Skip to main content Accessibility help

A Domain Decomposition Algorithm for Contact Problems: Analysis and Implementation

  • J. Haslinger (a1), R. Kučera (a2) and T. Sassi (a3)


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.


Corresponding author


Hide All
[1] L. Baillet, T. Sassi. Simulations numériques de différentes méthodes d'éments finis pour les problémes contact avec frottement. C. R. Acad. Sci, Paris, Ser. IIB, 331 (2003),789–796.
[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.
[3] Bayada, G., Sabil, J., Sassi, T.. A Neumann-Neumann domain decomposition algorithm for the Signorini problem. Appl. Math. Letters, 17 (2004), 11531159.
[4] Bjorstad, P. E., Widlund, O. B.. Iterative methods for the solution of elliptic problems on regions partitioned into substructures. SIAM J. Numerical Analysis, 23 (1986), No. 6, 10971120.
[5] Christensen, P. W., Klarbring, A., Pang, J. S., Strömberg, N.. Formulation and comparison of algorithms for frictional contact problems. Internat. J. Numer. Methods Engrg., 42 (1998), No. 1, 145173.
[6] Dostál, Z., Schöberl, J.. Minimizing quadratic functions over non-negative cone with the rate of convergence and finite termination. Comput. Optim. Appl., 30 (2005), No. 1, 2344.
[7] Eck, C., Wohlmuth, B.. Convergence of a Contact-Neumann iteration for the solution of two-body contact problems. Mathematical Models and Methods in Applied Sciences, 13 (2003), No. 8, 1103-1118.
[8] R. Glowinski, J. L. Lions, R. Trémoliére. Numerical analysis of variational inequalities. Studies in Mathematics and its Applications, Volume VIII, North-Holland, Amsterdam, 1981.
[9] G. H. Golub, C. F. Van Loan. Matrix computation. The Johns Hopkins University Press, Baltimore, 1996.
[10] Haslinger, J., Dostál, Z., Kučera, R.. 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, 22612281.
[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.
[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.
[14] Kornhuber, R., Krause, R.. Adaptive multigrid methods for Signorini's problem in linear elasticity. Comput. Vis. Sci., 4 (2001), No. 1, 920.,
[15] Krause, R., Wohlmuth, B.. A Dirichlet-Neumann type algorithm for contact problems with friction. Comput. Vis. Sci., 5 (2002), No. 3, 139148.
[16] Le Tallec, P.. Domain decomposition methods in computational mechanics. Comput. Mech. Adv., 1 (1994), No. 2, 121220.
[17] J. Sabil. Modélisation et méthodes de décomposition de domaine pour des problémes de contact. Thesis, INSA de Lyon, 2004.



Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed