explained in Section \[sub:Discrete-approximation-of\].

In our numerical experiments, we choose the band parameters $\sigma_{i,j}$ to be either equally spaced or logarithmically spaced between the minimum and maximum opacity values in each group, $$\min_{E_{i}\leq E\leq E_{i+1}}\sigma_{\varepsilon}\left(E\right),\,\,\,\,\max_{E_{i}\leq E\leq E_{i+1}}\sigma_{\varepsilon}\left(E\right).$$ This choice for the band parameters $\sigma_{i,j}$ is justified in Section \[sub:Discrete-approximation-of\].

To summarize: we solve the multigroup-type equations (\[eq:transport multiband-multigroup, intro\]) for each group interval $\left[E_{i},E_{i+1}\right]$ and for each opacity band $\left[\sigma_{i,j},\sigma_{i,j+1}\right]$, and then average with respect to the discrete Young measure, (\[eq:formula for psi\_o, discretized Young measures\]). The opacity bands $\left[\sigma_{i,j},\sigma_{i,j+1}\right]$ can be chosen to be equally spaced or log-spaced within the range of $\sigma_{\varepsilon}\left(E\right)$, $E\in\left[E_{i},E_{i+1}\right]$.

Equations (\[eq:transport multiband-multigroup, intro\]) and (\[eq:formula for psi\_o, discretized Young measures\]) are analogous to the multiband method, but are derived from within a homogenization framework. Unlike the multiband method, however, no closure assumption (i.e., weighting spectrum) is needed to compute the multiband parameters $\sigma_{i,j}$. In addition, the group average (\[eq:formula for psi\_o, discretized Young measures\]) is not a direct sum as in the multiband method, but instead uses the discrete Young measure to weight the multiband solutions within each group. As previously remarked, the homogenization approach is also related to the correlated k-Distribution method [@ARK-GRO:1972] 