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This work studies three multigrid variants for matrix-free finite-elementcomputations on locally refined meshes: geometric local smoothing, geometricglobal coarsening, and polynomial global coarsening. We have integrated thealgorithms into the same framework-the open-source finite-element librarydeal.II-, which allows us to make fair comparisons regarding theirimplementation complexity, computational efficiency, and parallel scalabilityas well as to compare the measurements with theoretically derived performancemodels. Serial simulations and parallel weak and strong scaling on up to147,456 CPU cores on 3,072 compute nodes are presented. The results obtainedindicate that global coarsening algorithms show a better parallel behavior forcomparable smoothers due to the better load balance particularly on theexpensive fine levels. In the serial case, the costs of applying hanging-nodeconstraints might be significant, leading to advantages of local smoothing,even though the number of solver iterations needed is slightly higher.

Efficient distributed matrix-free multigrid methods on locally refined meshes for FEM computations