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. | Progress in Nuclear Energy 98 2017 177e186 Contents lists available at ScienceDirect Progress in Nuclear Energy journal homepage locate pnucene 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 B. O Malley a J. Ko pha zi a . Smedley-Stevenson b . Eaton a a Nuclear Engineering Group Department of Mechanical Engineering City and Guilds Building Imperial College London Exhibition Road South Kensington London SW7 2AZ United Kingdom b AWE PLC Aldermaston Reading Berkshire RG7 4PR UK a r t i c l e i n f o a b s t r a c t Article history Effective preconditioning of neutron diffusion problems is necessary for the development of efficient DSA Received 29 December 2016 schemes for neutron transport problems. This paper uses P-multigrid techniques to expand two pre- Received in revised form conditioners designed to solve the MIP diffusion neutron diffusion equation with a discontinuous 27 February 2017 Galerkin DG-FEM framework using first-order elements. These preconditioners are based on projecting Accepted 10 March 2017 Available online 23 March 2017 the first-order DG-FEM formulation to either a linear continuous or a constant discontinuous FEM sys- tem. 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 precondi- tioner. The results obtained demonstrate that all preconditioners studied in this paper provide good convergence with the continuous method generally being the most .
