  This paper presents nonlinear iterative methods for the fundamental thermal
radiative transfer (TRT) model defined by the time-dependent multifrequency
radiative transfer (RT) equation and the material energy balance (MEB)
equation. The iterative methods are based on the nonlinear projection approach
and use multiple grids in photon frequency. They are formulated by the
high-order RT equation on a given grid in photon frequency and low-order moment
equations on a hierarchy of frequency grids. The material temperature is
evaluated in the subspace of the lowest dimensionality from the MEB equation
coupled to the effective grey low-order equations. The algorithms apply various
multigrid cycles to visit frequency grids. Numerical results are presented to
demonstrate convergence of the multigrid iterative algorithms in TRT problems
with large number of photon frequency groups.
