, Experimental and numerical POD study of the Coanda effect used to reduce self-sustained tones, Mechanics Research Communications, vol.31, issue.1, pp.105-120, 2004.
DOI : 10.1016/j.mechrescom.2003.08.003
URL : https://hal.archives-ouvertes.fr/hal-00312149
, An optimal projection method for the reduced-order modeling of incompressible flows, Computer Methods in Applied Mechanics and Engineering, vol.200, issue.33-36, pp.33-36, 2011.
DOI : 10.1016/j.cma.2011.04.020
, An efficient method of solving the Navier?Stokes equations for flow controls, Phys. Rep, vol.287, pp.337-384, 1997.
, Proper orthogonal decomposition for reduced basis feedback controllers for parabolic equations, Mathematical and Computer Modelling, vol.33, issue.1-3, pp.1-3, 2001.
DOI : 10.1016/S0895-7177(00)00225-9
, Reliable real-time solution of parametrized partial differential equations: reducedbasis output bound methods, Journal of Fluids Engineering, vol.124, issue.1, pp.70-80, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00798326
, Reduction procedure for parametrized fluid dynamics problems based on proper orthogonal decomposition and calibration, Chemical Engineering Science, vol.65, issue.23, pp.6238-6246, 2010.
DOI : 10.1016/j.ces.2010.09.005
, Applying proper orthogonal decomposition to the computation of particle dispersion in a two-dimensional ventilated cavity, Communications in Nonlinear Science and Numerical Simulation, vol.10, issue.8, pp.907-920, 2005.
DOI : 10.1016/j.cnsns.2004.05.005
URL : https://hal.archives-ouvertes.fr/hal-00312147
, On investigation of particle dispersion by a POD approach, International Applied Mechanics, vol.3, issue.11, pp.110-119, 2008.
DOI : 10.1007/s10778-008-0025-2
URL : https://hal.archives-ouvertes.fr/hal-00404055
, A new error bound for reduced basis approximation of parabolic partial differential equations, Comptes Rendus Mathematique, vol.350, issue.3-4, pp.3-4
DOI : 10.1016/j.crma.2012.01.026
, 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
, Certified real-time solution of the parametrized steady incompressible Navier-Stokes equations: rigorous reduced-basisa posteriori error bounds, International Journal for Numerical Methods in Fluids, vol.42, issue.8-9, pp.8-9, 2005.
DOI : 10.1002/fld.867
, Numerical solution of parametrized Navier???Stokes equations by reduced basis methods, Numerical Methods for Partial Differential Equations, vol.47, issue.4, pp.923-948, 2007.
DOI : 10.1002/num.20249
, Reduced basis method for multi-parameter-dependent steady Navier???Stokes equations: Applications to natural convection in a cavity, Journal of Computational Physics, vol.228, issue.12, pp.4359-4378, 2009.
DOI : 10.1016/j.jcp.2009.03.008
, 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
, Norm of the residual according to the number of functions for each PGD and FULL SVD decomposition for intermediate horizontal velocity and for the pressure at Re ¼ 100 with N ¼ 20. [16] D. Ryckelynck, D. Missoum Benziane, Multi-level A Priori Hyper-Reduction of mechanical models involving internal variables, Computer Methods in Applied Mechanics and Engineering, vol.16, issue.199, pp.17-20, 2010.
, A priori reduction method for solving the two-dimensional Burgers??? equations, Applied Mathematics and Computation, vol.217, issue.15, pp.6671-6679, 2011.
DOI : 10.1016/j.amc.2011.01.065
URL : https://hal.archives-ouvertes.fr/hal-00585095
, Reduced-order modelling for solving linear and non-linear equations, International Journal for Numerical Methods in Biomedical Engineering, vol.2, issue.1, pp.43-58, 2011.
DOI : 10.1002/cnm.1286
URL : https://hal.archives-ouvertes.fr/hal-00541925
, An error estimator for separated representations of highly multidimensional models, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.25-28, pp.1872-1880, 2010.
DOI : 10.1016/j.cma.2010.02.012
URL : https://hal.archives-ouvertes.fr/hal-01004991
, 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
, On the verification of model reduction methods based on the proper generalized decomposition, Computer Methods in Applied Mechanics and Engineering, vol.200, issue.23-24, pp.23-24, 2011.
DOI : 10.1016/j.cma.2011.02.019
, Non linear Computational Structural Mechanics: New Approaches and Non-incremental Methods of Calculation, Mechanical Engineering Series, 2009.
, The LATIN multiscale computational method and the Proper Generalized Decomposition, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.21-22, pp.21-22, 2010.
