hp-Adaptive discontinuous Galerkin methods for neutron transport criticality problems

Hall, Edward; Houston, Paul; Murphy, Steven

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.

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), Article B916-B942

• Journal Article Type: Article
• Acceptance Date: Jun 21, 2017
• Online Publication Date: Sep 28, 2017
• Deposit Date: Jun 22, 2017
• Publicly Available Date: Sep 28, 2017
• 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
• Keywords: Discontinuous Galerkin methods, A posteriori error estimation, hp–adaptivity, Neutron transport, Criticality
• Public URL: https://nottingham-repository.worktribe.com/output/884949
• Publisher URL: http://epubs.siam.org/doi/10.1137/16M1079944