. Dans-cette-partie, nous présentons l'´ etat de la réflexion conduite en collaboration avec Chritian Rey, Frédéric Feyel et Laurent Séries sur l'organisation de la partieparalì ele d'un codé eléments-finis basé sur des paradigmes modernes de programmation que l'on rassemble généralement sous la dénomination " langage orienté objet

K. Ach, P. Gosselet, C. Rey, F. Léné, and P. Dasset, Des explications sur la norme UML peuventêtrepeuventêtre trouvées sur le site http Approche séquentielles et paralì eles pour l'´ etude du comportement mécanique d'une butée flexible, Cette partie repose essentiellement sur l'explication de diagrammes UML représentant les parties les plus significatives du code dans Actes du cinquì eme colloque national en calcul des structures Achdou et Y. A. Kuznetsov, Substructuring preconditioners for finite element methods on nonmatching grids, pp.683-690, 1995.

Y. Achdou, Y. Maday, and O. B. Widlund, Méthode itérative de sous-structuration pour lesélémentsleséléments avec joints, C.R. Acad. Sci. Paris, vol.I, issue.322, pp.185-190, 1996.

J. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Archive for Rational Mechanics and Analysis, vol.8, issue.4, pp.337-403, 1977.
DOI : 10.1007/BF00279992

J. Batoz and G. Dhatt, Modélisation des structures parélémentsparéléments-finis, Hermès, 1990.

M. Bhardwaj, D. Day, C. Farhat, M. Lesoinne, K. Pierson et al., Application of the FETI method to ASCI problems : Scalability results on a thousandprocessor and discussion of highly heterogeneous problems, Int. J. Num. Meth . Eng, vol.47, issue.1-3, pp.513-536, 2000.
DOI : 10.2172/6127

J. Boufflet, P. Breitkopf, C. Denis, A. Rassineux, and M. Vayssade, Renumérotation desélémentsdeséléments-finis pour un solveurparalì ele multifrontal, dans Actes du 5éme Colloque National en Calcul des Structures, pp.699-708, 2001.

F. Brezzi and M. Fortin, Mixed and hybrid finite element methods, 1991.
DOI : 10.1007/978-1-4612-3172-1

F. Brezzi and L. Marini, A three-field domain decomposition method, Proceedings of the sixth international conference on domain decomposition methods, pp.27-34, 1993.
DOI : 10.1090/conm/157/01402

S. Cantournet, Endommagement et fatigue desélastomèresdesélastomères, Thèse de doctorat, Université P. et M. Curie, 2002.

A. Chapman and Y. Saad, Deflated and augmented Krylov subspace techniques, Numer, Linear Algebra Appl, 1997.

P. Ciarlet, The finite element method for elliptic problems, 1979.

P. Ciarlet and G. Geymonat, Sur les lois de comportement enélasticitéenélasticité nonlinéaire, CRAS, vol.295, pp.423-426, 1982.

R. Dautray and J. Lions, Analyse mathématique et calcul numérique, 1987.

A. De-la-bourdonnaye, C. Farhat, A. Macedo, F. Magoules, and F. Roux, Advances in Computational Mechanics with High Performance Computing, chapitre A BIBLIOGRAPHIE method of finite element tearing and interconnecting for the Helmholtz problem

G. Dhatt and G. Touzot, Une présentation de la méthode desélémentsdeséléments-finis, Maloine, 1984.

D. Dureisseix and C. Farhat, A numerically scalable domain decomposition method for the solution of frictionless contact problems, International Journal for Numerical Methods in Engineering, vol.28, issue.12, pp.2643-2666, 2001.
DOI : 10.1002/nme.140
URL : https://hal.archives-ouvertes.fr/hal-00321391

D. Dureissex, P. Ladevèze, and B. Schrefler, A LATIN computational strategy for multiphysics problems: application to poroelasticity, International Journal for Numerical Methods in Engineering, vol.2, issue.10, pp.1489-1510, 2003.
DOI : 10.1002/nme.622

G. Duvaut and J. Lions, Inequalities in mechanics and physics, 1976.

J. Erhel, K. Burrage, and B. Pohl, Restarted GMRES preconditioned by deflation, Journal of Computational and Applied Mathematics, vol.69, issue.2, pp.303-318, 1996.
DOI : 10.1016/0377-0427(95)00047-X

J. Erhel and F. , An Augmented Conjugate Gradient Method for Solving Consecutive Symmetric Positive Definite Linear Systems, SIAM Journal on Matrix Analysis and Applications, vol.21, issue.4, pp.1279-1299, 2000.
DOI : 10.1137/S0895479897330194
URL : https://hal.archives-ouvertes.fr/inria-00523682

C. Farhat, T. Chan, and G. Meurant, A saddle-point principle domain decomposition method for the solution of solid mechanics problems, dans Domain Decomposition Methods for Partial Differential Equations, J. Scroggs et R. Voigt), pp.271-292, 1992.

