A. Toselli and O. W. , Domain Decomposition Methods -Algorithms and Theory, Theory, vol.34, p.27, 2005.
DOI : 10.1007/b137868

A. Ammar, B. Mokdad, F. Chinesta, and R. Et-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.153-176, 2006.
DOI : 10.1016/j.jnnfm.2007.03.009

I. Babu?kababu?ka and J. Et-chleboun, Effects of uncertainties in the domain on the solution of neumann boundary value problems in two spatial dimensions, Mathematics of Computation, issue.240, pp.711339-1370, 2002.

I. Babuska, U. Banerjee, and J. E. Et-osborn, Survey of meshless and generalized finite element methods: A unified approach, Acta Numerica, vol.12, issue.45, pp.1-125, 2003.
DOI : 10.1017/CBO9780511550157.001

I. Babuska, R. Tempone, and G. E. Et-zouraris, Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation, Computer Methods in Applied Mechanics and Engineering, vol.194, issue.12-16, pp.1251-1294, 2005.
DOI : 10.1016/j.cma.2004.02.026

B. Dhia and H. , Multiscale mechanical problems : the Arlequin method, C. R. Acad. Sci. Paris, Série IIb, vol.326, pp.899-904, 1998.

B. Dhia, H. Et-rateau, and G. , Analyse math??matique de la m??thode Arlequin mixte, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.332, issue.7, pp.649-654, 2001.
DOI : 10.1016/S0764-4442(01)01900-0

Y. Ben-haim and I. Et-elishakoff, Convex models of uncertainty in applied mechanics, p.11, 1990.

M. Berveiller, Stochastic finite elements : intrusive and nonintrusive methods for reliability analysis, Thèse de doctorat, p.14, 2005.

M. Berveiller, B. Sudret, and M. Et-lemaire, Stochastic finite element: a non intrusive approach by regression, Revue europ??enne de m??canique num??rique, vol.15, issue.1-2-3, pp.81-92, 2006.
DOI : 10.3166/remn.15.81-92

P. Besold, Solutions to Stochastic Partial Differential Equations as Elements of Tensor Product Spaces, Thèse de doctorat, p.17, 2000.

G. Beylkin and M. J. Et-mohlenkamp, Algorithms for Numerical Analysis in High Dimensions, SIAM Journal on Scientific Computing, vol.26, issue.6, pp.2133-2159, 2005.
DOI : 10.1137/040604959

F. Brezzi, J. Lions, and O. Et-pironneau, Analysis of a Chimera method, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.332, issue.7, pp.655-660, 2001.
DOI : 10.1016/S0764-4442(01)01904-8

H. Brézis, Analyse fonctionnelle : théorie et applications, p.17, 1983.

C. Canuto and D. Et-fransos, Numerical solution of partialdifferential equations in random domains : An application to wind engineering, Communications in computational physics, vol.5, pp.2-4515, 2008.

C. Canuto and T. Et-kozubek, A fictitious domain approach to the numerical solution of PDEs in stochastic domains, Numerische Mathematik, vol.28, issue.2, pp.257-293, 2007.
DOI : 10.1007/s00211-007-0086-x

L. Chamoin, J. Oden, and S. Et-prudhomme, A stochastic coupling method for atomic-to-continuum Monte-Carlo simulations, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.43-44, pp.3530-3546, 2008.
DOI : 10.1016/j.cma.2008.04.013

T. F. Chan and T. P. Mathew, Domain decomposition algorithms, Acta Numerica, pp.61-143, 1994.
DOI : 10.1016/0041-5553(78)90012-5

M. Chevreuil and A. Et-nouy, Model order reduction based on proper generalized decomposition for the propagation of uncertainties in structural dynamics, International Journal for Numerical Methods in Engineering, vol.5, issue.2-4, pp.241-268, 2012.
DOI : 10.1002/nme.3249

URL : https://hal.archives-ouvertes.fr/hal-00603342

F. Chinesta, A. Ammar, and E. Et-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

M. Deb, I. Babu?kababu?ka, and J. T. Et-oden, Solution of stochastic partial differential equations using Galerkin finite element techniques, Computer Methods in Applied Mechanics and Engineering, vol.190, issue.48, pp.6359-6372, 2001.
DOI : 10.1016/S0045-7825(01)00237-7

