  The computational kernel in solving the $S_N$ transport equations is the
parallel sweep, which corresponds to directly inverting a block lower
triangular linear system that arises in discretizations of the linear transport
equation. Existing parallel sweep algorithms are fairly efficient on structured
grids, but still have polynomial scaling, $P^{1/d}$ for $d$ dimensions and $P$
processors. Moreover, an efficient scalable parallel sweep algorithm for use on
general unstructured meshes remains elusive. Recently, a classical algebraic
multigrid (AMG) method based on approximate ideal restriction (AIR) was
developed for nonsymmetric matrices and shown to be an effective solver for
linear transport. Motivated by the superior scalability of AMG methods
(logarithmic in $P$) as well as the simplicity with which AMG methods can be
used in most situations, including on arbitrary unstructured meshes, this paper
investigates the use of parallel AIR (pAIR) for solving the $S_N$ transport
equations with source iteration in place of parallel sweeps. Results presented
in this paper show that pAIR is a robust and scalable solver. Although sweeps
are still shown to be much faster than pAIR on a structured mesh of a unit
cube, pAIR is shown to perform similarly on both a structured and unstructured
mesh, and offers a new, simple, black box alternative to parallel transport
sweeps.
