Skip to main content
SpringerLink
Log in

A Nonoverlapping DD Preconditioner for a Weakly Over-Penalized Symmetric Interior Penalty Method

  • Conference paper
  • First Online:
Domain Decomposition Methods in Science and Engineering XX

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 91))

Abstract

In this paper we present a nonoverlapping domain decomposition preconditioner for a weakly over-penalized symmetric interior penalty method that is based on balancing domain decomposition by constraints (BDDC) methodology (cf. [2, 5, 7, 8]). The full analysis of the preconditioner can be found in [4].

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. S. C. Brenner and L. R. Scott. The mathematical theory of finite element methods (Third Edition). Springer, 2008.

    Google Scholar 

  2. S. C. Brenner and L.-Y. Sung. BDDC and FETI-DP without matrices or vectors. Comput. Methods Appl. Mech. Engrg., 196:1429–1435, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  3. S. C. Brenner, L. Owens, and L.-Y. Sung. A weakly over-penalized symmetric interior penalty method. Electron. Trans. Numer. Anal., 30: 107–127, 2008.

    MathSciNet  MATH  Google Scholar 

  4. S. C. Brenner, E.-H. Park, and L.-Y. Sung. A BDDC preconditioner for a weakly over-penalized symmetric interior penalty method. preprint, 2011.

    Google Scholar 

  5. C. R. Dohrmann. A preconditioner for substructuring based on constrained energy minimization. SIAM J. Sci. Comput., 25:246–258, 2003.

    Article  MathSciNet  MATH  Google Scholar 

  6. M. Dryja, J. Galvis, and M. Sarkis. BDDC methods for discontinuous Galerkin discretization of elliptic problems. J. Complex., 23:715–739, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  7. J. Li and O. B. Widlund. FETI-DP, BDDC, and block Cholesky methods. Internat. J. Numer. Methods Engrg., 66:250–271, 2006.

    Article  MathSciNet  MATH  Google Scholar 

  8. J. Mandel and C. R. Dohrmann. Convergence of a balancing domain decomposition by constraints and energy minimization. Numer. Linear Algebra Appl., 10:639–659, 2003.

    Article  MathSciNet  MATH  Google Scholar 

  9. L. Owens. Multigrid methods for weakly over-penalized interior penalty methods. Ph.D. thesis, University of South Carolina, 2007.

    Google Scholar 

  10. B. Smith, P. Bjørstad, and W. Gropp. Domain Decomposition. Cambridge University Press, Cambridge, 1996.

    MATH  Google Scholar 

  11. A. Toselli and O. B. Widlund. Domain Decomposition Methods - Algorithms and Theory. Springer-Verlag, Berlin, 2005.

    MATH  Google Scholar 

Download references

Acknowledgements

The work of the first author was supported in part by the National Science Foundation under Grant No. DMS-07-39382. The work of the second and forth authors was supported in part by the National Science Foundation under Grant No. DMS-10-16332. The work of the third author was supported in part by the National Research Foundation of Korea under Grant No. NRF-2009-352-C00009. The work of all four authors was supported in part by the Institute for Mathematics and its Applications with funds provided by the National Science Foundation.

Author information

Authors and Affiliations

  1. Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, LA, 70803, USA

    Andrew T. Barker, Susanne C. Brenner, Eun-Hee Park & Li-Yeng Sung

Authors
  1. Andrew T. Barker
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Susanne C. Brenner
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Eun-Hee Park
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Li-Yeng Sung
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andrew T. Barker .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, University of California, San Diego, Gilman Drive 9500, La Jolla, 92093-0112, California, USA

    Randolph Bank

  2. , Department of Mathematics, University of California, San Diego, Gilman Drive 9500, La Jolla, 92093-0112, California, USA

    Michael Holst

  3. , Courant Institute of Mathematical, New York University, Mercer Street 251, New York, 10012-1185, New York, USA

    Olof Widlund

  4. , Department of Mathematics, Pennsylvania State University, State College, 16802, Pennsylvania, USA

    Jinchao Xu

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Barker, A.T., Brenner, S.C., Park, EH., Sung, LY. (2013). A Nonoverlapping DD Preconditioner for a Weakly Over-Penalized Symmetric Interior Penalty Method. In: Bank, R., Holst, M., Widlund, O., Xu, J. (eds) Domain Decomposition Methods in Science and Engineering XX. Lecture Notes in Computational Science and Engineering, vol 91. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35275-1_28

Download citation

Publish with us

Policies and ethics

Search

Navigation