECD/NEA SINBAD coupled neutron and gamma-ray photon transport ASPIS and Crank-duct benchmark verification test cases will be investigated.