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A massively parallel geometric multigrid solver on hierarchically distributed grids

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Computing and Visualization in Science

Abstract

A parallel geometric multigrid solver on hierarchically distributed grids is presented. Using a tree-structure for grid distribution onto the processing entities, the multigrid cycle is performed similarly to the serial algorithm, using additional vertical communication during transfer operations. The workload is gathered to fewer processes on coarser levels. Involved parallel structures are described in detail and the multigrid algorithm is formulated, discussing parallelization details. A performance study is presented that shows close to optimal efficiency for weak scaling up to 262k processes in 2 and 3 space dimensions.

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Acknowledgments

This work has been supported by the Goethe Universität Frankfurt, the German Ministry of Economy and Technology (BMWi) via grant 02E10568, the German Ministry of Education and Research (BMBF) via grant 02E10326 and 01IH08014A, and the DFG by grants No. WI 1037/24-1 and WI 1037/25-1. The authors gratefully acknowledge the Gauss Centre for Supercomputing (GCS) for providing computing time through the John von Neumann Institute for Computing (NIC) on the GCS share of the supercomputer JUGENE at Jülich Supercomputing Centre (JSC). GCS is the alliance of the three national supercomputing centres HLRS (Universität Stuttgart), JSC (Forschungszentrum Jülich), and LRZ (Bayerische Akademie der Wissenschaften), funded by the German Federal Ministry of Education and Research (BMBF) and the German State Ministries for Research of Baden-Württemberg (MWK), Bayern (StMWFK) and Nordrhein-Westfalen (MIWF).

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  1. Goethe Center for Scientific Computing (G-CSC), Goethe University Frankfurt am Main, Kettenhofweg 139, 60325, Frankfurt, Germany

    Sebastian Reiter, Andreas Vogel, Ingo Heppner, Martin Rupp & Gabriel Wittum

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  1. Sebastian Reiter
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  2. Andreas Vogel
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  3. Ingo Heppner
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  4. Martin Rupp
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  5. Gabriel Wittum
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Correspondence to Sebastian Reiter.

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Communicated by: Randolph E. Bank.

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Reiter, S., Vogel, A., Heppner, I. et al. A massively parallel geometric multigrid solver on hierarchically distributed grids. Comput. Visual Sci. 16, 151–164 (2013). https://doi.org/10.1007/s00791-014-0231-x

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  • DOI: https://doi.org/10.1007/s00791-014-0231-x

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