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.