  The opacity of FRTE depends on not only the material temperature but also the
frequency, whose values may vary several orders of magnitude for different
frequencies. The gray radiation diffusion and frequency-dependent diffusion
equations are two simplified models that can approximate the solution to FRTE
in the thick opacity regime. The frequency discretization for the two limit
models highly affects the numerical accuracy. However, classical frequency
discretization for FRTE considers only the absorbing coefficient. In this
paper, we propose a new decomposed multi-group method for frequency
discretization that is not only AP in both gray radiation diffusion and
frequency-dependent diffusion limits, but also the frequency discretization of
the limiting models can be tuned. Based on the decomposed multi-group method, a
full AP scheme in frequency, time, and space is proposed. Several numerical
examples are used to verify the performance of the proposed scheme.
