Parallel multigrid methods for transport equations: The anisotropic case

Abstract

An efficient parallel multilevel algorithm is developed for solving the transport equations on parallel computers for one-dimensional anisotropic scattering. The parallel algorithm is developed by using a multigrid in angle scheme that is known to attenuate both rapidly and slowly varying errors in angle. The spatial discretization scheme used is the modified linear discontinuous finite element method, which represents a lumped version of the standard linear discontinuous scheme. The angular discretization is accomplished by expanding the angular dependence in Legendre polynomials and is known as the SN approximation when the first N Legendre polynomials are used. Legendre transforms of complexity O(N) and a anisotropic parallel algorithm of complexity O(N log2 m log2 N) are developed.