Skip to main content
SpringerLink
Log in

A Moving Mesh Method for Time—dependent Problems Based on Schwarz Waveform Relaxation

  • Conference paper
Domain Decomposition Methods in Science and Engineering XVII

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 60))

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

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.

References

  1. G. Beckett and J. A. Mackenzie. Uniformly convergent high order finite element solutions of a singularly perturbed reaction-diffusion equation using mesh equidistribution. Appl. Numer. Math., 39(1):31–45, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  2. C.J. Budd, W. Huang, and R.D. Russell. Moving mesh methods for problems with blow-up. SIAM J. Sci. Comput., 17(2):305–327, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  3. C. de Boor. Good approximation by splines with variable knots. II. In Conference on the Numerical Solution of Differential Equations (Univ. Dundee, Dundee, 1973), pages 12–20. Lecture Notes in Math., Vol. 363. Springer, Berlin, 1974.

    Chapter  Google Scholar 

  4. M. J. Gander and A. M. Stuart. Space–time continuous analysis of waveform relaxation for the heat equation. SIAM J. Sci. Comput., 19(6):2014–2031, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  5. M.J. Gander. Optimized Schwarz methods. SIAM J. Numer. Anal., 44(2):699–731, 2006.

    Article  MATH  MathSciNet  Google Scholar 

  6. M.J. Gander and C. Rohde. Overlapping Schwarz waveform relaxation for convection-dominated nonlinear conservation laws. SIAM J. Sci. Comput., 27(2):415–439, 2005.

    Article  MATH  MathSciNet  Google Scholar 

  7. E. Giladi and H.B. Keller. Space-time domain decomposition for parabolic problems. Numer. Math., 93(2):279–313, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  8. R.D. Haynes. The Numerical Solution of Differential Equations: Grid Selection for Boundary Value Problems and Adaptive Time Integration Strategies. PhD thesis, Simon Fraser University, Burnaby, B.C. V5A 1S6, 2003.

    Google Scholar 

  9. R.D. Haynes and R.D. Russell. A Schwarz waveform moving mesh method. SIAM J. Sci. Comput., 2007. To Appear.

    Google Scholar 

  10. W. Huang. Practical aspects of formulation and solution of moving mesh partial differential equations. J. Comput. Phys., 171(2):753–775, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  11. W. Huang, Y. Ren, and R.D. Russell. Moving mesh methods based on moving mesh partial differential equations. J. Comput. Phys., 113(2):279–290, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  12. W. Huang, Y. Ren, and R.D. Russell. Moving mesh partial differential equations (MMPDES) based on the equidistribution principle. SIAM J. Numer. Anal., 31(3):709–730, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  13. W. Huang and R.D. Russell. A moving collocation method for solving time dependent partial differential equations. Appl. Numer. Math., 20(1–2):101–116, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  14. W. Huang and R.D. Russell. Moving mesh strategy based on a gradient flow equation for two-dimensional problems. SIAM J. Sci. Comput., 20(3):998–1015, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  15. W. Huang and W. Sun. Variational mesh adaptation. II. Error estimates and monitor functions. J. Comput. Phys., 184(2):619–648, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  16. L.R. Petzold. A description of DASSL: a differential/algebraic system solver. In Scientific computing (Montreal, Que., 1982), IMACS Trans. Sci. Comput., I, pages 65–68. IMACS, New Brunswick, NJ, 1983.

    Google Scholar 

  17. Y. Ren and R.D. Russell. Moving mesh techniques based upon equidistribution, and their stability. SIAM J. Sci. Statist. Comput., 13(6):1265–1286, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  18. J. M. Stockie, J. A. Mackenzie, and R. D. Russell. A moving mesh method for one-dimensional hyperbolic conservation laws. SIAM J. Sci. Comput., 22(5):1791–1813, 2000.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Acadia University, Wolfville, N.S., Canada

    Ronald D. Haynes

  2. University of Kansas, Lawrence, KS, USA

    Weizhang Huang

  3. Simon Fraser University, Burnaby, B.C., Canada

    Robert D. Russell

Authors
  1. Ronald D. Haynes
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Weizhang Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Robert D. Russell
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Computational Mathematics, Johannes Kepler University Linz, Altenbergerstr. 69, 4040, Linz, Austria

    Ulrich Langer  & Walter Zulehner  & 

  2. Institute of Analysis and Scientific Computing — CMCS, Ecole Polytechnique Fédérale de Lausanne EPFL SB IACS CMCS Bâtiment MA, Station 8, 1015, Lausanne, Switzerland

    Marco Discacciati

  3. Department of Applied Physics and Applied Mathematics, Columbia University, 500 W. 120th Street, MC 4701, 10027, New York, NY, USA

    David E. Keyes

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

    Olof B. Widlund

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Haynes, R.D., Huang, W., Russell, R.D. (2008). A Moving Mesh Method for Time—dependent Problems Based on Schwarz Waveform Relaxation. In: Langer, U., Discacciati, M., Keyes, D.E., Widlund, O.B., Zulehner, W. (eds) Domain Decomposition Methods in Science and Engineering XVII. Lecture Notes in Computational Science and Engineering, vol 60. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75199-1_25

Download citation

Publish with us

Policies and ethics

Search

Navigation