A Fast Multigrid Algorithm for Isotropic Transport Problems. II: With Absorption
Abstract
A multigrid method for solving the one-dimensional slab-geometry ${\text{S}}_N $ equations with isotropic scattering and absorption is presented. The case with no absorption was treated in part I of this paper [Manteuffel, McCormick, Morel, Oliveira, and Yang, SIAM J. Sci. Comput., 16 (1995), pp. 601–635]. Relaxation is based on a two-cell inversion, which is very efficient because it takes advantage of the structure of the two-cell problem. For interpolation we use kinked linear elements. The kink is based on the amount of absorption present. The restriction operator is full weighting. Numerical results show this algorithm to be faster than diffusion synthetic acceleration (DSA) in all regimes. This scheme is also well suited for massively parallel computer architectures.
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Published In
SIAM Journal on Scientific Computing
Pages: 1449 - 1474
ISSN (online): 1095-7197
Copyright
Copyright © 1996 Society for Industrial and Applied Mathematics.
History
Submitted: 1 July 1993
Accepted: 19 June 1995
Published online: 17 February 2012
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