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P-Multigrid expansion of hybrid multilevel solvers for discontinuous Galerkin finite element discrete ordinate (DG-FEM-SN) diffusion synthetic acceleration (DSA) of radiation transport algorithms

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Title: P-Multigrid expansion of hybrid multilevel solvers for discontinuous Galerkin finite element discrete ordinate (DG-FEM-SN) diffusion synthetic acceleration (DSA) of radiation transport algorithms
Authors: O'Malley, B
Kophazi, J
Smedley-Stevenson, RP
Eaton, MD
Item Type: Journal Article
Abstract: Effective preconditioning of neutron diffusion problems is necessary for the development of efficient DSA schemes for neutron transport problems. This paper uses P-multigrid techniques to expand two preconditioners designed to solve the MIP diffusion neutron diffusion equation with a discontinuous Galerkin (DG-FEM) framework using first-order elements. These preconditioners are based on projecting the first-order DG-FEM formulation to either a linear continuous or a constant discontinuous FEM system. The P-multigrid expansion allows the preconditioners to be applied to problems discretised with second and higher-order elements. The preconditioning algorithms are defined in the form of both a V-cycle and W-cycle and applied to solve challenging neutron diffusion problems. In addition a hybrid preconditioner using P-multigrid and AMG without a constant or continuous coarsening is used. Their performance is measured against a computationally efficient standard algebraic multigrid preconditioner. The results obtained demonstrate that all preconditioners studied in this paper provide good convergence with the continuous method generally being the most computationally efficient. In terms of memory requirements the preconditioners studied significantly outperform the AMG.
Issue Date: 23-Mar-2017
Date of Acceptance: 10-Mar-2017
URI: http://hdl.handle.net/10044/1/45566
DOI: https://dx.doi.org/10.1016/j.pnucene.2017.03.014
ISSN: 0149-1970
Publisher: Elsevier
Start Page: 177
End Page: 186
Journal / Book Title: Progress in Nuclear Energy
Volume: 98
Copyright Statement: © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (E
Funder's Grant Number: EP/J002011/1
EP/K503733/1
Keywords: Energy
Publication Status: Published
Appears in Collections:Mechanical Engineering
Faculty of Engineering