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hp-Adaptive discontinuous Galerkin methods for neutron transport criticality problems

Hall, Edward; Houston, Paul; Murphy, Steven

Authors

Edward Hall eh171@le.ac.uk

Paul Houston Paul.Houston@nottingham.ac.uk

Steven Murphy pmxsm2@nottingham.ac.uk



Abstract

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.

Journal Article Type Article
Journal SIAM Journal on Scientific Computing
Print ISSN 1064-8275
Electronic ISSN 1095-7197
Publisher Society for Industrial and Applied Mathematics
Peer Reviewed Peer Reviewed
Volume 39
Issue 5
Article Number B916-B942
APA6 Citation Hall, E., Houston, P., & Murphy, S. (in press). hp-Adaptive discontinuous Galerkin methods for neutron transport criticality problems. SIAM Journal on Scientific Computing, 39(5),
Keywords Discontinuous Galerkin methods, A posteriori error estimation, hp–adaptivity, Neutron transport, Criticality
Publisher URL http://epubs.siam.org/doi/10.1137/16M1079944
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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