PARALLEL MULTIGRID METHODS FOR TRANSPORT-EQUATIONS - THE ANISOTROPIC CASE

An efficient parallel multilevel algorithm is developed for solving th e transport equations on parallel computers for one-dimensional anisot ropic scattering. The parallel algorithm is developed by using a multi grid in angle scheme that is known to attenuate both rapidly and slowl y varying errors in angle. The spatial discretization scheme used is t he modified linear discontinuous finite element method, which represen ts a lumped version of the standard linear discontinuous scheme. The a ngular discretization is accomplished by expanding the angular depende nce in Legendre polynomials and is known as the S-N approximation when the first N Legendre polynomials are used. Legendre transforms of com plexity O(N) and a anisotropic parallel algorithm of complexity O(N lo g(2) m log(2) N) are developed.