Skip to main content
SpringerLink
Log in

A FETI-DP Algorithm for Saddle Point Problems in Three Dimensions

  • Conference paper
Book cover Domain Decomposition Methods in Science and Engineering XXII

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 104))

  • 1428 Accesses

Abstract

A FETI-DP algorithm is proposed for solving the system of linear equations arising from the mixed finite element approximations of a three dimensional saddle problem. A preconditioned conjugate gradient method is used in the algorithm with either a lumped or a Dirichlet preconditioner, and scalable convergence rates are proved without a divergence free condition for the coarse space. Numerical experiments of solving a three-dimensional incompressible Stokes problem demonstrate the performance of the proposed algorithm.

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

Access this chapter

Log in via an institution
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

Institutional subscriptions

References

  1. J. Li, A Dual-Primal FETI method for incompressible Stokes equations. Numer. Math. 102, 257–275 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  2. J. Li, X. Tu, A nonoverlapping domain decomposition method for incompressible Stokes equations with continuous pressures. SIAM J. Numer. Anal. 51(2), 1235–1253 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  3. J. Li, O.B. Widlund, BDDC algorithms for incompressible Stokes equations. SIAM J. Numer. Anal. 44(6), 2432–2455 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  4. L.F. Pavarino, O.B. Widlund, Balancing Neumann-Neumann methods for incompressible Stokes equations. Comm. Pure Appl. Math. 55(3), 302–335 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  5. A. Toselli, O.B. Widlund, in Domain Decomposition Methods - Algorithms and Theory, Springer Series in Computational Mathematics, vol. 34 (Springer, Berlin-Heidelberg-New York, 2005)

    MATH  Google Scholar 

  6. X. Tu, J. Li, A FETI-DP algorithm for incompressible stokes equations with continuous pressures, in Proceedings of the 21th Domain International Conference on Domain Decomposition Methods, 2012

    Google Scholar 

  7. X. Tu, J. Li, A unified dual-primal finite element tearing and interconnecting approach for incompressible Stokes equations. Int. J. Numer. Methods Eng. 94(2), 128–149 (2013)

    Article  MathSciNet  Google Scholar 

  8. X. Tu, J. Li, A FETI-DP type domain decomposition algorithm for three dimensional incompressible Stokes equations. SIAM J. Numer. Anal. 53(2), 720–742 (2015)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported in part by National Science Foundation Contracts No. DMS-1115759 and DMS-1419069.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Kansas, 1460 Jayhawk Blvd, Lawrence, Kansas, 66045-7594, USA

    Xuemin Tu

  2. Department of Mathematical Sciences, Kent State University, Kent, Ohio, 44242, USA

    Jing Li

Authors
  1. Xuemin Tu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jing Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xuemin Tu .

Editor information

Editors and Affiliations

  1. Fakultät für Mathematik, Technische Universität München, Garching, Germany

    Thomas Dickopf

  2. Section de Mathématiques, Université de Genève, Genève, Switzerland

    Martin J. Gander

  3. Laboratoire Analyse, Geométrie & Applications, Université Paris XIII, Villetaneuse, France

    Laurence Halpern

  4. Institute of Computational Science, University of Lugano, Lugano, Switzerland

    Rolf Krause

  5. Dipartimento di Matematica, Università degli Studi di Milano, Milano, Italy

    Luca F. Pavarino

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Tu, X., Li, J. (2016). A FETI-DP Algorithm for Saddle Point Problems in Three Dimensions. In: Dickopf, T., Gander, M., Halpern, L., Krause, R., Pavarino, L. (eds) Domain Decomposition Methods in Science and Engineering XXII. Lecture Notes in Computational Science and Engineering, vol 104. Springer, Cham. https://doi.org/10.1007/978-3-319-18827-0_32

Download citation

Publish with us

Policies and ethics

Search

Navigation