On the complexity of the block low-rank multifrontal factorization. Methods and Algorithms for Scientific Computing, pp.1710-1740, 2017. ,
On the Schwarz Alternating Method with More than two Subdomains for Nonlinear Monotone Problems, SIAM Journal on Numerical Analysis, vol.28, issue.1, pp.179-204, 1991. ,
DOI : 10.1137/0728010
A domain decomposition strategy for nonclassical frictional multi-contact problems, Computer Methods in Applied Mechanics and Engineering, vol.190, issue.37-38, pp.1904785-4803, 2001. ,
DOI : 10.1016/S0045-7825(00)00347-9
URL : https://hal.archives-ouvertes.fr/hal-01393140
Existence of H-matrix approximants to the inverse FE-matrix of elliptic operators with L8-coefficients, Numerische Mathematik, vol.95, issue.1, pp.1-28, 2003. ,
A new nonconforming approach to domain decomposition : the mortar element method, 1994. ,
Application of the FETI method to ASCI problems : Scalability results on one thousand processors and discussion of highly heterogeneous problems, Sandia National Labs, 1999. ,
DOI : 10.2172/6127
A large time increment method for elastoplastic problems, European journal of mechanics. A. Solids, vol.8, issue.4, pp.257-275, 1989. ,
The finite element method in solid mechanics, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01083772
Balancing domain decomposition with nonlinear relocalization : Parallel implementation for laminates, First international conference on parallel, distributed and grid computing for engineering, p.90, 2009. ,
DOI : 10.4203/ccp.90.4
URL : https://hal.archives-ouvertes.fr/hal-00437328
Post-buckling analysis using a nonincremental method, 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics, pp.449-454, 1997. ,
URL : https://hal.archives-ouvertes.fr/hal-01703453
Application of the LATIN method to the calculation of response surfaces, Proceeding of the First MIT Conference on Computational Fluid and Solid Mechanics, pp.78-81, 2001. ,
DOI : 10.1016/B978-008043944-0/50574-6
Une application de la m??thode LATIN au calcul multir??solution de structures non lin??aires, Revue Europ??enne des ??l??ments Finis, vol.10, issue.4, pp.903-920, 1999. ,
DOI : 10.2514/3.50119
Lower Bounds in Domain Decomposition, In Domain Decomposition Methods in Science and Engineering XVI, pp.27-39, 2007. ,
DOI : 10.1007/978-3-540-34469-8_3
The large time increment method for numerical simulation of metal forming processes, Proceedings of Numerical Methods in Engineering, pp.102-109, 1990. ,
Nonlinearly Preconditioned Inexact Newton Algorithms, SIAM Journal on Scientific Computing, vol.24, issue.1, pp.183-200, 2002. ,
DOI : 10.1137/S106482750037620X
URL : http://www.cs.odu.edu/~keyes/papers/sisc00.pdf
Non-linear additive Schwarz preconditioners and application in computational fluid dynamics, International Journal for Numerical Methods in Fluids, vol.15, issue.12, pp.401463-1470, 2002. ,
DOI : 10.1137/0915040
A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems, SIAM Journal on Scientific Computing, vol.21, issue.2, pp.792-797, 1999. ,
DOI : 10.1137/S106482759732678X
Domain decomposition algorithms, Acta numerica, vol.3, pp.61-143, 1994. ,
Deflated and augmented krylov subspace techniques. Numerical linear algebra with applications, pp.43-66, 1997. ,
DOI : 10.1002/(sici)1099-1506(199701/02)4:1<43::aid-nla99>3.0.co;2-z
Linear and nonlinear functional analysis with applications, 2013. ,
Une nouvelle approche des problèmes de plasticité et de viscoplasticité : la méthode à grand incrément de temps, 1989. ,
A large time increment approach for cyclic viscoplasticity, International Journal of Plasticity, vol.9, issue.2, pp.141-157, 1993. ,
DOI : 10.1016/0749-6419(93)90026-M
Trust region methods, 2000. ,
DOI : 10.1137/1.9780898719857
Décomposition de domaine et stratégies de relocalisation non-linéaire pour la simulation de grandes structures raidies avec flambage local, 2008. ,
