  This paper presents multilevel iterative schemes for solving the multigroup
Boltzmann transport equations (BTEs) with parallel calculation of group
equations. They are formulated with multigroup and grey low-order equations of
the Second-Moment (SM) method. The group high-order BTEs and low-order SM
(LOSM) equations are solved in parallel. To further improve convergence and
increase computational efficiency of algorithms Anderson acceleration is
applied to inner iterations for solving the system of multigroup LOSM
equations. Numerical results are presented to demonstrate performance of the
multilevel iterative methods.