C. Farhat, P. Chen, and F. Risler, A simple and unified framework for accelerating the convergence of iterative substructuring methods with Lagrange multipliers : Application to the design of new FETI coarse problems, Rapport technique CU-CAS-96-26, 1996.

C. Farhat, P. Chen, and F. Risler, A unified framework for accelerating the convergence of iterative substructuring methods with Lagrange multipliers, International Journal for Numerical Methods in Engineering, vol.38, issue.2, pp.257-288, 1998.
DOI : 10.1002/(SICI)1097-0207(19980530)42:2<257::AID-NME361>3.0.CO;2-R

C. Farhat, P. Chen, and F. Roux, The two-level FETI method Part II: Extension to shell problems, parallel implementation and performance results, Computer Methods in Applied Mechanics and Engineering, vol.155, issue.1-2, pp.153-180, 1998.
DOI : 10.1016/S0045-7825(97)00145-X

C. Farhat and M. Géradin, On the computation of the null space and generalized invers of large matrix, and the zero energy modes of a structure, Rapport technique CU-CAS-96-15, Center for aerospace structures, 1996.

C. Farhat, M. Lesoinne, P. Letallec, K. Pierson, and D. Rixen, FETI-DP: a dual-primal unified FETI method?part I: A faster alternative to the two-level FETI method, International Journal for Numerical Methods in Engineering, vol.7, issue.7, pp.1523-1544, 2001.
DOI : 10.1002/nme.76

C. Farhat, M. Lesoinne, and K. Pierson, A scalable dual-primal domain decomposition method, Numerical Linear Algebra with Applications, vol.46, issue.7-8, pp.687-714, 2000.
DOI : 10.1002/1099-1506(200010/12)7:7/8<687::AID-NLA219>3.0.CO;2-S

C. Farhat, A. Macedo, and M. Lesoinne, A two-level domain decomposition method for the iterative solution of high frequency exterior Helmholtz problems, Numerische Mathematik, vol.85, issue.2, pp.283-308, 2000.
DOI : 10.1007/PL00005389

C. Farhat, A. Macedo, and R. Tezaur, FETI-H : a scalable domaine decomposition method for high frequency exterior Helmholtz problems, dans Domain decomposition methods in science and engineering, Domain decomposition press, 1999.

C. Farhat and J. Mandel, The two-level FETI method for static and dynamic plate problems Part I: An optimal iterative solver for biharmonic systems, Computer Methods in Applied Mechanics and Engineering, vol.155, issue.1-2
DOI : 10.1016/S0045-7825(97)00146-1

C. Farhat, J. Mandel, and F. Roux, Optimal convergence properties of the FETI domain decomposition method, Computer Methods in Applied Mechanics and Engineering, vol.115, issue.3-4, pp.365-385, 1994.
DOI : 10.1016/0045-7825(94)90068-X

C. Farhat, K. Pierson, and M. Lesoinne, The second generation FETI methods and their application to the parallel solution of large-scale linear and geometrically non-linear structural analysis problems, Computer Methods in Applied Mechanics and Engineering, vol.184, issue.2-4, pp.333-374, 2000.
DOI : 10.1016/S0045-7825(99)00234-0

C. Farhat and F. Roux, A method of finite element tearing and interconnecting and its parallel solution algorithm, International Journal for Numerical Methods in Engineering, vol.28, issue.6, pp.1205-1227, 1991.
DOI : 10.1002/nme.1620320604

C. Farhat and F. Roux, The dual Schur complement method with well-posed local Neumann problems, Contemporary Mathematics, vol.157, pp.193-201, 1994.
DOI : 10.1090/conm/157/01418

C. Farhat and F. X. Roux, Implicit parallel processing in structural mechanics, Computational Mechanics Advances, vol.2, issue.1, pp.1-124, 1994.

