Skip to main content
SpringerLink
Log in

A Study of Prolongation Operators Between Non-nested Meshes

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

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 78))

Summary

For a class of multilevel preconditioners based on non-nested meshes, we study numerically several selected prolongation and restriction operators. Robustness with respect to the mesh size and to jumps in the coefficients is demonstrated.

* Supported by Bonn International Graduate School in Mathematics

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
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. R. Blaheta. Algebraic multilevel methods with aggregations: an overview. In I. Lirkov, S. Margenov, and J. Waśniewski, editors, Large-Scale Scientific Computing, volume 3743 of Lecture Notes in Computer Science, pp. 3–14. Springer, 2006.

    Google Scholar 

  2. J.H. Bramble, J.E. Pasciak, and P.S. Vassilevski. Computational scales of Sobolev norms with applications to preconditioning. Math. Comput., 69 (230): 463–480, 2000.

    MATH  MathSciNet  Google Scholar 

  3. J.H. Bramble, J.E. Pasciak, J. Wang, and J. Xu. Convergence estimates for multigrid algorithms without regularity assumptions. Math. Comput., 57 (195): 23–45, 1991.

    MATH  MathSciNet  Google Scholar 

  4. X. Cai. The use of pointwise interpolation in domain decomposition methods with non-nested meshes. SIAM J. Sci. Comput., 16 (1): 250–256, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  5. T. Chan, B. Smith, and J. Zou. Overlapping Schwarz methods on unstructured meshes using non-matching coarse grids. Numer. Math., 73 (2): 149–167, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  6. T. Chan, J. Xu, and L. Zikatanov. An agglomeration multigrid method for unstructured grids. In J. Mandel, C. Farhat, and X.-C. Cai, editors, Domain Decomposition Methods 10, volume 218 of Contemporary Mathematics, pp. 67–81. AMS, Providence, RI, 1998.

    Google Scholar 

  7. P. Clément. Approximation by finite element functions using local regularization. RAIRO Anal. Numér., 9 (R-2): 77–84, 1975.

    Google Scholar 

  8. T. Dickopf and R. Krause. A pseudo-L 2-projection for multilevel methods based on non-nested meshes. INS Preprint No. 0908 (University of Bonn) and ICS Preprint No. 2009-04 (University of Lugano), 2009.

    Google Scholar 

  9. M. Griebel, D. Oeltz, and M.A. Schweitzer. An algebraic multigrid method for linear elasticity. SIAM J. Sci. Comput., 25 (2): 385–407, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  10. L.R. Scott and S. Zhang. Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comput., 54 (190): 483–493, 1990.

    MATH  MathSciNet  Google Scholar 

  11. O. Steinbach. On a generalized L 2-projection and some related stability estimates in Sobolev spaces. Numer. Math., 90 (4): 775–786, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  12. K. Stüben. An introduction to algebraic multigrid. In U. Trottenberg et al., editors, Multigrid, pp. 413–532. Academic Press, London, 2001.

    Google Scholar 

  13. A. Toselli and O. Widlund. Domain Decomposition Methods – Algorithms and Theory, volume 34 of Springer Series in Computational Mathematics. Springer, Berlin 2005.

    MATH  Google Scholar 

  14. P. Vaněk, M. Brezina, and J. Mandel. Convergence of algebraic multigrid based on smoothed aggregation. Numer. Math., 88 (3): 559–579, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  15. J. Xu. The auxiliary space method and optimal multigrid preconditioning techniques for unstructured grids. Computing, 56 (3): 215–235, 1996.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Numerical Simulation, University of Bonn, 53115, Bonn, Germany

    Thomas Dickopf*

  2. Institute of Computational Science, University of Lugano, 6904, Lugano, Switzerland

    Rolf Krause

Authors
  1. Thomas Dickopf*
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rolf Krause
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Thomas Dickopf* .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, Xiangtan University, Xiangtan, 411105, China, People's Republic

    Yunqing Huang

  2. FB Mathematik und Informatik, Freie Universität Berlin, Arnimallee 6, Berlin, 14195, Berlin, Germany

    Ralf Kornhuber

  3. Department of Mathematics, Courant Institute of Math. Sciences, New York University, Mercer St. 251, New York, 10012, New York, USA

    Olof Widlund

  4. Eberly College of Science, Dept. Mathematics, Pennsylvania State University, University Park, 16802, Pennsylvania, USA

    Jinchao Xu

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dickopf*, T., Krause, R. (2011). A Study of Prolongation Operators Between Non-nested Meshes. In: Huang, Y., Kornhuber, R., Widlund, O., Xu, J. (eds) Domain Decomposition Methods in Science and Engineering XIX. Lecture Notes in Computational Science and Engineering, vol 78. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11304-8_39

Download citation

Publish with us

Policies and ethics

Search

Navigation