Nonlinear localization strategies for domain decomposition methods: Application to post-buckling analyses, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.8, pp.1961436-1446, 2007. ,
DOI : 10.1016/j.cma.2006.03.013
URL : https://hal.archives-ouvertes.fr/hal-00118192
Direct methods for sparse linear systems, 2006. ,
DOI : 10.1137/1.9780898718881
A domain-decomposed solver for nonlinear elasticity, Computer Methods in Applied Mechanics and Engineering, vol.99, issue.2-3, pp.187-207, 1992. ,
Inexact Newton Methods, SIAM Journal on Numerical Analysis, vol.19, issue.2, pp.400-408, 1982. ,
DOI : 10.1137/0719025
Nonlinear Preconditioning: How to Use a Nonlinear Schwarz Method to Precondition Newton's Method, SIAM Journal on Scientific Computing, vol.38, issue.6, 2016. ,
DOI : 10.1137/15M102887X
An introduction to domain decomposition methods : algorithms, theory, and parallel implementation, 2015. ,
DOI : 10.1137/1.9781611974065
URL : https://hal.archives-ouvertes.fr/cel-01100932
Some Domain Decomposition Algorithms for Elliptic Problems, 1990. ,
DOI : 10.1016/B978-0-12-407475-0.50022-X
Direct methods for sparse matrices, 1986. ,
DOI : 10.1093/acprof:oso/9780198508380.001.0001
Globally Convergent Inexact Newton Methods, SIAM Journal on Optimization, vol.4, issue.2, pp.393-422, 1994. ,
DOI : 10.1137/0804022
URL : http://users.wpi.edu/~walker/Papers/global_inexact_newton,SIOPT_4,1994,393-422.pdf
Choosing the Forcing Terms in an Inexact Newton Method, SIAM Journal on Scientific Computing, vol.17, issue.1, pp.16-32, 1996. ,
DOI : 10.1137/0917003
Hilbert Space Methods for, Partial Differential Equations (Monographs and Studies in Mathematics, vol.1, 1978. ,
Implicit parallel processing in structural mechanics, Compt. Mech. Adv, vol.2, pp.1-124, 1994. ,
The Dual Schur Complement Method with Well-Posed Local Neumann Problems: Regularization with a Perturbed Lagrangian Formulation, SIAM Journal on Scientific Computing, vol.14, issue.3, pp.752-759, 1993. ,
DOI : 10.1137/0914047
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.501523-1544, 2001. ,
DOI : 10.1002/1099-1506(200010/12)7:7/8<687::AID-NLA219>3.0.CO;2-S
A scalable dual-primal domain decomposition method. Numerical linear algebra with applications, pp.687-714, 2000. ,
DOI : 10.1002/1099-1506(200010/12)7:7/8<687::aid-nla219>3.0.co;2-s
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
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
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 : 10.1016/B978-0-12-068650-6.50029-0
Finite element solution of nonlinear elliptic problems, Numerische Mathematik, vol.10, issue.4, pp.451-475, 1986. ,
DOI : 10.1016/B978-0-12-068650-6.50030-7
FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials, Computer Methods in Applied Mechanics and Engineering, vol.183, issue.3-4, pp.309-330, 2000. ,
DOI : 10.1016/S0045-7825(99)00224-8
Optimized Schwarz Methods, SIAM Journal on Numerical Analysis, vol.44, issue.2, pp.699-731, 2006. ,
DOI : 10.1137/S0036142903425409
URL : https://hal.archives-ouvertes.fr/hal-00107263
Optimized Schwarz methods for a diffusion problem with discontinuous coefficient, Numerical Algorithms, vol.13, issue.2, pp.109-144, 2015. ,
DOI : 10.1137/0913032
Schwarz methods over the course of time, Electron. Trans. Numer. Anal, issue.5, pp.31228-255, 2008. ,
Optimal Interface Conditions for an Arbitrary Decomposition into Subdomains, Domain Decomposition Methods in Science and Engineering XIX, vol.78, pp.101-108, 2011. ,
DOI : 10.1007/978-3-642-11304-8_9
URL : http://www.unige.ch/~gander/Preprints/gander_kwok_mini_1.pdf
Optimized Interface Preconditioners for the FETI Method, In Domain Decomposition Methods in Science and Engineering XXI, pp.657-665, 2014. ,
DOI : 10.1007/978-3-319-05789-7_63
