hp-Adaptive discontinuous Galerkin methods for neutron transport criticality problems
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 de...
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| Format: | Article |
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Society for Industrial and Applied Mathematics
2017
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| Online Access: | https://eprints.nottingham.ac.uk/43702/ |
| _version_ | 1848796747722129408 |
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| author | Hall, Edward Houston, Paul Murphy, Steven |
| author_facet | Hall, Edward Houston, Paul Murphy, Steven |
| author_sort | Hall, Edward |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:52:54Z |
| format | Article |
| id | nottingham-43702 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:52:54Z |
| publishDate | 2017 |
| publisher | Society for Industrial and Applied Mathematics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-437022020-05-04T19:09:00Z https://eprints.nottingham.ac.uk/43702/ hp-Adaptive discontinuous Galerkin methods for neutron transport criticality problems Hall, Edward Houston, Paul Murphy, Steven 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. Society for Industrial and Applied Mathematics 2017-09-28 Article PeerReviewed Hall, Edward, 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 Discontinuous Galerkin methods A posteriori error estimation hp–adaptivity Neutron transport Criticality http://epubs.siam.org/doi/10.1137/16M1079944 |
| spellingShingle | Discontinuous Galerkin methods A posteriori error estimation hp–adaptivity Neutron transport Criticality Hall, Edward Houston, Paul Murphy, Steven hp-Adaptive discontinuous Galerkin methods for neutron transport criticality problems |
| title | hp-Adaptive discontinuous Galerkin methods for neutron transport criticality problems |
| title_full | hp-Adaptive discontinuous Galerkin methods for neutron transport criticality problems |
| title_fullStr | hp-Adaptive discontinuous Galerkin methods for neutron transport criticality problems |
| title_full_unstemmed | hp-Adaptive discontinuous Galerkin methods for neutron transport criticality problems |
| title_short | hp-Adaptive discontinuous Galerkin methods for neutron transport criticality problems |
| title_sort | hp-adaptive discontinuous galerkin methods for neutron transport criticality problems |
| topic | Discontinuous Galerkin methods A posteriori error estimation hp–adaptivity Neutron transport Criticality |
| url | https://eprints.nottingham.ac.uk/43702/ https://eprints.nottingham.ac.uk/43702/ |