Smoothers with localized residual computations for geometric multigrid methods for higher-order finite elements
We improve the performance of multigrid solvers on many-core architectures with cache hierarchies by reorganizing operations in the smoothing step to minimize memory transfers. We focus on patch smoothers, which offer robust convergence rates with respect to the finite element degree for various equ...
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| Hauptverfasser: | , , , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
May 16, 2025
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| In: |
SIAM journal on scientific computing
Year: 2025, Jahrgang: 47, Heft: 3, Pages: B645-B664 |
| ISSN: | 1095-7197 |
| DOI: | 10.1137/23M1625962 |
| Online-Zugang: | Verlag, kostenfrei, Volltext: https://doi.org/10.1137/23M1625962 Verlag, kostenfrei, Volltext: https://epubs.siam.org/doi/10.1137/23M1625962 
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| Verfasserangaben: | Michał Wichrowski, Peter Munch, Martin Kronbichler, and Guido Kanschat |
| Zusammenfassung: | We improve the performance of multigrid solvers on many-core architectures with cache hierarchies by reorganizing operations in the smoothing step to minimize memory transfers. We focus on patch smoothers, which offer robust convergence rates with respect to the finite element degree for various equations in the setting of multiplicative subspace correction for numerical efficiency. By combining the computation of local residuals with local solvers, we increase the locality of the problem and thus reduce data transfers. The thread-parallel implementation of this algorithm is based on coloring, which contradicts cache efficiency. We improve data locality by rearranging the loop into batches so that more data can be reused. The organization of consecutive batches prioritizes data locality. |
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| Beschreibung: | Gesehen am 22.10.2025 |
| Beschreibung: | Online Resource |
| ISSN: | 1095-7197 |
| DOI: | 10.1137/23M1625962 |