  In this paper we present a multilevel projection-based iterative scheme for
solving thermal radiative transfer problems that performs iteration cycles on
the high-order Boltzmann transport equation (BTE) and low-order moment
equations. Fully implicit temporal discretization based on the backward Euler
time-integration method is used for all equations. The multilevel iterative
scheme is designed to perform iteration cycles over collections of multiple
time steps, each of which can be interpreted as a coarse time interval with a
subgrid of time steps. This treatment is demonstrated to transform implicit
temporal integrators to diagonally-implicit multi-step schemes on the coarse
time grid formed with the amalgamated time intervals. A multilevel set of
moment equations are formulated by the nonlinear projective approach. The
Eddington tensor defined with the BTE solution provides exact closure for the
moment equations. During each iteration, a number of chronological time steps
are solved with the BTE alone, after which the same collection of time steps is
solved with the moment equations and material energy balance. Numerical results
are presented to demonstrate the effectiveness of this iterative scheme for
simulating evolving radiation and heat waves in 2D geometry.
