Abstract
The effectiveness of the three-dimensional (3-D) diffusion synthetic acceleration preconditioning procedure is proved in various asymptotic regimes for the discretized, mono-energetic, steady-state, linear Boltzmann transport equation with isotropic scattering. The discretizations consist of a discrete ordinate collocation in angle and a Petrov--Galerkin finite element method in space. Following the path initiated by Faber and Manteuffel, we pursue the 3-D development of Brown by providing a 3-D extension of the slab geometry convergence results of Ashby et al. Our theoretical results confirm the good numerical results of Brown in thin and thick limits and hold for problems with nonconstant coefficients and nonuniform spatial zoning posed on finite domains with an incident flux prescribed at the boundaries.
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