Summary
In this paper, we propose and study a Robin domain decomposition algorithm to approximate a frictionless unilateral problem between two elastic bodies. Indeed this algorithm combines, in the contact zone, the Dirichlet and Neumann boundaries conditions (Robin boundary condition). The primary feature of this algorithm is the resolution on each sub-domain of variational inequality.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Agoshkov, V.I.: Poincaré-Steklov’s operators and domain decomposition methods in finite-dimensional spaces. First International Symposium on Domain Decomposition Methods for Partial Differential Equations (Paris, 1987), 73–112, SIAM, Philadelphia, PA, 1988.
Bayada, G., Sabil, J., Sassi, T.: Algorithme de Neumann-Dirichlet pour des problèmes de contact unilatéral: résultat de convergence. (French) [Neumann-Dirichlet algorithm for unilateral contact problems: convergence results] C. R. Math. Acad. Sci. Paris 335 (2002), no. 4, 381–386.
Bayada, G., Sabil, J., Sassi, T.: A Neumann-Neumann domain decomposition algorithm for the Signorini problem. Appl. Math. Lett. 17 (2004), no. 10, 1153–1159.
Dostal, Z., Schöberl, J.: Minimizing quadratic functions over non-negative cone with the rate of convergence and finite termination. Optim. Appl., 30, (2000), no. 1, 23–44.
Duvaut, G., Lions, J.-L.: Les inéquations en mécanique et en physique, Dunod, Paris, (1972).
Glowinski, R., Lions, J.-L., Trémolière, R.: Numerical Analysis of variational Inequalities, North-Holland, 1981.
Guo, W., Hou, L.S.: Generalizations and acceleration s of Lions’ nonoverlapping domain decomposition method for linear elliptic PDE. SIAM J. Numer. Anal. 41 (2003), no. 6, 2056–2080
Haslinger, J., Hlavacek, I., Nečas, J.: Numerical methods for unilateral problems in solid mechanics. Handbook of numerical analysis, Vol. IV, 313–485, Handb. Numer. Anal., IV, North-Holland, Amsterdam, 1996.
Ipopa, M.A.: Algorithmes de d’composition de domaine pour les problèmes de contact: Convergence et simulations numériques. Thesis, Université de Caen, 2008.
Ipopa, M.A., Sassi, T.: A Robin algorithm for unilateral contact problems. C.R. Math Acad. Sci. Paris, Ser. I, 346 (2008), 357–362.
Sassi, T., Ipopa, M.A., Roux, F.-X.: Generalization of Lion’s nonoverlapping domain decomposition method for contact problems. Lect. Notes Comput. Sci. Eng., Vol 60, pp 623–630, 2008.
Kikuchi, N., Oden, J.T.: Contact problems in elasticity: a study of variational inequalities and finite element methods, SIAM, Philadelphia, (1988)
Koko, J.: An Optimization-Based Domain Decomposition Method for a Two-Body Contact Problem. Num. Funct. Anal. Optim., Vol. 24, no. 5-6, 587–605, (2003).
Krause, R.H., Wohlmuth, B.I.: Nonconforming domain decomposition techniques for linear elasticity. East-West J. Numer. Math. 8 (2000), no. 3, 177–206.
Lions, P.-L.: On the Schwarz alternating method. III. A variant for nonover-lapping subdomains. Third International Symposium on Domain Decomposition Methods for Partial Differential Equations (Houston, TX, 1989), 202–223, SIAM, Philadelphia, PA, 1990.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ipopa, M., Sassi, T. (2009). A Robin Domain Decomposition Algorithm for Contact Problems: Convergence Results. In: Bercovier, M., Gander, M.J., Kornhuber, R., Widlund, O. (eds) Domain Decomposition Methods in Science and Engineering XVIII. Lecture Notes in Computational Science and Engineering, vol 70. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02677-5_14
Download citation
DOI: https://doi.org/10.1007/978-3-642-02677-5_14
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02676-8
Online ISBN: 978-3-642-02677-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)