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The paper focuses on developing and studying efficient block preconditionersbased on classical algebraic multigrid for the large-scale sparse linearsystems arising from the fully coupled and implicitly cell-centered finitevolume discretization of multi-group radiation diffusion equations, whosecoefficient matrices can be rearranged into the $(G+2)\times(G+2)$ block form,where $G$ is the number of energy groups. The preconditioning techniques arebased on the monolithic classical algebraic multigrid method, physical-variablebased coarsening two-level algorithm and two types of block Schur complementpreconditioners. The classical algebraic multigrid is applied to solve thesubsystems that arise in the last three block preconditioners. The couplingstrength and diagonal dominance are further explored to improve performance. Weuse representative one-group and twenty-group linear systems from capsuleimplosion simulations to test the robustness, efficiency, strong and weakparallel scaling properties of the proposed methods. Numerical resultsdemonstrate that block preconditioners lead to mesh- and problem-independentconvergence, and scale well both algorithmically and in parallel.

Algebraic multigrid block preconditioning for multi-group radiation diffusion equations