  This paper presents approximation methods for time-dependent thermal
radiative transfer problems in high energy density physics. It is based on the
multilevel quasidiffusion method defined by the high-order radiative transfer
equation (RTE) and the low-order quasidiffusion (aka VEF) equations for the
moments of the specific intensity. A large part of data storage in TRT problems
between time steps is determined by the dimensionality of grid functions of the
radiation intensity. The approximate implicit methods with reduced memory for
the time-dependent Boltzmann equation are applied to the high-order RTE,
discretized in time with the backward Euler (BE) scheme. The high-dimensional
intensity from the previous time level in the BE scheme is approximated by
means of the low-rank proper orthogonal decomposition (POD). Another version of
the presented method applies the POD to the remainder term of P2 expansion of
the intensity. The accuracy of the solution of the approximate implicit methods
depends of the rank of the POD. The proposed methods enable one to reduce
storage requirements in time dependent problems. Numerical results of a
Fleck-Cummings TRT test problem are presented.
