For problems featuring anisotropies, modifications of the multigrid coarsening process are usually required to achieve good convergence. With algebraic multigrid methods, such modifications are automated and good convergence properties are observed in practice.

These favorable convergence properties typically come at the cost of a less aggressive coarsening, so it is vital that the coarsening process guarantee that the coarse-level operators maintain good sparsity. In the context of smoothed aggregation methods, the tentative multigrid transfer operators are subjected to a subsequent smoothing, which naturally increases the supports of the coarse-level basis functions, further emphasizing the need to control the sparsity of the coarse-level operators. Several such approaches have been recently considered. This presentation aims to explain the treatment currently utilized by our smoothed aggregation multilevel iterative solver, parSAMIS.