Y. Maday and E. Ronquist, The Reduced Basis Element Method: Application to a Thermal Fin Problem, SIAM Journal on Scientific Computing, vol.26, issue.1, pp.240-258, 2004.
DOI : 10.1137/S1064827502419932

URL : https://hal.archives-ouvertes.fr/hal-00021699

M. Barrault, Y. Maday, N. Nguyen, and A. Patera, An ???empirical interpolation??? method: application to efficient reduced-basis discretization of partial differential equations, Comptes Rendus Mathematique, vol.339, issue.9, pp.667-672, 2004.
DOI : 10.1016/j.crma.2004.08.006

URL : https://hal.archives-ouvertes.fr/hal-00021702

T. Lieu, C. Farhat, and A. Lesoinne, Reduced-order fluid/structure modeling of a complete aircraft configuration, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.41-43, pp.41-43, 2006.
DOI : 10.1016/j.cma.2005.08.026

M. Gunzburger, J. Peterson, and J. Shadid, Reduced-order modeling of time-dependent PDEs with multiple parameters in the boundary data, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.4-6, pp.1030-1047, 2007.
DOI : 10.1016/j.cma.2006.08.004

A. T. Patera and G. Rozza, Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations, 2006.

G. Rozza and K. Veroy, On the stability of the reduced basis method for Stokes equations in parametrized domains, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.7, pp.1244-1260, 2007.
DOI : 10.1016/j.cma.2006.09.005

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

A. Ammar, B. Mokdad, F. Chinesta, and R. Keunings, A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids, Journal of Non-Newtonian Fluid Mechanics, vol.139, issue.3, pp.98-121, 2007.
DOI : 10.1016/j.jnnfm.2006.07.007

URL : https://hal.archives-ouvertes.fr/hal-01004909

F. Chinesta, P. Ladevèze, and E. Cueto, A Short Review on Model Order Reduction Based on Proper Generalized Decomposition, Archives of Computational Methods in Engineering, vol.69, issue.9, pp.395-404, 2011.
DOI : 10.1007/s11831-011-9064-7

URL : https://hal.archives-ouvertes.fr/hal-01004940

N. Relun, D. Néron, and P. Boucard, A model reduction technique based on the PGD for elastic-viscoplastic computational analysis, Computational Mechanics, vol.20, issue.7???8, pp.83-92, 2013.
DOI : 10.1007/s00466-012-0706-x

M. Cremonesi, D. Néron, P. Guidault, and P. Ladevèze, A PGD-based homogenization technique for the resolution of nonlinear multiscale problems, Computer Methods in Applied Mechanics and Engineering, vol.267, pp.275-292, 2013.
DOI : 10.1016/j.cma.2013.08.009

URL : https://hal.archives-ouvertes.fr/hal-01403834

D. Néron, P. Boucard, and N. Relun, Time-space PGD for the rapid solution of 3D nonlinear parametrized problems in the many-query context, International Journal for Numerical Methods in Engineering, vol.8, issue.8, pp.275-292, 2015.
DOI : 10.1002/nme.4893

F. Chinesta, R. Keunings, and A. Leygue, The Proper Generalized Decomposition for Advanced Numerical Simulations: a Primer, SpringerBriefs in Applied Sciences and Technology, 2014.
DOI : 10.1007/978-3-319-02865-1

D. González, I. Alfaro, C. Quesada, E. Cueto, and F. Chinesta, Computational vademecums for the real-time simulation of haptic collision between nonlinear solids, Computer Methods in Applied Mechanics and Engineering, vol.283, issue.1, pp.210-223, 2015.
DOI : 10.1016/j.cma.2014.09.029

I. Alfaro, D. González, F. Bordeu, A. Leygue, A. Ammar et al., Real-time in silico experiments on gene regulatory networks and surgery simulation on handheld devices, Journal of Computational Surgery, vol.1, issue.1
DOI : 10.1002/cnm.2476

