Adaptive mesh h(p)-refinement of a discontinuous Bubnov-Galerkin isogeometric analysis spatial discretisation of the first-order form of the neutron transport equation with goal-based error measures and diffusion acceleration
File(s)
Published version
Author(s)
Wilson, SG
Eaton, MD
Kópházi, J
Type
Journal Article
Abstract
This paper presents the first application of self-adaptive mesh h(p)-refinement (AMR), with goal-based error measures (DWR), to a discontinuous Bubnov-Galerkin (DBG) NURBS-based isogeometric analysis (IGA) spatial discretisation of the first-order form of the neutron transport equation with partially-consistent diffusion synthetic acceleration (DSA) schemes. A modified (symmetric) interior penalty (MIP) scheme is proposed for the spatial discretisation of the diffusion acceleration equation. The penalty parameters are calculated to be sufficiently large, without being arbitrarily so, for general element types; and where they become negligibly small for increasingly thick cells, a minimum penalisation is borrowed, from Wang and Ragusa [1], from a consistent diffusion-conforming form of the acceleration equation. The MIP-DBG-IGA discretisation yields linear systems that are symmetric positive definite; and so, the diffusion acceleration equation can be solved efficiently by the preconditioned conjugate gradient method. Importantly, the proposed MIP-DBG-IGA DSA schemes are stable and compatible over the increasingly irregular spatial meshes of complex, rational geometries generated at each iteration of the proposed DWR-AMR-h(p) algorithm, which employs duality arguments to minimise the error in some prescribed quantity of interest.
Date Issued
2026-06-15
Date Acceptance
2026-03-01
Citation
Computer Methods in Applied Mechanics and Engineering, 2026, 455
ISSN
0045-7825
Publisher
Elsevier BV
Journal / Book Title
Computer Methods in Applied Mechanics and Engineering
Volume
455
Copyright Statement
© 2026 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ).
License URL
Publication Status
Published
Article Number
118872
Date Publish Online
2026-03-06