A. Ammar, D. Ryckelynck, F. Chinesta, and R. Keunings, On the reduction of kinetic theory models related to finitely extensible dumbbells, Journal of Non-Newtonian Fluid Mechanics, vol.134, issue.1-3, pp.136-147, 2006.
DOI : 10.1016/j.jnnfm.2006.01.007
URL : https://hal.archives-ouvertes.fr/hal-01007150

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.153-176, 2006.
DOI : 10.1016/j.jnnfm.2006.07.007
URL : https://hal.archives-ouvertes.fr/hal-01004909

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 modelling of complex fluids, Journal of Non-Newtonian Fluid Mechanics, vol.144, issue.2-3, pp.98-121, 2007.
DOI : 10.1016/j.jnnfm.2007.03.009

A. Ammar, E. Pruliere, F. Chinesta, and M. Laso, Reduced numerical modeling of flows involving liquid-crystalline polymers, Journal of Non-Newtonian Fluid Mechanics, vol.160, issue.2-3, pp.140-156, 2009.
DOI : 10.1016/j.jnnfm.2009.03.013

A. Ammar, M. Normandin, F. Daim, D. Gonzalez, E. Cueto et al., Non incremental strategies based on separated representations: applications in computational rheology, Communications in Mathematical Sciences, vol.8, issue.3, pp.671-695, 2010.
DOI : 10.4310/CMS.2010.v8.n3.a4
URL : https://hal.archives-ouvertes.fr/hal-01007108

A. Ammar, F. Chinesta, and A. Falco, On the Convergence of a Greedy Rank-One Update Algorithm for??a??Class of Linear Systems, Archives of Computational Methods in Engineering, vol.21, issue.4, pp.473-486, 2010.
DOI : 10.1007/s11831-010-9048-z
URL : https://hal.archives-ouvertes.fr/hal-01007145

A. Ammar, M. Normandin, and F. Chinesta, Solving parametric complex fluids models in rheometric flows, Journal of Non-Newtonian Fluid Mechanics, vol.165, issue.23-24, pp.1588-1601, 2010.
DOI : 10.1016/j.jnnfm.2010.08.006
URL : https://hal.archives-ouvertes.fr/hal-01007311

R. A. Bialecki, A. J. Kassab, and A. Fic, Proper orthogonal decomposition and modal analysis for acceleration of transient FEM thermal analysis, International Journal for Numerical Methods in Engineering, vol.33, issue.6, pp.774-797, 2005.
DOI : 10.1002/nme.1205

J. Burkardt, M. Gunzburger, and H. , POD and CVT-based reduced-order modeling of Navier???Stokes flows, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.1-3, pp.337-355, 2006.
DOI : 10.1016/j.cma.2006.04.004

F. Chinesta, A. Ammar, A. Falco, and M. Laso, On the reduction of stochastic kinetic theory models of complex fluids, Modeling and Simulation in, Materials Science and Engineering, vol.15, pp.639-652, 2007.

F. Chinesta, A. Ammar, and P. Joyot, The nanometric and micrometric scales of the structure and mechanics of materials revisited: an introduction to the challenges of fully deterministic numerical descriptions, International Journal for Multiscale Computational Engineering, vol.63, pp.191-213, 2008.

F. Chinesta, A. Ammar, and E. Cueto, Recent Advances and New Challenges in the Use of the Proper Generalized Decomposition for Solving Multidimensional Models, Archives of Computational Methods in Engineering, vol.190, issue.1, pp.327-350, 2010.
DOI : 10.1007/s11831-010-9049-y
URL : https://hal.archives-ouvertes.fr/hal-01007235

F. Chinesta, A. Ammar, and E. Cueto, Proper generalized decomposition of multiscale models, International Journal for Numerical Methods in Engineering, vol.197, issue.5, pp.8-9, 2010.
DOI : 10.1002/nme.2794
URL : https://hal.archives-ouvertes.fr/hal-01007222

F. Chinesta, A. Ammar, and E. Cueto, On the use of proper generalized decompositions for solving the multidimensional chemical master equation, Revue europ??enne de m??canique num??rique, vol.19, issue.1-3, pp.53-64, 2010.
DOI : 10.3166/ejcm.19.53-64
URL : https://hal.archives-ouvertes.fr/hal-01007161

D. Gonzalez, A. Ammar, F. Chinesta, and E. Cueto, Recent advances on the use of separated representations, International Journal for Numerical Methods in Engineering, vol.30, issue.1, pp.637-659, 2010.
DOI : 10.1002/nme.2710

M. D. Gunzburger, J. S. Peterson, and J. N. 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

R. Keunings, Micro-macro methods for the multiscale simulation viscoelastic flow using molecular models of kinetic theory, Rheology Reviews, pp.67-98, 2004.

