A Domain Decomposition Algorithm for Contact Problems: Analysis and Implementation

J. Haslinger; R. Kučera; T. Sassi

Mathematical Modelling of Natural Phenomena (2009)

  • Volume: 4, Issue: 1, page 123-146
  • ISSN: 0973-5348

Abstract

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The paper deals with an iterative method for numerical solving frictionless contact problems for two elastic bodies. Each iterative step consists of a Dirichlet problem for the one body, a contact problem for the other one and two Neumann problems to coordinate contact stresses. Convergence is proved by the Banach fixed point theorem in both continuous and discrete case. Numerical experiments indicate scalability of the algorithm for some choices of the relaxation parameter.

How to cite

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Haslinger, J., Kučera, R., and Sassi, T.. "A Domain Decomposition Algorithm for Contact Problems: Analysis and Implementation." Mathematical Modelling of Natural Phenomena 4.1 (2009): 123-146. <http://eudml.org/doc/222400>.

@article{Haslinger2009,
abstract = { The paper deals with an iterative method for numerical solving frictionless contact problems for two elastic bodies. Each iterative step consists of a Dirichlet problem for the one body, a contact problem for the other one and two Neumann problems to coordinate contact stresses. Convergence is proved by the Banach fixed point theorem in both continuous and discrete case. Numerical experiments indicate scalability of the algorithm for some choices of the relaxation parameter.},
author = {Haslinger, J., Kučera, R., Sassi, T.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {contact problem; domain decomposition method},
language = {eng},
month = {1},
number = {1},
pages = {123-146},
publisher = {EDP Sciences},
title = {A Domain Decomposition Algorithm for Contact Problems: Analysis and Implementation},
url = {http://eudml.org/doc/222400},
volume = {4},
year = {2009},
}

TY - JOUR
AU - Haslinger, J.
AU - Kučera, R.
AU - Sassi, T.
TI - A Domain Decomposition Algorithm for Contact Problems: Analysis and Implementation
JO - Mathematical Modelling of Natural Phenomena
DA - 2009/1//
PB - EDP Sciences
VL - 4
IS - 1
SP - 123
EP - 146
AB - The paper deals with an iterative method for numerical solving frictionless contact problems for two elastic bodies. Each iterative step consists of a Dirichlet problem for the one body, a contact problem for the other one and two Neumann problems to coordinate contact stresses. Convergence is proved by the Banach fixed point theorem in both continuous and discrete case. Numerical experiments indicate scalability of the algorithm for some choices of the relaxation parameter.
LA - eng
KW - contact problem; domain decomposition method
UR - http://eudml.org/doc/222400
ER -

References

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  2. G. Bayada, J. Sabil, T. Sassi. Algorithme de décomposition de domaine pour un probléme de Signorini sans frottement. C. R. Acad. Sci. Paris, Ser. I335 (2002), 381–386.  
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  10. J. Haslinger, Z. Dostál, R. Kučera. On a splitting type algorithm for the numerical realization of contact problems with Coulomb friction. Comput. Methods Appl. Mech. Engrg., 191 (2002), No. 21-22, 2261–2281.  Zbl1131.74344
  11. J. Haslinger, I. Hlaváček, J. Nečas. Numerical methods for unilateral problems in solid mechanics. Handbook of Numerical Analysis, Volume IV, Part 2, North Holland, Amsterdam, 1996.  Zbl0873.73079
  12. M. A. Ipopa. Algorithmes de Décomposition de Domaine pour les problémes de Contact: Convergence et simulations numériques. Thesis, Université de Caen, 2008.  
  13. N. Kikuchi, J. T. Oden. Contact problems in elasticity: A study of variational inequalities and finite element methods. SIAM, Philadelphia, 1988.  Zbl0685.73002
  14. R. Kornhuber, R. Krause. Adaptive multigrid methods for Signorini's problem in linear elasticity. Comput. Vis. Sci., 4 (2001), No. 1, 9–20.,  Zbl1051.74045
  15. R. Krause, B. Wohlmuth. A Dirichlet-Neumann type algorithm for contact problems with friction. Comput. Vis. Sci., 5 (2002), No. 3, 139–148.  Zbl1099.74536
  16. P. Le Tallec. Domain decomposition methods in computational mechanics. Comput. Mech. Adv., 1 (1994), No. 2, 121–220.  Zbl0802.73079
  17. J. Sabil. Modélisation et méthodes de décomposition de domaine pour des problémes de contact. Thesis, INSA de Lyon, 2004.  

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