Skip to main content

Adaptive BDDC and FETI-DP Methods with Change of Basis Formulation

  • Conference paper
  • First Online:
  • 687 Accesses

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 125))

Abstract

In this paper, BDDC (Balancing Domain Decomposition by Constraints) and FETI-DP (Dual-Primal Finite Element Tearing and Interconnecting) algorithms with a change of basis for adaptive primal constraints are analyzed.

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
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

  1. W.N. Anderson Jr., R.J. Duffin, Series and parallel addition of matrices. J. Math. Anal. Appl. 26, 576–594 (1969)

    Article  MathSciNet  Google Scholar 

  2. J.G. Calvo, O.B. Widlund, An adaptive choice of primal constraints for BDDC domain decomposition algorithms. Electron. Trans. Numer. Anal. 45, 524–544 (2016)

    MathSciNet  MATH  Google Scholar 

  3. C.R. Dohrmann, C. Pechstein, Modern domain decomposition solvers: BDDC, deluxe scaling, and an algebraic approach, 2013. http://people.ricam.oeaw.ac.at/c.pechstein/pechstein-bddc2013.pdf

  4. V. Dolean, F. Nataf, R. Scheichl, N. Spillane, Analysis of a two-level Schwarz method with coarse spaces based on local Dirichlet-to-Neumann maps. Comput. Methods Appl. Math. 12(4), 391–414 (2012)

    Article  MathSciNet  Google Scholar 

  5. J. Galvis, Y. Efendiev, Domain decomposition preconditioners for multiscale flows in high-contrast media. Multiscale Model. Simul. 8(4), 1461–1483 (2010)

    Article  MathSciNet  Google Scholar 

  6. H.H. Kim, E. Chung, J. Wang, BDDC and FETI-DP mathods with enriched coarse spaces for elliptic problems with oscillatory and high contrast coefficients, in Domain Decomposition Methods in Science and Engineering XXIII. Lecture Notes in Computer Science and Engineering, vol. 116 (Springer, Heidelberg, 2017), pp. 179–186

    Google Scholar 

  7. H.H. Kim, E. Chung, J. Wang, BDDC and FETI-DP preconditioners with adaptive coarse spaces for three-dimensional elliptic problems with oscillatory and high contrast coefficients. J. Comput. Phys. 349, 191–214 (2017)

    Article  MathSciNet  Google Scholar 

  8. H.H. Kim, E. Chung, J. Wang, Adaptive BDDC and FETI-DP algorithms with a change of basis formulation on adaptive primal constraints, Electron. Trans. Numer. Anal. 49, 64–80 (2018)

    Article  MathSciNet  Google Scholar 

  9. A. Klawonn, O.B. Widlund, Dual-primal FETI methods for linear elasticity. Commun. Pure Appl. Math. 59(11), 1523–1572 (2006)

    Article  MathSciNet  Google Scholar 

  10. A. Klawonn, M. Kühn, O. Rheinbach, Adaptive coarse spaces for FETI-DP in three dimensions. SIAM J. Sci. Comput. 38(5), A2880–A2911 (2016)

    Article  MathSciNet  Google Scholar 

  11. J. Mandel, B. Sousedík, J. Šístek, Adaptive BDDC in three dimensions. Math. Comput. Simul. 82(10), 1812–1831 (2012)

    Article  MathSciNet  Google Scholar 

  12. N. Spillane, D.J. Rixen, Automatic spectral coarse spaces for robust finite element tearing and interconnecting and balanced domain decomposition algorithms. Int. J. Numer. Methods Eng. 95(11), 953–990 (2013)

    Article  MathSciNet  Google Scholar 

  13. N. Spillane, V. Dolean, P. Hauret, F. Nataf, D.J. Rixen, Solving generalized eigenvalue problems on the interfaces to build a robust two-level FETI method. C. R. Math. Acad. Sci. Paris 351(5–6), 197–201, 2013

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The first author was supported by the National Research Foundation of Korea(NRF) grants funded by NRF20151009350, the second author was supported by the Hong Kong RGC General Research Fund (Project 14317516) and the CUHK Direct Grant for Research 2016–2017, and the third author was supported by the National Natural Science Foundation of China (Grant No. 11201398) and Open Foundation of Guangdong Provincial Engineering Technology Research Center for Data Science(2016KF07).

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Hyea Hyun Kim , Eric T. Chung or Junxian Wang .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Kim, H.H., Chung, E.T., Wang, J. (2018). Adaptive BDDC and FETI-DP Methods with Change of Basis Formulation. In: Bjørstad, P., et al. Domain Decomposition Methods in Science and Engineering XXIV . DD 2017. Lecture Notes in Computational Science and Engineering, vol 125. Springer, Cham. https://doi.org/10.1007/978-3-319-93873-8_42

Download citation

Publish with us

Policies and ethics