G. M. Amdahl, Validity of the single processor approach to achieving large scale computing capabilities, Proceedings of the Spring Joint Computer Conference, vol.67, pp.483-485, 1967.

A. Toselli and O. Widlund, Domain Decomposition Methods-Algorithms and Theory, vol.34, 2005.
DOI : 10.1007/b137868

U. Elsner, Graph Partitioning: A Survey, 1997.

S. Ghanemi, A domain decomposition method for helmholtz scattering problems, Ninth International Conference on Domain Decomposition Methods, pp.105-112, 1996.

P. Chevalier and F. Nataf, Symmetrized method with optimized second-order conditions for the Helmholtz equation, Domain decomposition methods, vol.10, pp.400-407, 1997.
DOI : 10.1090/conm/218/03035
URL : http://ams.org/publications/books/monographs/B0-8218-0988-1-03035-1.pdf

M. Gander, L. Halpern, and F. Magoulès, An optimized Schwarz method with twosided Robin transmission conditions for the Helmholtz equation, International Journal for Numerical Methods in Fluids, vol.55, issue.2, pp.163-175, 2007.
DOI : 10.1002/fld.1433
URL : https://hal.archives-ouvertes.fr/hal-00623843

F. Magoulès, F. Roux, and S. Salmon, Optimal discrete transmission conditions for a non-overlapping domain decomposition method for the Helmholtz equation, SIAM Journal on Scientific Computing, vol.25, issue.5, pp.1497-1515, 2004.

F. Roux, F. Magoulès, L. Series, and Y. Boubendir, Approximation of optimal interface boundary conditions for two-Lagrange multiplier FETI method, Proceedings of the 15th International Conference on Domain Decomposition Methods, 2003.
DOI : 10.1007/3-540-26825-1_27
URL : https://hal.archives-ouvertes.fr/hal-00827450

F. Magoulès, F. Roux, and L. Series, Algebraic approach to absorbing boundary conditions for the Helmholtz equation, International Journal of Computer Mathematics, vol.84, issue.2, pp.231-240, 2007.

E. Lelarasmee, A. E. Ruehli, and A. L. Sangiovanni-vincentelli, The waveform relaxation method for time-domain analysis of large scale integrated circuits, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol.1, issue.3, pp.131-145, 1982.

M. J. Gander and H. Zhao, Overlapping Schwarz waveform relaxation for the heat equation in n dimensions, BIT Numerical Mathematics, vol.42, issue.4, pp.779-795, 2002.

P. Chartier and B. Philippe, A parallel shooting technique for solving dissipative ODE's, Computing, vol.51, issue.3, pp.209-236, 1993.
DOI : 10.1007/bf02238534

B. Leimkuhler, Timestep acceleration of waveform relaxation, SIAM Journal on Numerical Analysis, vol.35, issue.1, pp.31-50, 1998.

J. Lions, Y. Maday, and G. Turinici, Résolution d'EDP par un schéma en temps "pararéel, C. R. Acad. Sci. Paris Sér. I Math, vol.332, issue.7, pp.661-668, 2001.

C. Farhat and M. Chandesris, Time-decomposed parallel time-integrators: theory and feasibility studies for fluid, structure, and fluid-structure applications, International Journal for Numerical Methods in Engineering, vol.58, issue.9, pp.1397-1434, 2003.
DOI : 10.1002/nme.860

D. P. Bertsekas and J. N. Tsitsiklis, Some aspects of parallel and distributed iterative algorithms-a survey, Automatica, vol.27, issue.1, pp.3-21, 1991.

J. C. Miellou, Algorithmes de relaxation chaotique à retards, ESAIM: Mathematical Modelling and Numerical Analysis-Modélisation Mathématique et Analyse Numérique, vol.9, pp.55-82, 1975.
DOI : 10.1051/m2an/197509r100551
URL : https://www.esaim-m2an.org/articles/m2an/pdf/1975/01/m2an197509R100551.pdf

G. M. Baudet, Asynchronous iterative methods for multiprocessors, Journal of the ACM, vol.25, issue.2, pp.226-244, 1978.
DOI : 10.1145/322063.322067

M. N. Tarazi, Some convergence results for asynchronous algorithms, Numerische Mathematik, vol.39, issue.3, pp.325-340, 1982.

D. P. Bertsekas, Distributed asynchronous computation of fixed points, Mathematical Programming, vol.27, issue.1, pp.107-120, 1983.

D. Chazan and W. Miranker, Chaotic relaxation, Linear Algebra and its Applications, vol.2, pp.199-222, 1969.

A. Frommer and D. B. Szyld, Asynchronous two-stage iterative methods, Numerische Mathematik, vol.69, issue.2, pp.141-153, 1994.
DOI : 10.1007/s002110050085

J. C. Miellou, D. E. Baz, and P. Spiteri, A new class of asynchronous iterative algorithms with order intervals, vol.67, pp.237-255, 1998.

D. E. Baz, A. Frommer, and P. Spiteri, Asynchronous iterations with flexible communication: contracting operators, Journal of Computational and Applied Mathematics, vol.176, issue.1, pp.91-103, 2005.

