Parallel Multigrid Methods for Transport Equations: The Anisotropic Case

A eecient 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 modiied linear discontinu-ous nite element method, which represents a lumped version of the standard linear discontinuous scheme. The angular discretization is accomplished by expanding the angular dependence in Legen-dre polynomials and is known as the S N approximation when the rst N Legendre polynomials are used. Legendre transforms of complexity O(N) and a anisotropic parallel algorithm of complexity O(N log 2 m log 2 N) are developed.