Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

BDDC for Higher-Order Discontinuous Galerkin Discretizations

  • 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))

Summary

The BDDC algorithm is extended to a large class of discontinuous Galerkin (DG) discretizations of second order elliptic problems in two spatial dimensions. An estimate of C(1 + log(p 2 H ∕ h))2 is obtained for the condition number of the preconditioned system where C is a constant independent of p, h or H. Numerical simulations are presented which confirm the theoretical results

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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.

Similar content being viewed by others

Bibliography

  1. P. Antonietti and B. Ayuso. Schwarz domain decomposition preconditioners for discontinuous Galerkin approximations of elliptic problems: Non-overlapping case. Math. Model. Numer. Anal., 41(1): 21–54, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  2. D. Arnold, F. Brezzi, B. Cockburn, and D. Marini. Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal., 39(5):1749–1779, 2002.

    Article  MathSciNet  MATH  Google Scholar 

  3. F. Bassi and S. Rebay. A high-order discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations. J. Comput. Phys., 131:267–279, 1997.

    Article  MathSciNet  MATH  Google Scholar 

  4. F. Brezzi, G. Manzini, D. Marini, P. Pietra, and A. Russo. Discontinuous Galerkin approximations for elliptic problems. Numer. Meth. Part. D. E., 16(4):365–378, July 2000.

    Article  MathSciNet  MATH  Google Scholar 

  5. B. Cockburn and C.W. Shu. The local discontinuous Galerkin method for time-dependent convection-diffusion systems. SIAM J. Numer. Anal., 35(6):2440–2463, December 1998.

    Article  MathSciNet  Google Scholar 

  6. L. Cowsar, J. Mandel, and M. Wheeler. Balancing domain decomposition for mixed finite elements. Math. Comp., 64(211): 989–1015, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  7. Laslo T. Diosady and David L. Darmofal. A Unified Analysis of Balancing Domain Decomposition by Constraints for Discontinuous Galerkin Discretizations. SIAM J. Numer. Anal., 50(3):1695–1712, 2012.

    Google Scholar 

  8. Clark R. Dohrmann. A preconditioner for substructuring based on constrained energy minimization. SIAM J. Sci. Comput., 25(1):246–258, 2003.

    Google Scholar 

  9. M. Dryja, J. Galvis, and M. Sarkis. BDDC methods for discontinuous Galerkin discretization of elliptic problems. J. Complexity, 23(4): 715–739, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  10. X. Feng and O.A. Karakashian. Two-level additive Schwarz methods for a discontinuous Galerkin approximation of second order elliptic problems. SIAM J. Numer. Anal., 39(4):1343–1365, 2002.

    Article  MathSciNet  Google Scholar 

  11. Axel Klawonn, Luca F. Pavarino, and Oliver Rheinbach. Spectral element FETI-DP and BDDC preconditioners with multi-element subdomains. Comput. Methods Appl. Mech. Engrg., 198:511–523, 2008.

    Google Scholar 

  12. 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 

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

    Google Scholar 

  14. Jan Mandel and B. Sousedik. BDDC and FETI-DP under minimalist assumptions. Computing, 81:269–280, 2007.

    Google Scholar 

  15. L.F. Pavarino. BDDC and FETI-DP preconditioners for spectral element discretizations. Comput. Methods Appl. Mech. Engrg., 196(8): 1380–1388, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  16. J. Peraire and P-O. Persson. The compact discontinuous Galerkin (CDG) method for elliptic problems. SIAM J. Sci. Comput., 30(4): 1806–1824, 2008.

    Google Scholar 

  17. X. Tu. A BDDC algorithm for flow in porous media with a hybrid finite element discretization. Electron. Trans. Numer. Anal., 26:146–160, 2007.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Massachusetts Institute of Technology, Cambridge, USA

    Laslo Diosady & David Darmofal

Authors
  1. Laslo Diosady
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David Darmofal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Laslo Diosady .

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

Diosady, L., Darmofal, D. (2013). BDDC for Higher-Order Discontinuous Galerkin Discretizations. 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_66

Download citation

Publish with us

Policies and ethics

Search

Navigation