Improving the Parallel Performance of Overlapping Schwarz Methods by Using a Smaller Energy Minimizing Coarse Space

  • Alexander HeinleinEmail author
  • Axel KlawonnEmail author
  • Oliver RheinbachEmail author
  • Olof B. Widlund
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 125)


We consider a recent overlapping Schwarz method with an energy-minimizing coarse space of reduced size. In numerical experiments for up to 64,000 cores, we show that the parallel efficiency and the total time to solution is improved significantly, compared to our previous overlapping Schwarz method using an alternative energy-minimizing coarse space.



This work was supported in part by the German Research Foundation (DFG) through the Priority Programme 1648 “Software for Exascale Computing” (SPPEXA) under grants KL 2094/4-2 and RH 122/3-2. The work of the fourth author was supported by the National Science Foundation Grant DMS-1522736.

The authors gratefully acknowledge the computing time granted by the Center for Computational Sciences and Simulation (CCSS) at Universität Duisburg-Essen and provided on the supercomputer magnitUDE (DFG grants INST 20876/209-1 FUGG, INST 20876/243-1 FUGG) at Zentrum für Informations- und Mediendienste (ZIM).

The authors also gratefully acknowledge the Gauss Centre for Supercomputing e.V. ( for providing computing time on the GCS Supercomputer JUQUEEN BG/Q supercomputer [15] at JSC Jülich. 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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Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität zu KölnKölnGermany
  2. 2.Institut für Numerische Mathematik und Optimierung, Fakultät für Mathematik und InformatikTechnische Universität Bergakademie FreibergFreibergGermany
  3. 3.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

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