Self-Adaptive, Parallel, Isogeometric Analysis (IGA) Using T-Splines and LR-B-Splines for the First-Order Form of the Neutron Transport Equation with

这个博士项目的目的是开发新的，自适应的，并行的，伊加算法应用于反应堆物理和辐射屏蔽问题，使用T样条和LR-B样条技术。更具体地说，这些自适应伊加算法将被应用到一阶形式的中子输运方程的离散纵坐标角（SN）近似和扫描为基础的和扩散合成加速（DSA）求解器方法。伊加是近年来发展起来的一种数值计算技术，它采用计算机辅助设计（CAD）的几何描述，通常由非均匀有理B样条（NURBS）曲面描述符形成。这意味着可以在一个简单的步骤中执行设计和分析，并消除对辅助网格生成器的需求。此外，这些基于NURBS的方法是基本几何的精确描述。

The aim of this PhD project is to develop novel, self-adaptive, parallel, IGA algorithms for application to reactor physics and radiation shielding problems using T-Spline and LR-B-Spline technology. More specifically these self-adaptive IGA algorithms will be applied to the first-order form of the neutron transport equation with discrete ordinate angular (SN) approximation and sweep based and diffusion synthetic acceleration (DSA) solver methods. IGA is a numerical technology that has been developed recently that takes the underlying Computer-Aided Design (CAD) geometry description, which are usually formed by Non-Uniform Rational B-Spline (NURBS) surface descriptors. This means one can perform design and analysis in one simple step and remove the requirement for an ancillary mesh generator. Moreover, these NURBS based approaches are exact descriptions of the underlying geometry.