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 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