J. Fill and D. Fishkind, The Moore--Penrose Generalized Inverse for Sums of Matrices, SIAM Journal on Matrix Analysis and Applications, vol.21, issue.2, pp.629-635, 1999.
DOI : 10.1137/S0895479897329692

V. Frayssé, L. Giraud, and H. Kharraz-aroussi, On the influence of the orthogonalization scheme on the parallel performance of GMRes, Rapport technique, CERFACS, 1998.

R. Glowinski and P. L. Tallec, Augmented lagrangian interpretation of the nonoverlapping Schwartz alternating method, Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, pp.224-231, 1990.

P. Goldfeld, Balancing Neumann-Neumann for (in)compressible linear elasticity and (generalized) Stokes ? parallel implementation, Proceedings of the 14 th international conference on domain decomposition method, pp.209-216, 2002.

P. Gosselet, V. Chiaruttini, C. Rey, and F. Feyel, Une approche hybride de décomposition de domaine pour lesprobì emes multiphysiques : applicationàapplication`applicationà la poroélasticité, dans Actes dusixì eme colloque national en calcul de structures, pp.297-304, 2003.

P. Gosselet and C. Rey, On a selective reuse of krylov subspaces in newton-krylov approaches for nonlinear elasticity, dans Proceedings of the 14 th conference on domain decomposition methods, pp.419-426, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00277780

P. Gosselet and C. Rey, An hybrid domain decomposition, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00277630

P. Gosselet and C. Rey, An hybrid domain decomposition, en préparation, 2003.

P. Gosselet, C. Rey, P. Dasset, and F. Léné, A domain decomposition method for quasi incompressible formulations with discontinuous pressure field , Revue européenne desélementsdesélements finis, pp.363-377, 2002.

P. Gosselet, C. Rey, and D. Rixen, Etude comparative des méthodes de décomposition de domaine primale et duale : vers une meilleure initialisation de FETI, 2003.

P. Gosselet, C. Rey, and D. Rixen, On the initial estimate of interface forces in FETI methods, Computer Methods in Applied Mechanics and Engineering, vol.192, issue.25, pp.2749-2764, 2003.
DOI : 10.1016/S0045-7825(03)00288-3
URL : https://hal.archives-ouvertes.fr/hal-00277622

A. Klawonn and O. Widlund, Dual and dual-primal FETI methods for elliptic problems with discontinuous coefficients, Proceedings of the 12th International Conference on Domain Decomposition Methods, 1999.

A. Klawonn and O. Widlund, FETI and Neumann-Neumann iterative substructuring methods : connections and new results, Comm. pure and appl. math, pp.57-0090, 2001.

P. Ladevèze, Nonlinear Computational Structural Mechanics -New Approaches and Non-Incremental Methods of Calculation, 1999.

P. Ladevèze, O. Loiseau, and D. Dureisseix, A micro???macro and parallel computational strategy for highly heterogeneous structures, International Journal for Numerical Methods in Engineering, vol.46, issue.12, pp.121-138, 2001.
DOI : 10.1002/nme.274

J. Lambert-diani and C. Rey, New phenomenological behavior laws for rubbers and thermoplastic elastomers, European Journal of Mechanics - A/Solids, vol.18, issue.6, pp.1027-1043, 1999.
DOI : 10.1016/S0997-7538(99)00147-3

M. Lesoinne, K. Pierson, and . Feti-dp, An efficient, scalable, and unified Dual- Primal FETI method , dans Domain Decomposition Methods in Sciences and Engineering, pp.421-428, 1999.

F. Lingen, Efficient Gram-Schmidt orthonormalisation on parallel computers, Communications in Numerical Methods in Engineering, vol.41, issue.198, pp.57-66, 2000.
DOI : 10.1002/(SICI)1099-0887(200001)16:1<57::AID-CNM320>3.0.CO;2-I

J. Lions, Contrôle optimal de systèmes gouvernés par deséquationsdeséquations aux dérivées partielles , Dunod, 1986.

J. Mandel, Balancing domain decomposition, Communications in Numerical Methods in Engineering, vol.13, issue.3, pp.233-241, 1993.
DOI : 10.1002/cnm.1640090307

J. Mandel and M. Brezina, Balancing domain decomposition for problems with large jumps in coefficients, Mathematics of Computation, vol.65, issue.216, pp.1387-1401, 1996.
DOI : 10.1090/S0025-5718-96-00757-0

