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IGA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IGA算法将应用于中子输运方程的一阶形式，采用离散纵坐标角（SN）近似和基于扫描和扩散合成加速（DSA）求解方法。IGA是最近发展起来的一种数值技术，它采用底层计算机辅助设计（CAD）几何描述，通常由非均匀有理b样条（NURBS）表面描述符形成。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要求。此外，这些基于NURBS的方法是对底层几何结构的精确描述。

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.