Parallelised Krylov subspace method for reactor kinetics by IQS approach

Abstract

Nuclear reactor kinetics involves numerical solution of space–time-dependent multi-group neutron diffusion equation. Two distinct approaches exist for this purpose: the direct (implicit time differencing) approach and the improved quasi-static (IQS) approach. Both the approaches need solution of static space-energy-dependent diffusion equations at successive time-steps; the step being relatively smaller for the direct approach. These solutions are usually obtained by Gauss–Seidel type iterative methods. For a faster solution, the Krylov sub-space methods have been tried and also parallelised by many investigators. However, these studies seem to have been done only for the direct approach. In the present paper, parallelised Krylov methods are applied to the IQS approach in addition to the direct approach. It is shown that the speed-up obtained for IQS is higher than that for the direct approach. The reasons for this are also discussed. Thus, the use of IQS approach along with parallelised Krylov solvers seems to be a promising scheme.