URL : https://hal.archives-ouvertes.fr/hal-01206921

J. V. Aguado, A. Huerta, F. Chinesta, and E. Cueto, Real-time monitoring of thermal processes by reduced-order modeling, International Journal for Numerical Methods in Engineering, vol.18, issue.1, pp.991-1017, 2015.
DOI : 10.1002/nme.4784

A. Ammar, A. Zghal, F. Morel, and F. Chinesta, On the space-time separated representation of integral linear viscoelastic models, Comptes Rendus M??canique, vol.343, issue.4, pp.247-263, 2015.
DOI : 10.1016/j.crme.2015.02.002

D. Néron and D. , A computational strategy for poroelastic problems with a time interface between coupled physics, International Journal for Numerical Methods in Engineering, vol.195, issue.44-47, pp.783-804, 2008.
DOI : 10.1002/nme.2091

D. Néron and D. , A computational strategy for thermo-poroelastic structures with a time-space interface coupling, International Journal for Numerical Methods in Engineering, vol.15, issue.4, pp.1053-1084, 2008.
DOI : 10.1002/nme.2283

H. and B. Dhia, Multiscale mechanical problems: the Arlequin method, Comptes Rendus de l'Académie des Sciences, pp.899-904, 1998.

H. B. Dhia and G. Rateau, The Arlequin method as a flexible engineering design tool, International Journal for Numerical Methods in Engineering, vol.193, issue.11, pp.1442-1462, 2005.
DOI : 10.1002/nme.1229

URL : https://hal.archives-ouvertes.fr/hal-00018915

H. and B. Dhia, Further Insights by Theoretical Investigations of the Multiscale Arlequin Method, International Journal for Multiscale Computational Engineering, vol.6, issue.3, pp.215-232, 2008.
DOI : 10.1615/IntJMultCompEng.v6.i3.30

URL : https://hal.archives-ouvertes.fr/hal-00751336

R. Cottereau, D. Clouteau, H. B. Dhia, and C. Zaccardi, A stochasticdeterministic coupling method for continuum mechanics, Computer Methods in Applied Mechanics and Engineering, vol.200, pp.47-48, 2011.

S. Nazeer, F. Bordeu, A. Leygue, and F. Chinesta, Arlequin based PGD domain decomposition, Computational Mechanics, vol.23, issue.1, pp.1175-1190, 2014.
DOI : 10.1007/s00466-014-1048-7

H. B. Dhia, N. Elkhodja, and F. Roux, Multimodeling of multialterated structures in the arlequin framework. solution with a domaindecomposition solver, European Journal of Computational Mechanics, vol.17, pp.969-980, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00314527

P. Ladevèze, J. Passieux, and D. Néron, The LATIN multiscale computational method and the Proper Generalized Decomposition, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.21-22, pp.1287-1296, 2010.
DOI : 10.1016/j.cma.2009.06.023

D. Néron and P. Ladevèze, Proper Generalized Decomposition for Multiscale and??Multiphysics Problems, Archives of Computational Methods in Engineering, vol.193, issue.1???4, pp.351-372, 2010.
DOI : 10.1007/s11831-010-9053-2

O. Allix, P. Gosselet, P. Kerfriden, and K. Saavedra, Virtual delamination testing through non-linear multi-scale computational methods: Some recent progress, Materials & Continua, vol.32, issue.2, pp.2012-107
URL : https://hal.archives-ouvertes.fr/hal-00818003

H. B. Dhia and G. Rateau, Application of the arlequin method to some structures with defects, European Journal of Computational Mechanics, vol.11, issue.2- 3-4, pp.291-304, 2002.

A. Nouy, A priori model reduction through Proper Generalized Decomposition for solving time-dependent partial differential equations, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.23-24, pp.23-24, 2010.
DOI : 10.1016/j.cma.2010.01.009

URL : https://hal.archives-ouvertes.fr/hal-00455635

C. Heyberger, P. Boucard, and D. Néron, Multiparametric analysis within the proper generalized decomposition framework, Computational Mechanics, vol.191, issue.25???26, pp.277-289, 2012.
DOI : 10.1007/s00466-011-0646-x