A two-scale approximation of the Schur complement and its use for non-intrusive coupling, International Journal for Numerical Methods in Engineering, vol.64, issue.1-4, pp.889-905, 2011. ,
DOI : 10.1016/S0045-7949(96)00165-4
URL : https://hal.archives-ouvertes.fr/hal-01224373
Non-intrusive and exact global/local techniques for structural problems with local plasticity, Computational Mechanics, vol.36, issue.1, pp.233-245, 2009. ,
DOI : 10.1007/s00466-009-0372-9
URL : https://hal.archives-ouvertes.fr/hal-00437023
Méthodes à pas multiples et de directions alternées pour la discrétisation d'équations d'évolution, Thèse de 3 e cycle, 1980. ,
Non-overlapping domain decomposition methods in structural mechanics. Archives of computational methods in engineering, pp.515-572, 2006. ,
URL : https://hal.archives-ouvertes.fr/hal-00277626
A domain decomposition method for quasi-incompressible formulations with discontinuous pressure field, Revue Europ??enne des ??l??ments Finis, vol.48, issue.2-4, pp.363-377, 2002. ,
DOI : 10.1002/(SICI)1097-0207(19990210)44:4<489::AID-NME514>3.0.CO;2-Z
URL : https://hal.archives-ouvertes.fr/hal-00277628
Total and selective reuse of Krylov subspaces for the resolution of sequences of nonlinear structural problems, International Journal for Numerical Methods in Engineering, vol.2, issue.2, pp.60-83, 2013. ,
DOI : 10.1002/nla.1680020205
URL : https://hal.archives-ouvertes.fr/hal-00782841
An Introduction to Algorithms for Nonlinear Optimization, Frontiers in numerical analysis, pp.109-197, 2003. ,
DOI : 10.1007/978-3-642-55692-0_4
URL : http://cds.cern.ch/record/603361/files/cm-p00045838.pdf
A multiscale extended finite element method for crack propagation, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.5, pp.381-399, 2008. ,
DOI : 10.1016/j.cma.2007.07.023
URL : https://hal.archives-ouvertes.fr/hal-01578820
Sur les problèmes aux dérivées partielles et leur signification physique, Princeton university bulletin, vol.13, pp.49-5228, 1902. ,
An additive schwarz method type theory for lions' algorithm and optimized schwarz methods, 2015. ,
DOI : 10.1137/16m1060066
URL : https://hal.archives-ouvertes.fr/hal-01278347/document
The p-Dirichlet-to-Neumann operator with applications to elliptic and parabolic problems, Journal of Differential Equations, vol.259, issue.8, pp.3615-3655, 2015. ,
DOI : 10.1016/j.jde.2015.04.030
Méthodes numériques pour la dynamique des structures non-linéaires incompressibles à deux échelles, 2004. ,
Domain decomposition methods with nonlinear localization for the buckling and post-buckling analyses of large structures, Advances in Engineering Software, pp.13-24, 2014. ,
DOI : 10.1016/j.advengsoft.2013.12.010
URL : https://hal.archives-ouvertes.fr/hal-01578748
Strong coupling methods in multi-phase and multi-scale modeling of inelastic behavior of heterogeneous structures, Computer Methods in Applied Mechanics and Engineering, issue.28, pp.1923089-3107, 2003. ,
The optimized order 2 method, Future Generation Computer Systems, vol.18, issue.1, pp.17-30, 2001. ,
DOI : 10.1016/S0167-739X(00)00072-8
Présentation de synthese des méthodes de gradient conjugué . RAIRO-Modélisation mathématique et analyse numérique, pp.639-665, 1986. ,
An explicit formulation of the multiplicative Schwarz preconditioner, Applied Numerical Mathematics, vol.57, issue.11-12, pp.571197-1213, 2007. ,
DOI : 10.1016/j.apnum.2007.01.009
Nonlinear FETI-DP and BDDC Methods, SIAM Journal on Scientific Computing, vol.36, issue.2, pp.737-765, 2014. ,
DOI : 10.1137/130920563
New Nonlinear FETI-DP Methods Based on a Partial Nonlinear Elimination of Variables, In Domain Decomposition Methods in Science and Engineering XXIII, vol.37, issue.6, pp.207-215, 2017. ,
DOI : 10.1137/140997907
Dual and dual-primal FETI methods for elliptic problems with discontinuous coefficients in three dimensions, DDM. org, pp.29-39, 1999. ,
