hp-Adaptive discontinuous Galerkin methods for neutron transport criticality problems

Hall, Edward and Houston, Paul and Murphy, Steven (2017) hp-Adaptive discontinuous Galerkin methods for neutron transport criticality problems. SIAM Journal on Scientific Computing, 39 (5). B916-B942. ISSN 1095-7197

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In this article we consider the application of high-order/hp-version adaptive discontinuous Galerkin finite element methods (DGFEMs) for the discretization of the keff-eigenvalue problem associated with the neutron transport equation. To this end, we exploit the dual weighted residual approach to derive a reliable and efficient a posteriori error estimate for the computed critical value of keff. Moreover, by exploiting the underlying block structure of the hp-version DGFEM, we propose and implement an efficient numerical solver based on exploiting Tarjan's strongly connected components algorithm to compute the inverse of the underlying transport operator; this is then utilised as an efficient preconditioner for the keff-eigenvalue problem. Finally, on the basis of the derived a posteriori error estimator we propose an hp-adaptive refinement algorithm which automatically refines both the angular and spatial domains. The performance of this adaptive strategy is demonstrated on a series of multi-energetic industrial benchmark problems. In particular, we highlight the computational advantages of employing hp-refinement for neutron transport criticality problems in comparison with standard low-order h-refinement techniques.

Item Type: Article
Keywords: Discontinuous Galerkin methods, A posteriori error estimation, hp–adaptivity, Neutron transport, Criticality
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Depositing User: Houston, Paul
Date Deposited: 22 Jun 2017 12:12
Last Modified: 13 Oct 2017 08:54
URI: http://eprints.nottingham.ac.uk/id/eprint/43702

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