Nonuniformly weighted Schwarz smoothers for spectral element multigrid

Stiller, Joerg

doi:10.48550/arxiv.1512.02390

Cited by 1 publication

(1 citation statement)

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“…For a very fine, unstructured mesh with low-order elements, it is not as trivial to explicitly construct enough multigrid levels and one might need to fall back to non-nested multilevel algorithms [6,7] or algebraic multigrid (AMG; see the review by Stüben [8]). These basic multigrid strategies can be nested in hybrid multigrid solvers [9][10][11][12][13][14][15] and, in doing so, one can exploit the advantages of all of them regarding robustness. Most common are hp-multigrid, which combines h-and p-multigrid, and AMG as black-box coarse-grid solver of geometric or polynomial multigrid solvers.…”

Section: Multigrid Variantsmentioning

confidence: 99%

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

Münch¹,

Heister²,

Saavedra³

et al. 2022

Preprint

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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.

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