FETI and Neumann-Neumann iterative substructuring methods: Connections and new results, Communications on Pure and Applied Mathematics, vol.16, issue.1, pp.57-90, 2001. ,
DOI : 10.1007/978-3-322-85997-6_11
Thomas Simpson and 'Newton's method of approximation' : an enduring myth. The British journal for the history of science, pp.347-354, 1992. ,
Sur une famille d'algorithmes en mécanique des structures. Comptes-rendus des séances de l'Académie des sciences. Série 2, Mécanique-physique, chimie, sciences de l'univers, sciences de la terre, pp.41-44, 1985. ,
M??canique non lin??aire des structures, Revue Fran??aise de G??nie Civil, vol.1, issue.2, 1996. ,
DOI : 10.1080/12795119.1997.9692126
Nonlinear computational structural mechanics : new approaches and non-incremental methods of calculation, 2012. ,
DOI : 10.1007/978-1-4612-1432-8
Une nouvelle stratégie de calcul micro/macro en mécanique des structures. Comptes Rendus de l'Académie des Sciences-Series IIB-Mechanics-Physics-Astronomy, pp.3271237-1244, 1999. ,
On a mixed and multiscale domain decomposition method, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.8, pp.1961526-1540, 2007. ,
DOI : 10.1016/j.cma.2006.05.014
On Multiscale Computational Mechanics with Time-Space Homogenization, Multiscale methods?Bridging the scales in Science and Engineering, pp.247-282, 2010. ,
DOI : 10.1093/acprof:oso/9780199233854.003.0009
URL : https://hal.archives-ouvertes.fr/hal-00708499
On a multiscale computational strategy with time and space homogenization for structural mechanics, Computer Methods in Applied Mechanics and Engineering, vol.192, issue.28-30, pp.1923061-3087, 2003. ,
DOI : 10.1016/S0045-7825(03)00341-4
URL : https://hal.archives-ouvertes.fr/hal-00366648
The LATIN multiscale computational method and the Proper Generalized Decomposition, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.21-22, pp.1991287-1296, 2010. ,
DOI : 10.1016/j.cma.2009.06.023
URL : https://hal.archives-ouvertes.fr/hal-00414447
Analyse numérique matricielle appliquée à l'art de l'ingénieur, 1987. ,
Domain decomposition methods in computational mechanics, Computational mechanics advances, vol.1, issue.2, pp.121-220, 1994. ,
On the Schwarz alternating method, II. Domain Decomposition Methods for Partial Differential Equations, Lions and Lions, pp.1-42, 1988. ,
On the Schwarz alternating method. I, First international symposium on domain decomposition methods for partial differential equations, pp.1-42, 1988. ,
On the Schwarz alternating method. III : a variant for nonoverlapping subdomains, Third international symposium on domain decomposition methods for partial differential equations, pp.202-223, 1990. ,
On the limited memory BFGS method for large scale optimization, Mathematical Programming, vol.32, issue.2, pp.1-3503, 1989. ,
DOI : 10.1007/BF01589116
Automated solution of differential equations by the finite element method : The FEniCS book, 2012. ,
DOI : 10.1007/978-3-642-23099-8
Optimal Discrete Transmission Conditions for a Nonoverlapping Domain Decomposition Method for the Helmholtz Equation, SIAM Journal on Scientific Computing, vol.25, issue.5, pp.251497-1515, 2004. ,
DOI : 10.1137/S1064827502415351
Algebraic approximation of Dirichlet-to-Neumann maps for the equations of linear elasticity, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.29-32, pp.1953742-3759, 2006. ,
DOI : 10.1016/j.cma.2005.01.022
Asynchronous iterative sub-structuring methods, Mathematics and Computers in Simulation, vol.145, 2016. ,
DOI : 10.1016/j.matcom.2016.05.009
Balancing domain decomposition, Communications in Numerical Methods in Engineering, vol.13, issue.3, pp.233-241, 1993. ,
DOI : 10.1137/1.9781611971057.ch5
URL : http://ftp.ccs.uky.edu/mgnet/www/mgnet/www/mgnet/papers/Mandel/bdd.ps.gz
An algebraic theory for primal and dual substructuring methods by constraints, Applied Numerical Mathematics, vol.54, issue.2, pp.167-193, 2005. ,
