Skip to main content
SpringerLink
Log in
Book cover

Domain Decomposition Methods in Science and Engineering XX pp 345–352Cite as

A Comparison of TFETI and TBETI for Numerical Solution of Engineering Problems of Contact Mechanics

  • Conference paper
  • First Online:

  • 2029 Accesses

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 91))

Summary

Since the introduction of Finite Element Tearing and Interconnecting (FETI) by Farhat and Roux in 1991, the method has been recognized to be an efficient parallel technique for the solution of partial differential equations. In 2003 Langer and Steinbach formulated its boundary element counterpart (BETI), which reduces the problem dimension to subdomain boundaries. Recently, we have applied both FETI and BETI to contact problems of mechanics.In this paper we numerically compare their variants bearing the prefix Total (TFETI/TBETI)on a frictionless Hertz contact problem and on a realistic problem with a given friction.

This is a preview of subscription content, 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
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. P. Avery and C. Farhat. The FETI family of domain decomposition methods for inequality-constrained quadratic programming: Application to contact problems with conforming and nonconforming interfaces. Comput Method Appl M, 198:1673–1683, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  2. J. Bouchala, Z. Dostál, and M. Sadowská. Theoretically supported scalable BETI method for variational inequaltities. Computing, 82: 53–75, 2008.

    Article  MathSciNet  MATH  Google Scholar 

  3. J. Bouchala, Z. Dostál, and M. Sadowská. Scalable Total BETI based algorithm for 3D coercive contact problems for linear elastostatics. Computing, 85:189–217, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  4. Z. Dostál. An optimal algorithm for bound and equality constrained quadratic programming problems with bounded spectrum. Computing, 78:311–328, 2006.

    Article  MathSciNet  MATH  Google Scholar 

  5. Z. Dostál. Optimal Quadratic Programming Algorithms with Applications to Variational Inequalities. 1dt edition. SOIA, volume 23. Springer - Verlag, New York, 2009.

    Google Scholar 

  6. Z. Dostál, D. Horák, and R. Kučera. Total FETI - an easier implementable variant of the FETI method for numerical solution of elliptic PDE. Commun Numer Meth En, 196:1155–1162, 2006.

    Article  Google Scholar 

  7. Z. Dostál, T. Kozubek, V. Vondrák, T. Brzobohatý, and A. Markopoulos. Scalable TFETI algorithm for the solution of multibody contact problems of elasticity. Int J Numer Meth Engng, 82:1384–1405, 2010.

    MATH  Google Scholar 

  8. C. Farhat and F.-X. Roux. A method of finite element tearing and interconnecting and its parallel solution algorithm. Int J Numer Meth Eng, 32:1205–1227, 1991.

    Article  MATH  Google Scholar 

  9. C. Farhat, J. Mandel, and F.-X. Roux. Optimal convergence properties of the FETI domain decomposition method. Comput Method Appl Mech Eng, 115:365–385, 1994.

    Article  MathSciNet  Google Scholar 

  10. A. Klawonn and O.B. Widlund. FETI and Neumann-Neumann iterative substructuring methods: Connections and new results. Comm Pure Appl Math, 54:57–90, 2001.

    Article  MathSciNet  MATH  Google Scholar 

  11. R. Kornhuber and R. Krause. Adaptive multigrid methods for Signorini’s problem in linear elasticity. Comput Visual Sci, 4:9–20, 2001.

    Article  MathSciNet  MATH  Google Scholar 

  12. T. Kozubek, A. Markopoulos, T. Brzobohatý, R. Kučera, V. Vondrák, and Z. Dostál. MatSol – MATLAB efficient solvers for problems in engineering. http://www.am.vsb.cz/matsol.

  13. U. Langer and O. Steinbach. Boundary element tearing and interconnecting methods. Computing, 71:205–228, 2003.

    Article  MathSciNet  MATH  Google Scholar 

  14. U. Langer, G. Of, O. Steinbach, and W. Zulehner. Inexact data-sparse boundary element tearing and interconnecting methods. SIAM J Sci Comp, 29:290–314, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  15. J. Mandel and R. Tezaur. Convergence of a substructuring method with Lagrange multipliers. Numer Math, 73:473–487, 1996.

    Article  MathSciNet  MATH  Google Scholar 

  16. G. Of. The All-floating BETI method: numerical results. In Domain Decomposition Methods in Science and Engineering XVII, volume 60 of LNCSE, pages 295–302. Springer, Berlin, Heidelberg, 2008.

    Google Scholar 

  17. G. Of and O. Steinbach. The all-floating boundary element tearing and interconnecting method. J Numer Math, 17:277–298, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  18. G. Of, O. Steinbach, and W.L. Wendland. Applications of a fast multipole Galerkin in boundary element method in linear elastostatics. Comput Visual Sci, 8:201–209, 2005.

    Article  MathSciNet  Google Scholar 

  19. M. Sadowská, Z. Dostál, T. Kozubek, A. Markopoulos, and J. Bouchala. Scalable total BETI based solver for 3D multibody frictionless contact problems in mechanical engineering. Eng Anal Bound Elem, 35:330–341, 2011.

    Article  MathSciNet  MATH  Google Scholar 

  20. J. Schöberl. Solving the Signorini problem on the basis of domain decomposition technique. Computing, 60:323–344, 1998.

    Article  MathSciNet  MATH  Google Scholar 

  21. O. Steinbach and W.L. Wendland. The construction of some efficient preconditioners in the boundary element method. Adv Comput Math, 9:191–216, 1998.

    Article  MathSciNet  MATH  Google Scholar 

  22. B.I. Wolmuth and R. Krause. Monotone methods on nonmatching grids for nonlinear contact problems. SIAM J Sci Comput, 25:324–347, 2003.

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This research has been financially supported by the grants GA CR 201/07/0294 and the Ministry of Education of the Czech Republic No. MSM6198910027. This work was also supported by the European Regional Development Fund in the IT4Innovations Centre of Excellence project (CZ.1.05/1.1.00/02.0070).

Author information

Authors and Affiliations

  1. FEECS, VŠB - TU Ostrava, Ostrava, Czech Republic

    M. Sadowská & T. Kozubek

  2. FME, VŠB - TU Ostrava, Ostrava, Czech Republic

    D. Lukáš, A. Markopoulos & T. Brzobohatý

Authors
  1. D. Lukáš
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Sadowská
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. T. Kozubek
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. Markopoulos
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. T. Brzobohatý
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. Lukáš .

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

Lukáš, D., Sadowská, M., Kozubek, T., Markopoulos, A., Brzobohatý, T. (2013). A Comparison of TFETI and TBETI for Numerical Solution of Engineering Problems of Contact Mechanics. 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_40

Download citation

Publish with us

Policies and ethics

Search

Navigation