Finite element methods for Boltzmann neutron transport equation on polygonal and polyhedral meshes

核反应堆的设计和安全研究需要解决许多多物理场问题。这种近似通常是令人望而却步的计算昂贵，因为它需要复杂的神经元和热工水力动力学的耦合。新的技术，既有效又准确的需要被开发，以满足挑战。这个博士工作的目标是构思和开发数值方案，以解决玻尔兹曼方程的多边形和多面体网格内的空间离散化和其他变量的相关技术的有限元方法的背景下，中子输运。此外，这项博士工作还将包括对一组有序机械细胞进行分区的图形算法的研究。结果;一个快速算法，以促进并行计算。该项目将与CEA（法国替代能源和原子能委员会）合作。

The design and safety studies of nuclear reactors require the solution of many multi-physics problems. This approximation is often prohibitively computationally expensive as it requires the coupling of complex neuronic and thermal hydraulic dynamics. New techniques that are both efficient and accurate need to be developed to meet the challenge.The goal of this PhD work is to conceive and develop numerical schemes to solve the Boltzmann equation for neutron transport on polygonal and polyhedral meshes within the context of finite element methods for the spatial discretisation and related techniques for other variables. Furthermore, this PhD work will also encompass research on graph algorithms for partitioning a set of ordered mech cells. The result; a fast algorithm to facilitate parallel computation.This project will be in partnership with the CEA (French Alternative Energies and Atomic Energy Commission).