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

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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.