J. Mandel and R. Tezaur, Convergence of a substructuring method with Lagrange multipliers, Numerische Mathematik, vol.73, issue.4, pp.473-487, 1996.
DOI : 10.1007/s002110050201

J. Mandel and R. Tezaur, On the convergence of a dual-primal substructuring method, Numerische Mathematik, vol.88, issue.3, 2000.
DOI : 10.1007/s211-001-8014-1

R. Matteazzi, B. Schrefler, and B. Vitaliani, Comparaison of partitioned solution procedures for transient coupled problems in sequential and parallel processing, Adv. Comput. Struct. Tech, pp.351-357, 1996.

R. Ogden, Large Deformation Isotropic Elasticity: On the Correlation of Theory and Experiment for Compressible Rubberlike Solids, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.328, issue.1575, pp.567-583, 1972.
DOI : 10.1098/rspa.1972.0096

C. Paige, Approximate solutions and eigenvalue bounds from Krylov subspaces, Numerical Linear Algebra with Applications, vol.48, issue.2, pp.115-133, 1995.
DOI : 10.1002/nla.1680020205

K. Park, M. Justino, and C. Felippa, An algebraically partitioned FETI method for parallel structural analysis: algorithm description, International Journal for Numerical Methods in Engineering, vol.47, issue.15, pp.2717-2737, 1997.
DOI : 10.1002/(SICI)1097-0207(19970815)40:15<2717::AID-NME185>3.0.CO;2-B

K. Park, M. Justino, and C. Felippa, An algebraically partitioned FETI method for parallel structural analysis : performance evaluation, Int. J. Num. Meth . Eng, vol.40, issue.15, pp.2739-2758, 1997.

L. Pavarino and O. Widlund, Balancing Neumann-Neumann methods for incompressible Stokes equations, Communications on Pure and Applied Mathematics, vol.11, issue.3, pp.302-335, 2002.
DOI : 10.1002/cpa.10020

C. Rey, Développement d'algorithmesparalì eles de résolution en calcul non-linéaire de structures hétérogènes : application au cas d'une butée acier-´ elastomère, Thèse de doctorat, 1994.

C. Rey, Une technique d'accélération de la résolution deprobì emes d'´ elasticité non linéaire par décomposition de domaines, C.R. Acad. Sci. Paris, vol.322, pp.601-606, 1996.

C. Rey, Approches itératives pour le calcul de structures non linéaires, HabilitationàHabilitationà diriger des recherches, 2000.

C. Rey and P. Gosselet, Solution to large nonlinear systems : acceleration strategies based on domain decomposition and reuse of krylov subspaces, Proceedings of the 6 t h ESAFORM conference on material forming, 2003.
URL : https://hal.archives-ouvertes.fr/hal-01224419

C. Rey and F. Risler, A Rayleigh-Ritz preconditioner for the iterative solution to large scale nonlinear problems, Numerical Algorithms, vol.17, issue.3/4, pp.279-311, 1998.
DOI : 10.1023/A:1016680306741

F. Risler, Algorithmesparalì eles de résolution deprobì emes non linéaire de grande taille. ApplicationàApplication`Applicationà la simulation numérique de structures hyperélastiques, Thèse de doctorat, 1999.

F. Risler and C. Rey, On the reuse of Ritz vectors for the solution to nonlinear elasticity problems by domain decomposition methods, DD10 Proceedings, Contemporary Mathematics, pp.334-340, 1998.
DOI : 10.1090/conm/218/03026

F. Risler and C. Rey, Iterative accelerating algorithms with Krylov subspaces for the solution to large-scale nonlinear problems, Numerical Algorithms, vol.23, issue.1, pp.1-30, 2000.
DOI : 10.1023/A:1019187614377

R. Rivlin and D. Saunders, Large Elastic Deformations of Isotropic Materials. VII. Experiments on the Deformation of Rubber, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.243, issue.865, pp.251-288, 1951.
DOI : 10.1098/rsta.1951.0004

D. Rixen, Substructuring and dual methods in structural analysis, Thèse de doctorat, 1997.

D. Rixen and C. Farhat, A simple and efficient extension of a class of substructure based preconditioners to heterogeneous structural mechanics problems, International Journal for Numerical Methods in Engineering, vol.93, issue.4, pp.489-516, 1999.
DOI : 10.1002/(SICI)1097-0207(19990210)44:4<489::AID-NME514>3.0.CO;2-Z

