A Two-Grid Acceleration Scheme for the Multigroup S_n Equations with Neutron Upscattering

A two-grid acceleration scheme for the multigroup S_n equations with neutron upscattering is developed. Although it has been tested only in one-dimensional slab geometry with linear-discontinuous spatial differencing, previous experience suggests that it should be applicable in any geometry with any spatial differencing scheme for which an unconditionally efficient diffusion-synthetic acceleration scheme exists. The method is derived, theoretically analyzed, and computationally tested. The results indicate that the scheme is unconditionally effective in terms of error reduction per iteration and highly efficient in terms of computational cost.