Skip to main content

Block Preconditioners for the Incompressible Stokes Problem

  • Conference paper
Book cover Large-Scale Scientific Computing (LSSC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5910))

Included in the following conference series:

Abstract

This paper discusses the solution of the Stokes problem using block preconditioned iterative methods. Block preconditioners are based on the block factorization of the discretized problem. We focus on two specific types: SIMPLE-type preconditioners and the LSC preconditioner. Both methods use scaling to improve their performance. We test convergence of GCR in combination with these preconditioners both for a constant and a non-constant viscosity Stokes problem.

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

Access this chapter

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

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. Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  2. Elman, H.C., Silvester, D., Wathen, A.J.: Finite Elements and Fast Iterative Solvers with applications in incompressible fluids dynamics. Oxford University Press, Oxford (2005)

    Google Scholar 

  3. Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM J. Numerical Analysis 12(4), 617–629 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  4. Eisenstat, C., Elman, H.C., Schultz, M.H.: Variational iterative methods for nonsymmetric systems of linear equations. SIAM J. Numer. Anal. 20(2), 345–357 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  5. Meijerink, J.A., van der Vorst, H.A.: An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix. Math. Comp. 31, 148–162 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  6. Balay, S., Gropp, W.D., McInnes, L.C., Smith, B.F.: Efficient Management of Parallelism in Object Oriented Numerical Software Libraries. Modern Software Tools in Scientific Computing, 163–202 (1997)

    Google Scholar 

  7. van der Vorst, H.A., Vuik, C.: GMRESR: a family of nested GMRES methods. Num. Lin. Alg. Appl. 1, 369–386 (1994)

    Article  MATH  Google Scholar 

  8. Vuik, C., Saghir, A., Boerstoel, G.P.: The Krylov accelerated SIMPLE(R) method for flow problems in industrial furnaces. Int. J. Numer. Meth. Fluids 33, 1027–1040 (2000)

    Article  MATH  Google Scholar 

  9. ur Rehman, M., Vuik, C., Segal, G.: SIMPLE-Type preconditioners for the Oseen problem. Int. J. Numer. Meth. Fluids. Published Online (2008)

    Google Scholar 

  10. Elman, H., Howle, V.E., Shadid, J., Shuttleworth, R., Tuminaro, R.: Block Preconditioners Based on Approximate Commutators. SIAM J. Sci. Comput. 27(5), 1651–1666 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  11. May, D.A., Moresi, L.: Preconditioned iterative methods for Stokes flow problems arising in computational geodynamics. Physics of the Earth and Planetary Interiors 171, 33–47 (2008)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

ur Rehman, M., Vuik, C., Segal, G. (2010). Block Preconditioners for the Incompressible Stokes Problem. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2009. Lecture Notes in Computer Science, vol 5910. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12535-5_99

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-12535-5_99

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12534-8

  • Online ISBN: 978-3-642-12535-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics