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

Lead Research Organisation: Imperial College London
Department Name: Dept of Mechanical Engineering


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.


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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/N509486/1 01/10/2016 31/03/2022
1869743 Studentship EP/N509486/1 01/10/2016 30/06/2020 Seth Wilson
Description Work was focused mainly on developing continuous and discontinuous spatial discretisations of elliptic and hyperbolic partial differential equations, namely the multigroup neutron diffusion equations, second-order and first-order forms of the neutron transport equations; and significant gains in accuracy and performance were achieved when employing:
- exact geometry representation of the underlying geometry in a Galerkin NURBS-based Isogeometric Analysis spatial discretisation
- energy-dependent meshes
- energy-driven and goal-based hp-adaptive local refinement
- acceleration techniques for the transport equations, namely diffusion synthetic acceleration with a GMRes (Krylov) wrapper
Exploitation Route to be adapted / implemented in production codes
incorporated within existing codes - interest potentially from the sponsor
to be linked with existing CAD programs in order to facilitate more general geometries and problems that the analysis can be performed upon
Sectors Aerospace, Defence and Marine,Energy