Two-level multigrid preconditioning of a neutron noise diffusion solver

This paper presents the utilization of a two-level multigrid preconditioner for the acceleration of a two-energy-group neutron noise diffusion solver for fine grid applications. The highly localized nature of most neutron noise sources requires the fine discretization of the spatial domain leading to large systems of algebraic equations. These systems are solved with iterative methods whose performances are usually determined by the accompanying preconditioners. This work applies a two-level multigrid approach aiming to enhance the convergence behavior of the GMRES iterative linear solver. The results show that the two-level scheme improves significantly the performance of GMRES in the solution of two problems. In particular, it outperforms two general-purpose alternative acceleration methods, i.e. ILU(0) and ILUC