H. B. Dhia and G. Et-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

A. Doostan and G. Et-iaccarino, A least-squares approximation of partial differential equations with high-dimensional random inputs, Journal of Computational Physics, vol.228, issue.12, pp.4332-4345, 2009.
DOI : 10.1016/j.jcp.2009.03.006

A. Düster, A. Niggl, and E. Et-rank, Applying the hp???d version of the FEM to locally enhance dimensionally reduced models, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.37-40, pp.3524-3533, 2007.
DOI : 10.1016/j.cma.2006.10.018

I. Elishakoff, Whys and hows in uncertainty modelling-probability , fuzziness, and anti-optimization, 1999.

A. Falco and A. Et-nouy, A Proper Generalized Decomposition for the solution of elliptic problems in abstract form by using a functional Eckart???Young approach, Journal of Mathematical Analysis and Applications, vol.376, issue.2, pp.469-480, 2011.
DOI : 10.1016/j.jmaa.2010.12.003

URL : https://hal.archives-ouvertes.fr/hal-00461094

A. Falco and A. Et-nouy, Proper generalized decomposition for nonlinear convex problems in tensor Banach spaces, Numerische Mathematik, vol.115, issue.45???48, p.23, 2012.
DOI : 10.1007/s00211-011-0437-5

URL : https://hal.archives-ouvertes.fr/hal-00609108

C. Farhat, P. Chen, and F. Et-risler, A simple and unified framework for accelerating the convergence of iterative substructuring methods with Lagrange multipliers : Application to the design of new FETI coarse problems, p.27, 1996.

C. Farhat and F. Et-roux, 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 : 10.1002/nme.1620320604

D. Fokkema, G. Sleijpen, and H. A. Der-vorst, Generalized conjugate gradient squared, Journal of Computational and Applied Mathematics, vol.71, issue.1, pp.125-146, 1996.
DOI : 10.1016/0377-0427(95)00227-8

URL : http://doi.org/10.1016/0377-0427(95)00227-8

P. Frauenfelder, C. Schwab, and R. A. Et-todor, Finite elements for elliptic problems with stochastic coefficients, Computer Methods in Applied Mechanics and Engineering, vol.194, issue.2-5, pp.205-228, 2005.
DOI : 10.1016/j.cma.2004.04.008

B. Ganapathysubramanian and N. Et-zabaras, A stochastic multiscale framework for modeling flow through random heterogeneous porous media, Journal of Computational Physics, vol.228, issue.2, pp.591-618, 2009.
DOI : 10.1016/j.jcp.2008.10.006

C. W. Gardiner, Handbook of stochastic methods, 1985.

L. Gendre, O. Allix, and P. Et-gosselet, 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 : 10.1002/nme.3142

URL : https://hal.archives-ouvertes.fr/hal-01224373

L. Gendre, O. Allix, P. Gosselet, and F. Et-comte, 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

R. Ghanem, Ingredients for a general purpose stochastic finite elements implementation, Computer Methods in Applied Mechanics and Engineering, vol.168, issue.1-4, pp.19-34, 1999.
DOI : 10.1016/S0045-7825(98)00106-6

R. Ghanem and P. Et-spanos, Stochastic finite elements : a spectral approach, p.19, 1991.
DOI : 10.1007/978-1-4612-3094-6

R. Glowinski, J. He, A. Lozinski, J. Rappaz, and J. Et-wagner, Finite element approximation of multi-scale elliptic problems using patches of elements, Numerische Mathematik, vol.49, issue.4, pp.663-687, 2005.
DOI : 10.1007/s00211-005-0614-5

URL : https://hal.archives-ouvertes.fr/hal-00113130

R. Glowinski, T. Pan, R. Wells, and X. Et-zhou, Wavelet and Finite Element Solutions for the Neumann Problem Using Fictitious Domains, Journal of Computational Physics, vol.126, issue.1, pp.40-51, 1996.
DOI : 10.1006/jcph.1996.0118

W. Hackbusch, Tensor Spaces and Numerical Tensor Calculus, de Series in Computational Mathematics, pp.79-84, 2012.
DOI : 10.1007/978-3-642-28027-6

