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- W3094360093 abstract "We employ textbook multigrid efficiency (TME), as introduced by Achi Brandt, to construct an asymptotically optimal monolithic multigrid solver for the Stokes system. The geometric multigrid solver builds upon the concept of hierarchical hybrid grids, which is extended to higher-order finite element discretizations, and a corresponding matrix-free implementation. The computational cost of the full multigrid iteration is quantified, and the solver is applied to multiple benchmark problems. Through a parameter study, we suggest configurations that achieve theoretical TME for both stabilized equal order and Taylor--Hood discretizations. We then identify and quantify the gaps to achieve TME for parallel multigrid implementations in practice. The excellent node-level performance of the relevant compute kernels is presented via a roofline analysis. Finally, we demonstrate the weak and strong scalability to up to 147,456 parallel processes and solve Stokes systems with more than $3.6times 10^{12}$ (trillion) unknowns." @default.
- W3094360093 created "2020-10-29" @default.
- W3094360093 creator A5032938194 @default.
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- W3094360093 date "2022-04-01" @default.
- W3094360093 modified "2023-09-26" @default.
- W3094360093 title "Textbook Efficiency: Massively Parallel Matrix-Free Multigrid for the Stokes System" @default.
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- W3094360093 doi "https://doi.org/10.1137/20m1376005" @default.
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