P. Ladeveze, Nonlinear Computational Structural Mechanics, 1999.
DOI : 10.1007/978-1-4612-1432-8

P. Ladeveze, J. Passieux, and D. Neron, The LATIN multiscale computational method and the proper orthogonal decomposition, Computer Methods in Applied Mechanics and Engineering, vol.199, pp.21-22, 2010.

C. , L. Bris, T. Lelièvre, and Y. Maday, Results and Questions on a Nonlinear Approximation Approach for Solving High-dimensional Partial Differential Equations, Constructive Approximation, pp.365-374, 1007.

G. M. Leonenko and T. N. Phillips, On the solution of the Fokker???Planck equation using a high-order reduced basis approximation, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.1-4, pp.1-4, 2009.
DOI : 10.1016/j.cma.2009.09.028

Y. Maday and E. M. 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

B. Mokdad, E. Pruliere, A. Ammar, and F. Chinesta, On the simulation of kinetic theory models of complex fluids using the Fokker-Planck approach, Applied Rheology, vol.17, issue.2, pp.1-14, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00287203

B. Mokdad, A. Ammar, M. Normandin, F. Chinesta, and J. R. Clermont, A fully deterministic micro???macro simulation of complex flows involving reversible network fluid models, Mathematics and Computers in Simulation, vol.80, issue.9, pp.1936-1961, 2010.
DOI : 10.1016/j.matcom.2010.03.002
URL : https://hal.archives-ouvertes.fr/hal-01004833

A. Nouy and P. Ladeveze, Multiscale Computational Strategy With Time and Space Homogenization: A Radial-Type Approximation Technique for Solving Microproblems, International Journal for Multiscale Computational Engineering, vol.2, issue.4, 2004.
DOI : 10.1615/IntJMultCompEng.v2.i4.40
URL : https://hal.archives-ouvertes.fr/hal-00368058

H. M. Park and D. H. Cho, The use of the Karhunen-Lo??ve decomposition for the modeling of distributed parameter systems, Chemical Engineering Science, vol.51, issue.1, pp.81-98, 1996.
DOI : 10.1016/0009-2509(95)00230-8

E. Pruliere, A. Ammar, N. Kissi, and F. Chinesta, Recirculating flows involving short fiber suspensions: numerical difficulties and efficient advanced micro-macro solvers, Archives of Computational Methods in Engineering, State of the Art Reviews, vol.16, pp.1-30, 2009.

E. Pruliere, F. Chinesta, and A. Ammar, On the deterministic solution of multidimensional parametric models using the Proper Generalized Decomposition, Mathematics and Computers in Simulation, vol.81, issue.4, pp.791-810, 2010.
DOI : 10.1016/j.matcom.2010.07.015
URL : https://hal.archives-ouvertes.fr/hal-00704427

D. Ryckelynck, A priori hyperreduction method: an adaptive approach, Journal of Computational Physics, vol.202, issue.1, pp.346-366, 2005.
DOI : 10.1016/j.jcp.2004.07.015

D. Ryckelynck, L. Hermanns, F. Chinesta, and E. Alarcon, An efficient ???a priori??? model reduction for boundary element models, Engineering Analysis with Boundary Elements, vol.29, issue.8, pp.796-801, 2005.
DOI : 10.1016/j.enganabound.2005.04.003
URL : https://hal.archives-ouvertes.fr/hal-00020778

D. Ryckelynck, F. Chinesta, E. Cueto, and A. Ammar, On thea priori model reduction: Overview and recent developments, Archives of Computational Methods in Engineering, vol.43, issue.5, pp.91-128, 2006.
DOI : 10.1007/BF02905932