An Aggregation Based Algebraic Multigrid Method Applied to Convection-Diffusion Operators

The paper focuses on an aggregation-based algebraic multigrid method applied to convection/diffusion problems. We show that for an unstructured finite volume approach on arbitrary shaped cells, the separation of the two operators associated with suitable smoothers improves the aggregation-based multigrid. While the convection is treated by a piecewise constant prolongation, the off-diagonals entries of the diffusion P-0 Galerkin operator are scaled by a parameter representative of the mesh spacing ratio between the fine and coarse mesh in the vicinity of the coarse mesh cell boundaries. Some numerical examples are shown to assess the rate of convergence and the robustness of the proposed approach.