DOI : 10.1016/j.apnum.2004.09.022
Restarted block-GMRES with deflation of eigenvalues, Applied Numerical Mathematics, vol.54, issue.2, pp.222-236, 2005. ,
DOI : 10.1016/j.apnum.2004.09.028
Recent Developments on Optimized Schwarz Methods, In Domain Decomposition Methods in Science and Engineering XVI, pp.115-125, 2007. ,
DOI : 10.1007/978-3-540-34469-8_10
URL : http://www.cims.nyu.edu/dd16/proceedings/nataf_plenary.pdf
A new impedance accounting for short and long range effects in mixed substructured formulations of nonlinear problems, International Journal for Numerical Methods in Engineering, 2017. ,
DOI : 10.1002/nme.5758
URL : https://hal.archives-ouvertes.fr/hal-01488615
Substructured formulations of nonlinear structure problems??-??influence of the interface condition, International Journal for Numerical Methods in Engineering, vol.270, issue.1, 2016. ,
DOI : 10.1016/j.cma.2013.12.001
URL : https://hal.archives-ouvertes.fr/hal-01332214
Remarques sur les algorithmes de décomposition de domaines, Séminaire Équations, vol.2054, pp.1-24, 1998. ,
The block conjugate gradient algorithm and related methods, Linear Algebra and its Applications, vol.29, pp.293-322, 1980. ,
DOI : 10.1016/0024-3795(80)90247-5
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 : 10.1137/1.9781611971057.ch4
A FETI-2LM Method for Non-Matching Grids, In Domain Decomposition Methods in Science and Engineering XVIII, pp.121-128, 2009. ,
DOI : 10.1007/978-3-642-02677-5_11
29. optimization of interface operator based on algebraic approach, Domain Decomposition Methods in Science and Engineering, p.297, 2002. ,
Une approche des problémes de dynamique nonlineaires par la méthode à grand incrément de temps, 1990. ,
On the Lanczos method for solving symmetric linear systems with several right-hand sides, Mathematics of computation, vol.48, issue.178, pp.651-662, 1987. ,
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
Iterative methods for sparse linear systems, Siam, 2003. ,
DOI : 10.1137/1.9780898718003
On a multiscale strategy and its optimization for the simulation of combined delamination and buckling, International Journal for Numerical Methods in Engineering, vol.31, issue.1, pp.91772-798, 2012. ,
DOI : 10.1016/0263-8223(95)00002-X
URL : https://hal.archives-ouvertes.fr/hal-00724273
An enhanced nonlinear multi-scale strategy for the simulation of buckling and delamination on 3D composite plates, Computer Methods in Applied Mechanics and Engineering, vol.317, pp.952-969, 2017. ,
DOI : 10.1016/j.cma.2017.01.015
URL : https://hal.archives-ouvertes.fr/hal-01622095
Ueber einige Abbildungsaufgaben., Journal für die reine und angewandte Mathematik, pp.105-120, 1869. ,
DOI : 10.1515/crll.1869.70.105
Monotone operators in Banach space and nonlinear partial differential equations, 2013. ,
DOI : 10.1090/surv/049
Domain Decomposition, 2004. ,
DOI : 10.1007/978-3-540-70529-1_411
Méthodes numériques pour les écoulements souterrains et couplage avec le ruissellement, 2008. ,
Mathematics and implementation details of a block MINRES algorithm, Review by Journal, 2013. ,
Méthodes de décomposition de domaine robustes pour les problèmes symétriques définis positifs, 2014. ,
Automatic spectral coarse spaces for robust finite element tearing and interconnecting and balanced domain decomposition???algorithms, International Journal for Numerical Methods in Engineering, vol.54, issue.2, pp.95953-990, 2013. ,
DOI : 10.1016/j.apnum.2004.09.022
Optimized Multiplicative, Additive, and Restricted Additive Schwarz Preconditioning, SIAM Journal on Scientific Computing, vol.29, issue.6, pp.292402-2425, 2007. ,
DOI : 10.1137/060652610
URL : https://archive-ouverte.unige.ch/unige:6269/ATTACHMENT01
Domain decomposition methods : algorithms and theory, 2005. ,
DOI : 10.1007/b137868