A Fast Multigrid Algorithm for Isotropic Transport Problems. II: With Absorption

A multigrid method for solving the 1-D slab-geometry S N equations with isotropic scattering and absorption is presented. The case with no absorption was treated in part I of this paper 10]. Relaxation is based on a two-cell inversion, which is very eecient 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 DSA in all regimes. This scheme is also well-suited for massively parallel computer architectures. x1: Introduction In this paper we describe a fast method for solving the equations used to model the transport of neutral particles with isotropic scattering in slab geometry. These problems are important in many applications such as nuclear reactor design, radiation therapy in medical science, radiation eeects on global weather, and they are a fundamental part of many algorithms used to model more complicated applications such as coupled photon/electron scattering used to model satellite electronics shielding. We focus on the solution of the steady-state, monoenergetic, linear Boltzmann equation in slab geometry. The need to solve such equations arises from the time-dependent Boltzmann equations used in the applications mentioned above. The physical domain is assumed to be a semi-innnite slab of width b?a in the x dimension. Although three dimensional, we assume that the ux of particles is independent of the y and z coordinates. Let (x; ; e; t) represent the ux of particles at a position x, traveling at an angle to the x-axis, with energy e, at time t. The Boltzmann equation takes the form (1:1)