Cellwise Block Iteration as a Multigrid Smoother for Discrete-Ordinates Radiation-Transport Calculations

Abstract

ABSTRACTWe improve the convergence properties of cellwise block iteration for discrete-ordinates radiation-transport calculations by adapting it for use as a smoother within a multigrid method. Cellwise block iteration by itself converges very slowly for optically thin spatial cells. However, multigrid methods involve a sequence of increasingly coarser grids such that cells on the coarsest grid should be optically thick, for which cellwise block iteration converges quickly. This fast convergence on the coarsest grid should enable fast convergence overall. A novel aspect of this paper is that, along with the usual first-order form of the transport equation, we also consider the Self-Adjoint Angular Flux (SAAF) form. We present numerical results generated using several multigrid methods based on cellwise block iteration for smoothing that demonstrate our approach yields robust convergence regardless of cell optical thickness as specified by the finest grid as well as for heterogeneous media. In addition, we find that the multigrid methods for the SAAF form of the transport equation have superior convergence properties as compared to those for the first-order form.