A Fast Multigrid Algorithm for Isotropic Transport Problems I: Pure Scattering
Abstract
The authors present a multigrid method for solving the one-dimensional (1-D) slab-geometry $S_N $ equations with isotropic scattering and no absorption. This scheme is highly compatible with massively parallel computer architectures and represents a first step toward similar multigrid methods for the $S_N $ equations in curvilinear and multidimensional geometries. Extensive theoretical analyses are given for our scheme which indicate that it is extremely efficient. In fact, the method is so efficient that it very nearly represents an exact solution technique. Results from calculations are presented which validate the theoretical results. 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].
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Copyright © 1995 Society for Industrial and Applied Mathematics.
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Published online: 13 July 2006
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