Skip to main content

Parallel Displacement Decomposition Solvers for Elasticity Problems

  • Conference paper
  • First Online:
Parallel Processing and Applied Mathematics (PPAM 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2328))

Abstract

This article describes the displacement decomposition and its benefits for the parallelization of the preconditioned conjugate gradient method for finite element elasticity problems. It deals with both the fixed and variable preconditioning based on this decomposition. Numerical efficiency of the parallel algorithms is demonstrated on an academic benchmark and real-life modelling 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. Axelsson, O., Gustafsson, I.: Iterative Methods for the solution of the Navier equations of elasticity. Computer Methods in Applied Mechanics and Engineering, 15 (1978), 241–258

    Article  MathSciNet  MATH  Google Scholar 

  2. Blaheta, R.: Displacement decomposition-incomplete factorization preconditioning techniques for linear elasticity problems. Numerical Linear Algebra with Applications, 1 (1994), 107–128

    Article  MathSciNet  MATH  Google Scholar 

  3. Blaheta, R.: GPCG-generalized preconditioned CG method and its use with nonlinear and nonsymmetric displacement decomposition preconditioners. TR-DAM-2001/3, Institute of Geonics Cz. Acad. Sci., Ostrava (2001), submitted

    Google Scholar 

  4. Blaheta, R.: Parallel iterative methods. Lecture notes, VŠB-Technical University, Ostrava (2000)

    Google Scholar 

  5. Blaheta, R.: Space decomposition methods: Displacement decomposition, composite grid finite elements and overlapping domain decomposition. In: Modern mathematical methods in engineering. VSB-Technical University, Ostrava (2000) 7–16

    Google Scholar 

  6. Blaheta, R., Byczanski, P., Jakl, O., Starý, J.: Space decomposition preconditioners and their application in geomechanics. TR-DAM-2001/4, Institute of Geonics Cz. Acad. Sci., Ostrava (2001), submitted

    Google Scholar 

  7. Blaheta, R., Jakl, O., Starý, J.: Large-scale FE Modelling in Geomechanics: a Case Study in Parallelization. In: Dongarra, J., Luque, E., Margalef, T. (eds.): Recent Advances in Parallel Virtual Machine and Message Passing Interface. LNCS, Vol. 1697. Springer-Verlag, Berlin (1999) 299–306

    Chapter  Google Scholar 

  8. Dongarra, J. J.: Performance of various computers using standard linear equations software (18/01/01). http://www.netlib.org/benchmark/performance.ps

  9. Dongarra, J. J., Duff, I. S., Sorensen, D. C., van der Vorst, H.: Numerical linear algebra for high-performance computers. SIAM, Philadelphia (1998)

    Book  MATH  Google Scholar 

  10. Notay, Y.: Flexible conjugate gradients. SIAM J. Sci. Comp., Vol. 22 (2000), 1444–1460

    Article  MathSciNet  MATH  Google Scholar 

  11. Smith, B. F., Bjørstad, P. E., Gropp, W. D.: Domain Decomposition. Parallel multilevel methods for elliptic partial differential equations. Cambridge University Press (1996)

    Google Scholar 

  12. The Standard Performance Evaluation Corp. http://www.spec.org/ (25/01/01)

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Blaheta, R., Jakl, O., Starý, J. (2002). Parallel Displacement Decomposition Solvers for Elasticity Problems. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2001. Lecture Notes in Computer Science, vol 2328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48086-2_44

Download citation

  • DOI: https://doi.org/10.1007/3-540-48086-2_44

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43792-5

  • Online ISBN: 978-3-540-48086-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics