This work studies three multigrid variants for matrix-free finite-element
computations on locally refined meshes: geometric local smoothing, geometric
global coarsening, and polynomial global coarsening. We have integrated the
algorithms into the same framework-the open-source finite-element library
deal.II-, which allows us to make fair comparisons regarding their
implementation complexity, computational efficiency, and parallel scalability
as well as to compare the measurements with theoretically derived performance
models. Serial simulations and parallel weak and strong scaling on up to
147,456 CPU cores on 3,072 compute nodes are presented. The results obtained
indicate that global coarsening algorithms show a better parallel behavior for
comparable smoothers due to the better load balance particularly on the
expensive fine levels. In the serial case, the costs of applying hanging-node
constraints might be significant, leading to advantages of local smoothing,
even though the number of solver iterations needed is slightly higher.Comment: 34 pages, 17 figure