C. Hager, P. Hauret, P. L. Tallec, and B. I. Et-wohlmuth, Solving dynamic contact problems with local refinement in space and time, Computer Methods in Applied Mechanics and Engineering, vol.201, issue.204, pp.201-20425, 2012.
DOI : 10.1016/j.cma.2011.09.006

URL : https://hal.archives-ouvertes.fr/hal-01393141

J. He, A. Lozinski, and J. Et-rappaz, Accelerating the method of finite element patches using approximately harmonic functions, Comptes Rendus Mathematique, vol.345, issue.2, pp.107-112, 2007.
DOI : 10.1016/j.crma.2007.06.006

F. Hecht, A. Lozinski, A. Perronnet, and O. Et-pironneau, Numerical zoom for multiscale problems with an application to flows through porous media, Discrete and Continuous Dynamical Systems, vol.23, issue.1/2, pp.265-280, 2009.
DOI : 10.3934/dcds.2009.23.265

A. Keese and H. G. Et-mathhies, Numerical methods and Smolyak quadrature for nonlinear stochastic partial differential equations, SIAM J. Sci. Comput, vol.83, p.14, 2003.

A. Keese and H. G. Et-mathhies, Hierarchical parallelisation for the solution of stochastic finite element equations, Computers & Structures, vol.83, issue.14, pp.1033-1047, 2005.
DOI : 10.1016/j.compstruc.2004.11.014

T. G. Kolda and B. W. Et-bader, Tensor Decompositions and Applications, SIAM Review, vol.51, issue.3, pp.455-500, 2009.
DOI : 10.1137/07070111X

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.130.782

P. Ladevèze and E. Et-florentin, Verification of stochastic models in uncertain environments using the constitutive relation error method, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.1-3, pp.1-3225, 2006.
DOI : 10.1016/j.cma.2006.03.006

P. Ladevèze, J. Passieux, and D. Et-néron, The LATIN multiscale computational method and the Proper Generalized Decomposition, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.21-22, pp.21-221287, 2010.
DOI : 10.1016/j.cma.2009.06.023

L. Maître, O. Najm, H. Ghanem, R. Et-knio, and O. , Multi-resolution analysis of Wiener-type uncertainty propagation schemes, Journal of Computational Physics, vol.197, issue.2, pp.502-531, 2004.
DOI : 10.1016/j.jcp.2003.12.020

L. Maître, O. Reagan, M. Najm, H. Ghanem, R. Et-knio et al., A Stochastic Projection Method for Fluid Flow, Journal of Computational Physics, vol.181, issue.1, pp.9-44, 2002.
DOI : 10.1006/jcph.2002.7104

J. Lions and O. Et-pironneau, Domain decomposition methods for CAD, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.328, issue.1, pp.73-80, 1999.
DOI : 10.1016/S0764-4442(99)80015-9

M. Loève, Probability Theory. I, fourth edition, Graduate Texts in Mathematics, vol.45, p.11, 1977.

M. Loève, Probability Theory. II, fourth edition, Graduate Texts in Mathematics, vol.46, p.11, 1978.

A. Lozinski, Méthodes numériques et modélisation pour certains problèmes multi-échelles. Habilitation à diriger des recherches, pp.31-32, 2010.

A. Lozinski and O. Et-pironneau, Numerical zoom for advection diffusion problems with localized multiscales, Numerical Methods for Partial Differential Equations, vol.38, issue.1, pp.197-207, 2011.
DOI : 10.1002/num.20642

URL : https://hal.archives-ouvertes.fr/hal-00631122

X. Ma and N. Et-zabaras, A stochastic mixed finite element heterogeneous multiscale method for flow in porous media, Journal of Computational Physics, vol.230, issue.12, pp.4696-4722, 2011.
DOI : 10.1016/j.jcp.2011.03.001

O. P. Maître and O. M. Et-knio, Spectral Methods for Uncertainty Quantification With Applications to Computational Fluid Dynamics . Scientific Computation, p.12, 2010.

L. Mathelin, O. L. Et-maître, E. Oñate, and J. Et-périaux, A posteriori error analysis for stochastic finite elements solutions of fluid flows with parametric uncertainties The Netherlands, éditeurs : Proceedings of ECCOMAS CFD conference, p.15, 2006.

