  The paper focuses on developing and studying efficient block preconditioners
based on classical algebraic multigrid for the large-scale sparse linear
systems arising from the fully coupled and implicitly cell-centered finite
volume discretization of multi-group radiation diffusion equations, whose
coefficient matrices can be rearranged into the $(G+2)\times(G+2)$ block form,
where $G$ is the number of energy groups. The preconditioning techniques are
based on the monolithic classical algebraic multigrid method, physical-variable
based coarsening two-level algorithm and two types of block Schur complement
preconditioners. The classical algebraic multigrid is applied to solve the
subsystems that arise in the last three block preconditioners. The coupling
strength and diagonal dominance are further explored to improve performance. We
use representative one-group and twenty-group linear systems from capsule
implosion simulations to test the robustness, efficiency, strong and weak
parallel scaling properties of the proposed methods. Numerical results
demonstrate that block preconditioners lead to mesh- and problem-independent
convergence, and scale well both algorithmically and in parallel.
