Abstract
The parallel performance of several classical Algebraic Multigrid (AMG) methods applied to linear elasticity problems is investigated. These methods include standard AMG approaches for systems of partial differential equations such as the unknown and hybrid approaches, as well as the more recent global matrix (GM) and local neighborhood (LN) approaches, which incorporate rigid body modes (RBMs) into the AMG interpolation operator. Numerical experiments are presented for both two- and three-dimensional elasticity problems on up to 131,072 cores (and 262,144 MPI processes) on the Vulcan supercomputer (LLNL, USA) and up to 262,144 cores (and 524,288 MPI processes) on the JUQUEEN supercomputer (JSC, Jülich, Germany). It is demonstrated that incorporating all RBMs into the interpolation leads generally to faster convergence and improved scalability.
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Acknowledgements
This work was supported in part by the German Research Foundation (DFG) through the Priority Program 1648 “Software for Exascale Computing” (SPPEXA ) under KL 2094/4-1 and RH 122/2-1. The authors also gratefully acknowledge the use of the Vulcan supercomputer at Lawrence Livermore National Laboratory. Partial support for this work was provided through Scientific Discovery through Advanced Computing (SciDAC ) program funded by U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research (and Basic Energy Sciences/Biological and Environmental Research/High Energy Physics/Fusion Energy Sciences/Nuclear Physics). This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. 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 JUQUEEN [24] 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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Baker, A.H., Klawonn, A., Kolev, T., Lanser, M., Rheinbach, O., Yang, U.M. (2016). Scalability of Classical Algebraic Multigrid for Elasticity to Half a Million Parallel Tasks. In: Bungartz, HJ., Neumann, P., Nagel, W. (eds) Software for Exascale Computing - SPPEXA 2013-2015. Lecture Notes in Computational Science and Engineering, vol 113. Springer, Cham. https://doi.org/10.1007/978-3-319-40528-5_6
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