K. Li-shan, C. Yu-ping, S. Le-lin, and Q. Hui-yun, The asynchronous parallel algorithms s-cor for solving p.d.e.'s on multiprocessors, International Journal of Computer Mathematics, vol.18, issue.2, pp.163-172, 1985.

L. Hart and S. Mccormick, Asynchronous multilevel adaptive methods for solving partial differential equations on multiprocessors: Basic ideas, Parallel Computing, vol.12, issue.2, pp.131-144, 1989.

M. Chau, D. E. Baz, R. Guivarch, and P. Spiteri, MPI implementation of parallel subdomain methods for linear and nonlinear convection-diffusion problems, Journal of Parallel and Distributed Computing, vol.67, issue.5, pp.581-591, 2007.

R. Bru, V. Migallón, J. Penadés, and D. B. Szyld, Parallel, synchronous and asynchronous two-stage multisplitting methods, Electronic Transactions on Numerical Analysis, vol.3, pp.24-38, 1995.

P. Spiteri, J. Miellou, and D. E. Baz, Parallel asynchronous schwarz and multisplitting methods for a nonlinear diffusion problem, Numerical Algorithms, vol.33, issue.1, pp.461-474, 2003.

M. Chau, R. Couturier, J. Bahi, and P. Spiteri, Parallel solution of the obstacle problem in grid environments, International Journal of High Performance Computing Applications, vol.25, issue.4, pp.488-495, 2011.

E. D. Chajakis and S. A. Zenios, Synchronous and asynchronous implementations of relaxation algorithms for nonlinear network optimization, Parallel Computing, vol.17, issue.8, pp.873-894, 1991.

M. Chau, Algorithmes parallèles asynchrones pour la simulation numérique, 2005.

D. P. Bertsekas and J. N. Tsitsiklis, Convergence rate and termination of asynchronous iterative algorithms, pp.461-470, 1989.

D. E. Baz, A method of terminating asynchronous iterative algorithms on message passing systems, Parallel Algorithms and Applications, vol.9, issue.1-2, pp.153-158, 1996.
URL : https://hal.archives-ouvertes.fr/hal-01152363

S. A. Savari and D. P. Bertsekas, Finite termination of asynchronous iterative algorithms, Parallel Computing, vol.22, issue.1, pp.39-56, 1996.

D. J. Evans and S. Chikohora, Convergence testing on a distributed network of processors, International Journal of Computer Mathematics, vol.70, issue.2, pp.357-378, 1998.

J. M. Bahi, S. Contassot-vivier, and R. Couturier, An efficient and robust decentralized algorithm for detecting the global convergence in asynchronous iterative algorithms, High Performance Computing for Computational Science-VECPAR 2008, vol.5336, pp.240-254, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00336515

J. Bahi, S. Domas, and K. Mazouzi, Jace: a java environment for distributed asynchronous iterative computations, 12th Euromicro Conference on Parallel, Distributed and Network-Based Processing, pp.350-357, 2004.

J. M. Bahi, R. Couturier, and P. Vuillemin, Jacev: A programming and execution environment for asynchronous iterative computations on volatile nodes, High Performance Computing for Computational Science-VECPAR 2006, vol.4395, pp.79-92, 2007.

J. Charr, R. Couturier, and D. Laiymani, A decentralized and fault tolerant convergence detection algorithm for asynchronous iterative algorithms, The Journal of Supercomputing, vol.53, issue.2, pp.269-292, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00956774

J. Charr, R. Couturier, and D. Laiymani, JACEP2P-V2: A fully decentralized and fault tolerant environment for executing parallel iterative asynchronous applications on volatile distributed architectures, Advances in Grid and Pervasive Computing: 4th International Conference, pp.446-458, 2009.
URL : https://hal.archives-ouvertes.fr/hal-01222906

R. Couturier and S. Domas, Crac: a grid environment to solve scientific applications with asynchronous iterative algorithms, IEEE International Parallel and Distributed Processing Symposium, pp.1-8, 2007.

O. Widlund and M. Dryja, An additive variant of the Schwarz alternating method for the case of many subregions, p.131, 1987.

M. J. Gander, Schwarz methods over the course of time, Electronic Transactions on Numerical Analysis, vol.31, pp.228-255, 2008.

M. J. Gander and S. Vandewalle, Analysis of the parareal time-parallel timeintegration method, SIAM J. Sci. Comput, vol.29, issue.2, pp.556-578, 2007.

K. M. Chandy and L. Lamport, Distributed snapshots: Determining global states of distributed systems, ACM Trans. Comput. Syst, vol.3, issue.1, pp.63-75, 1985.

F. Magoulès and C. Venet, Asynchronous iterative sub-structuring methods, Mathematics and Computers in Simulation, vol.145, pp.34-49, 2018.

J. Miellou, P. Spiteri, and D. E. Baz, A new stopping criterion for linear perturbed asynchronous iterations, Journal of Computational and Applied Mathematics, vol.219, issue.2, pp.471-483, 2008.

