A FAST MULTIGRID ALGORITHM FOR ISOTROPIC TRANSPORT PROBLEMS .1. PURE SCATTERING

The authors present a multigrid method for solving the one-dimensional (1-D) slab-geometry SN equations with isotropic scattering and no abs orption. This scheme is highly compatible with massively parallel comp uter architectures and represents a first step toward similar multigri d methods for the SN equations in curvilinear and multidimensional geo metries. Extensive theoretical analyses are given for our scheme which indicate that it is extremely efficient. In fact, the method is so ef ficient that it very nearly represents an exact solution technique. Re sults from calculations ale presented which validate the theoretical r esults. The case with absorption is treated in a sequel to this paper [Manteuffel et al., A fast multigrid algorithm for transport problems II: With absorption, SIAM J. Sci. Comput., submitted].