Skip to main content

Parallel Overlapping Schwarz with an Energy-Minimizing Coarse Space

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 116))

Abstract

Parallel results obtained with a new implementation of an overlapping Schwarz method using an energy minimizing coarse space are presented. We consider structured and unstructured domain decompositions for scalar elliptic and linear elasticity model problems in two dimensions. In particular, strong and weak parallel scalability studies for up to 1024 processor cores are presented for both types of problems. Additionally, weak scalability results for a three-dimensional linear elasticity model problem using up to 4096 processor cores are discussed. Finally, an application from fully-coupled fluid-structure interaction using a nonlinear hyperelastic material model for the structure is shown.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • P.R. Amestoy, I.S. Duff, J.-Y. L’Excellent, J. Koster, A fully asynchronous multifrontal solver using distributed dynamic scheduling. SIAM J. Matrix Anal. Appl. 23 (1), 15–41 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  • D. Balzani, S. Deparis, S. Fausten, D. Forti, A. Heinlein, A. Klawonn, A. Quarteroni, O. Rheinbach, J. Schröder, Numerical modeling of fluid-structure interaction in arteries with anisotropic polyconvex hyperelastic and anisotropic viscoelastic material models at finite strains. Int. J. Numer. Methods Biomed. Eng. (2015). ISSN 2040-7947. http://dx.doi.org/10.1002/cnm.2756.

  • T.A. Davis, I.S. Duff, An unsymmetric-pattern multifrontal method for sparse LU factorization. SIAM J. Matrix Anal. Appl. 18 (1), 140–158 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  • S. Deparis, D. Forti, G. Grandperrin, A. Quarteroni, FaCSI: a block parallel preconditioner for fluid-structure interaction in hemodynamics, Technical Report 13, MATHICSE, EPFL, Lausanne, 2015

    Google Scholar 

  • C.R. Dohrmann, O.B. Widlund, Hybrid domain decomposition algorithms for compressible and almost incompressible elasticity. Int. J. Numer. Methods Eng. 82 (2), 157–183 (2010)

    MathSciNet  MATH  Google Scholar 

  • C.R. Dohrmann, A. Klawonn, O.B. Widlund, Domain decomposition for less regular subdomains: overlapping Schwarz in two dimensions. SIAM J. Numer. Anal. 46 (4), 2153–2168 (2008a). ISSN 0036-1429

    Google Scholar 

  • C.R. Dohrmann, A. Klawonn, O.B. Widlund, A family of energy minimizing coarse spaces for overlapping Schwarz preconditioners, in Domain Decomposition Methods in Science and Engineering XVII. Lecture Notes in Computational Science and Engineering, vol. 60 (Springer, Berlin, 2008b), pp. 247–254

    Google Scholar 

  • L. Formaggia, M. Fernandez, A. Gauthier, J.F. Gerbeau, C. Prud’homme, A. Veneziani, The LifeV Project. Web. http://www.lifev.org (2016)

  • A. Heinlein, A. Klawonn, O. Rheinbach, Parallel two-level overlapping Schwarz methods in fluid-structure interaction, in Proceedings of the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH), Ankara, September, 2015. Springer Lecture Notes on Computational Science and Engineering, vol. 112 (2016), pp. 521–530. TUBAF Preprint 15/2015: http://tu-freiberg.de/fakult1/forschung/preprints

  • M.A. Heroux, R.A. Bartlett, V.E. Howle, R.J. Hoekstra, J.J. Hu, T.G. Kolda, R.B. Lehoucq, K.R. Long, R.P. Pawlowski, E.T. Phipps, A.G. Salinger, H.K. Thornquist, R.S. Tuminaro, J.M. Willenbring, A. Williams, K.S. Stanley, An overview of the Trilinos project. ACM Trans. Math. Softw. 31 (3), 397–423 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  • G. Karypis, K. Schloegel, V. Kumar, ParMETIS - Parallel graph partitioning and sparse matrix ordering. Version 3.2, Technical Report, University of Minnesota, Department of Computer Science and Engineering, April 2011

    Google Scholar 

  • M. Stephan, J. Docter, JUQUEEN: IBM Blue Gene/QⓇ Supercomputer System at the Jülich Supercomputing Centre. J. Large-Scale Res. Facil. 1, A1 (2015). ISSN 2364-091X. doi:10.17815/jlsrf-1-18. http://dx.doi.org/10.17815/jlsrf-1-18

  • A. Toselli, O. Widlund, Domain Decomposition Methods—Algorithms and Theory. Springer Series in Computational Mathematics, vol. 34 (Springer, Berlin, 2005). ISBN 3-540-20696-5

    Google Scholar 

Download references

Acknowledgements

The authors acknowledge the use of the JUQUEEN BG/Q supercomputer (Stephan and Docter, 2015) at JSC Jülich, the use of the Cray XT6m at Universität Duisburg-Essen and the financial support by the German Science Foundation (DFG), project no. KL2094/3 and RH122/4.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Alexander Heinlein .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Heinlein, A., Klawonn, A., Rheinbach, O. (2017). Parallel Overlapping Schwarz with an Energy-Minimizing Coarse Space. In: Lee, CO., et al. Domain Decomposition Methods in Science and Engineering XXIII. Lecture Notes in Computational Science and Engineering, vol 116. Springer, Cham. https://doi.org/10.1007/978-3-319-52389-7_36

Download citation

Publish with us

Policies and ethics