F. Magoulès and G. Gbikpi-benissan, Distributed convergence detection based on global residual error under asynchronous iterations, IEEE Transactions on Parallel and Distributed Systems, 2017.

F. Magoulès and G. Gbikpi-benissan, Jack2: an mpi-based communication library with non-blocking synchronization for asynchronous iterations, Advances in Engineering Software, 2018.

G. Gbikpi-benissan and F. Magoulès, Proceedings of the Fifth International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering, 2017.

F. Magoulès and G. Gbikpi-benissan, JACK: an asynchronous communication kernel library for iterative algorithms, The Journal of Supercomputing, vol.73, issue.8, pp.3468-3487, 2017.

J. M. Bahi, S. Contassot-vivier, and R. Couturier, Parallel Iterative Algorithms: from sequential to grid computing, Numerical Analysis and Scientific Computing, 2007.
URL : https://hal.archives-ouvertes.fr/inria-00336524

K. Fan, Note on M-matrices, The Quarterly Journal of Mathematics, vol.11, issue.1, pp.43-49, 1960.

R. S. Varga, Springer Series in Computational Mathematics, vol.27, 2000.

A. Frommer and D. B. Szyld, H-splittings and two-stage iterative methods, Numerische Mathematik, vol.63, issue.1, pp.345-356, 1992.

A. Frommer and D. B. Szyld, On asynchronous iterations, Journal of Computational and Applied Mathematics, vol.123, issue.1-2, pp.201-216, 2000.
DOI : 10.1016/s0377-0427(00)00409-x
URL : https://doi.org/10.1016/s0377-0427(00)00409-x

A. Neumaier, New techniques for the analysis of linear interval equations, Linear Algebra and its Applications, vol.58, pp.273-325, 1984.

A. Frommer and D. B. Szyld, Asynchronous iterations with flexible communication for linear systems, Calculateurs Parallèles, vol.10, pp.421-429, 1998.

J. Bahi, E. Griepentrog, and J. C. Miellou, Parallel treatment of a class of differential-algebraic systems, SIAM Journal on Numerical Analysis, vol.33, issue.5, pp.1969-1980, 1996.

A. Frommer, H. Schwandt, and D. B. Szyld, Asynchronous weighted additive Schwarz methods, Electronic Transactions on Numerical Analysis, vol.5, pp.48-61, 1997.

P. Spitéri, J. Miellou, and D. E. Baz, Asynchronous Schwarz alternating method with flexible communication for the obstacle problem, Réseaux et Systèmes Répartis-Calculateurs Parallèles, vol.13, pp.47-66, 2001.

F. Magoulès, D. B. Szyld, and C. Venet, Numerische Mathematik, vol.137, issue.1, pp.199-227, 2017.

J. S. Przemieniecki, Matrix structural analysis of substructures, American Institute of Aeronautics and Astronautics Journal, vol.1, issue.1, pp.138-147, 1963.

D. E. Crabtree, Applications of M-matrices to non-negative matrices, Duke Math. J, vol.33, issue.1, pp.197-208, 1966.

D. E. Crabtree and E. V. Haynsworth, An identity for the Schur complement of a matrix, Proc. Amer. Math. Soc, vol.22, issue.2, pp.364-366, 1969.

D. P. Bertsekas and J. N. Tsitsiklis, Parallel and Distributed Computation: Numerical Methods, 1989.

E. W. Dijkstra and C. S. Scholten, Termination detection for diffusing computations, Information Processing Letters, vol.11, issue.1, pp.1-4, 1980.

N. Francez and M. Rodeh, Achieving distributed termination without freezing, IEEE Trans. Softw. Eng, vol.8, issue.3, pp.287-292, 1982.

S. P. Rana, A distributed solution of the distributed termination problem, Information Processing Letters, vol.17, issue.1, pp.43-46, 1983.

F. Mattern, Algorithms for distributed termination detection, Distributed Computing, vol.2, issue.3, pp.161-175, 1987.

A. D. Kshemkalyani, M. Raynal, and M. Singhal, An introduction to snapshot algorithms in distributed computing, Distributed Systems Engineering, vol.2, issue.4, pp.224-233, 1995.

J. M. Bahi, S. Contassot-vivier, R. Couturier, and F. Vernier, A decentralized convergence detection algorithm for asynchronous parallel iterative algorithms, IEEE Trans. Parallel Distrib. Syst, vol.16, issue.1, pp.4-13, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00096362

N. A. Lynch, Distributed Algorithms, 1996.

P. Balaji, D. Buntinas, D. Goodell, W. Gropp, S. Kumar et al., Recent Advances in Parallel Virtual Machine and Message Passing Interface: 16th European PVM/MPI Users' Group Meeting, pp.20-30, 2009.

J. Rumbaugh, I. Jacobson, and G. Booch, The unified modeling language reference manual, vol.1, 1999.

E. J. Chang, Echo algorithms: Depth parallel operations on general graphs, IEEE Transactions on Software Engineering SE, vol.8, issue.4, pp.391-401, 1982.

E. Aubanel, Scheduling of tasks in the parareal algorithm, Parallel Computing, vol.37, issue.3, pp.172-182, 2011.