DOI : 10.1016/j.cma.2009.06.023
URL : https://hal.archives-ouvertes.fr/hal-00414447
, A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.45-48, pp.45-48, 2007.
DOI : 10.1016/j.cma.2007.05.016
URL : https://hal.archives-ouvertes.fr/hal-00366619
, Generalized spectral decomposition for stochastic nonlinear problems, Journal of Computational Physics, vol.228, issue.1, pp.202-235, 2009.
DOI : 10.1016/j.jcp.2008.09.010
, 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 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.2-3, 2007.
DOI : 10.1016/j.jnnfm.2006.07.007
URL : https://hal.archives-ouvertes.fr/hal-01004909
, On the simulation of kinetic theory models of complex fluids using the Fokker?Planck approach, Applied Rheology, vol.2, pp.1-14, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00287203
, The nanometric and micrometric scales of the structure and mechanics of materials revisited: an introduction to he challenges of fully deterministic numerical descriptions, International Journal for Multiscale Computational Engineering, vol.63, pp.191-213, 2008.
, Advanced simulation of models defined in plate geometries: 3D solutions with 2D computational complexity, Computer Methods in Applied Mechanics and Engineering, vol.201, issue.204, pp.204-205, 2012.
DOI : 10.1016/j.cma.2011.08.025
URL : https://hal.archives-ouvertes.fr/hal-01462825
, Proper general decomposition (PGD) for the resolution of Navier???Stokes equations, Journal of Computational Physics, vol.230, issue.4, pp.1387-1407, 2011.
DOI : 10.1016/j.jcp.2010.11.010
URL : https://hal.archives-ouvertes.fr/hal-01061383
, Proper Generalized Decomposition method for incompressible flows in stream-vorticity formulation, Revue europ??enne de m??canique num??rique, vol.19, issue.5-7, pp.5-7, 2010.
DOI : 10.3166/ejcm.19.591-617
, A First Step Towards the Use of Proper General Decomposition Method for Structural Optimization, Archives of Computational Methods in Engineering, vol.3, issue.6, pp.465-472, 2010.
DOI : 10.1007/s11831-010-9052-3
URL : https://hal.archives-ouvertes.fr/hal-01004831
, 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
, 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
, 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
, 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
, On the existences, uniquness and approximation of saddle-point problems arising from lagrangian multipliers, pp.129-151, 1998.
, Spectral methods applied to porous media equations, East?West Journal of Numerical Mathematics, vol.2, issue.2, pp.91-105, 1994.
, Résolution des équations de Navier-Stokes par des schémas de projection Tchebychev, 1996.
, On the solution of the Navier-Stokes equations using Chebyshev projection schemes with third-order accuracy in time, Computers & Fluids, vol.26, issue.2, pp.107-116, 1997.
DOI : 10.1016/S0045-7930(96)00032-1
, A Second-Order Accurate Pressure-Correction Scheme for Viscous Incompressible Flow, SIAM Journal on Scientific and Statistical Computing, vol.7, issue.3, pp.271-288, 1986.
DOI : 10.1137/0907059
, An overview of projection methods for incompressible flows, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.44-47, pp.44-47, 2006.
DOI : 10.1016/j.cma.2005.10.010
, Factorization methods for the numerical approximation of Navier???Stokes equations, Computer Methods in Applied Mechanics and Engineering, vol.188, issue.1-3, pp.1-3, 2000.
DOI : 10.1016/S0045-7825(99)00192-9
, High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method, Journal of Computational Physics, vol.48, issue.3, pp.387-411, 1982.
DOI : 10.1016/0021-9991(82)90058-4
, Incompressible flow calculations with a consistent physical interpolation finite volume approach, Computers & Fluids, vol.23, issue.8, pp.1029-1047, 1994.
DOI : 10.1016/0045-7930(94)90003-5
, An explicit Chebyshev pseudospectral multigrid method for incompressible Navier???Stokes equations, Computers & Fluids, vol.39, issue.1, pp.178-188, 2010.
DOI : 10.1016/j.compfluid.2009.08.001
, Particle mixing and reactive front motion in unsteady open shallow flow ??? Modelled using singular value decomposition, Computers & Fluids, vol.36, issue.2, pp.248-258, 2007.
DOI : 10.1016/j.compfluid.2006.01.018
, A reduced finite difference scheme based on singular value decomposition and proper orthogonal decomposition for Burgers equation, Journal of Computational and Applied Mathematics, vol.229, issue.1, pp.97-107, 2009.
DOI : 10.1016/j.cam.2008.10.026