D. Rixen, C. Farhat, R. Tezaur, and J. Mandel, Theoretical comparison of the FETI and algebraically partitioned FETI methods, and performance comparisons with a direct sparse solver, International Journal for Numerical Methods in Engineering, vol.2, issue.4, pp.501-534, 1999.
DOI : 10.1002/(SICI)1097-0207(19991010)46:4<501::AID-NME685>3.0.CO;2-7

F. Roux, Parallel implementation of domain decomposition method for non-linear elasticity problems, dans Workshop on domain-based parallelism and problem decomposition methods in computational science and engineering, 1994.

F. Roux, Parallel implementation of direct solution strategies for the coarse grig solvers in 2-level FETI method , Rapport technique, 1997.

Y. Saad, On the Lanczos method for solving symmetric linear systems with several right hand sides, Math. Comp, vol.48, pp.651-662, 1987.

Y. Saad, Analysis of Augmented Krylov Subspace Methods, SIAM Journal on Matrix Analysis and Applications, vol.18, issue.2, pp.435-449, 1997.
DOI : 10.1137/S0895479895294289

Y. Saad, Iterative methods for sparse linear systems, 2000.
DOI : 10.1137/1.9780898718003

Y. Saad and M. H. Schultz, GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems, SIAM Journal on Scientific and Statistical Computing, vol.7, issue.3, pp.856-869, 1986.
DOI : 10.1137/0907058

J. Salençon, Mécanique des milieux continus, Ecole polytechnique, Ellipses, 1988.

L. Series, F. Feyel, and F. Roux, Une méthode de décomposition de domaine avec deux multiplicateurs de Lagrange, 2003.

L. Series, F. Feyel, and F. Roux, Une méthode de décomposition de domaine avec deux multiplicateurs de Lagrange, cas du contact, dans Actes dusixì eme colloque national en calcul des structures, pp.373-380, 2003.

D. Stefanica and A. Klawonn, The FETI method for mortar finite elements, dans Proceedings of 11th International Conference on Domain Decomposition Methods, pp.121-129, 1999.

R. Stenberg and M. Suri, Mixed $hp$ finite element methods for problems in elasticity and Stokes flow, Numerische Mathematik, vol.72, issue.3, pp.367-389, 1996.
DOI : 10.1007/s002110050174

P. L. Tallec, Domain-decomposition methods in computational mechanics, Computational Mechanics Advances, vol.1, issue.2, pp.121-220, 1994.

P. L. Tallec, Handbook of numerical analysis III, chapitre Numerical methods for nonlinear three-dimensional elasticity, Elsevier science, pp.465-622, 1994.

P. L. Tallec, J. Mandel, and M. Vidrascu, A Neumann--Neumann Domain Decomposition Algorithm for Solving Plate and Shell Problems, SIAM Journal on Numerical Analysis, vol.35, issue.2, pp.836-867, 1998.
DOI : 10.1137/S0036142995291019
URL : https://hal.archives-ouvertes.fr/inria-00077196

P. L. Tallec, Y. D. Roeck, and M. Vidrascu, Domain decomposition methods for large linearly elliptic three-dimensional problems, Journal of Computational and Applied Mathematics, vol.34, issue.1, pp.93-117, 1991.
DOI : 10.1016/0377-0427(91)90150-I
URL : https://hal.archives-ouvertes.fr/inria-00075376

P. L. Tallec and M. Vidrascu, Méthodes de décomposition de domaines en calcul de structures, dans Actes du premier colloque national en calcul des structures, pp.33-49, 1993.

P. L. Tallec and M. Vidrascu, Generalized Neumann-Neumann preconditioners for iterative substructuring, dans Proceedings of the ninth conference on Domain Decomposition, 1996.

A. Van-der-sluis, H. Can, and . Vorst, The rate of convergence of Conjugate Gradients, Numerische Mathematik, vol.17, issue.5, pp.543-560, 1986.
DOI : 10.1007/BF01389450

A. Van-genderen and N. Van-der-meijs, A frontal computation scheme for the Schur algorithm to efficiently solve large boundary-element problems, CompEuro 1992 Proceedings Computer Systems and Software Engineering, pp.568-573, 1992.
DOI : 10.1109/CMPEUR.1992.218471

K. Washizu, Variational methods in elasticity and plasticity