Algebraic Multigrid Block Triangular Preconditioning For Multidimensional Three-Temperature Radiation Diffusion Equations

In the paper, we are interested in block triangular preconditioning techniques based on algebraic multigrid approach for the large-scale, ill-conditioned and 3-by-3 block-structured systems of linear equations originating from multidimensional three-temperature radiation diffusion equations, discretized in space with the symmetry-preserving finite volume element scheme. Both lower and upper block triangular preconditioners are developed, analyzed theoretically, implemented via the two-level parallelization and tested numerically for such linear systems to demonstrate that they lead to mesh-independent convergence behavior and scale well both algorithmically and in parallel.