L. Mathelin and O. L. Et-maître, error estimate for stochastic finite element methods, Communications in Applied Mathematics and Computational Science, vol.2, issue.1, pp.83-116, 2007.
DOI : 10.2140/camcos.2007.2.83

H. G. Matthies, Stochastic finite elements : Computational approaches to stochastic partial differential equations. Zamm-Zeitschrift Fur, pp.849-873, 2008.
DOI : 10.1002/zamm.200800095

H. G. Matthies and A. Et-keese, Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations, Computer Methods in Applied Mechanics and Engineering, vol.194, issue.12-16, pp.12-161295, 2005.
DOI : 10.1016/j.cma.2004.05.027

J. M. Melenk and I. Et-babu?kababu?ka, The partition of unity method : basic theory and applications, Computer Methods in Applied Mechanics and Engineering, vol.39, pp.289-314, 1996.

N. Moës, J. Dolbow, and T. Et-belytschko, A finite element method for crack growth without remeshing, International Journal for Numerical Methods in Engineering, vol.46, issue.1, pp.131-150, 1999.
DOI : 10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.3.CO;2-A

P. S. Mohan, P. B. Nair, and A. J. Et-keane, Stochastic projection schemes for deterministic linear elliptic partial differential equations on random domains, International Journal for Numerical Methods in Engineering, vol.16, issue.3, pp.874-895, 2011.
DOI : 10.1002/nme.3004

A. Nouy, 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.45-484521, 2007.
DOI : 10.1016/j.cma.2007.05.016

URL : https://hal.archives-ouvertes.fr/hal-00366619

A. Nouy, Generalized spectral decomposition method for solving stochastic finite element equations: Invariant subspace problem and dedicated algorithms, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.51-52, pp.4718-4736, 2008.
DOI : 10.1016/j.cma.2008.06.012

URL : https://hal.archives-ouvertes.fr/hal-00366613

A. Nouy, Recent Developments in Spectral Stochastic Methods for??the??Numerical Solution of Stochastic Partial Differential Equations, Archives of Computational Methods in Engineering, vol.24, issue.2, pp.251-285, 2009.
DOI : 10.1007/s11831-009-9034-5

URL : https://hal.archives-ouvertes.fr/hal-00366636

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.23-241603, 2010.
DOI : 10.1016/j.cma.2010.01.009

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

A. Nouy, Proper Generalized Decompositions and Separated Representations for the Numerical Solution of High Dimensional Stochastic Problems, Archives of Computational Methods in Engineering, vol.225, issue.1, pp.403-434, 2010.
DOI : 10.1007/s11831-010-9054-1

URL : https://hal.archives-ouvertes.fr/hal-00461099

A. Nouy, M. Chevreuil, and E. Et-safatly, Fictitious domain method and separated representations for the solution of boundary value problems on uncertain parameterized domains, Computer Methods in Applied Mechanics and Engineering, vol.200, issue.45-46, 2011.
DOI : 10.1016/j.cma.2011.07.002

URL : https://hal.archives-ouvertes.fr/hal-00662564

A. Nouy, A. Clément, F. Schoefs, and N. Et-moës, An extended stochastic finite element method for solving stochastic partial differential equations on random domains, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.51-52, pp.4663-4682, 2008.
DOI : 10.1016/j.cma.2008.06.010

URL : https://hal.archives-ouvertes.fr/hal-00366617

A. Nouy and A. Et-falco, Constrained tensor product approximations based on penalized best approximations, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00577942

A. Nouy and O. Et-le-maître, 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. Nouy, F. Schoefs, and N. Et-moës, X-SFEM, a computational technique based on X-FEM to deal with random shapes, Revue europ??enne de m??canique num??rique, vol.16, issue.2, pp.277-293, 2007.
DOI : 10.3166/remn.16.277-293

URL : https://hal.archives-ouvertes.fr/hal-00368060

M. F. Pellissetti and R. G. Et-ghanem, Iterative solution of systems of linear equations arising in the context of stochastic finite elements, Advances in Engineering Software, vol.31, issue.8-9, pp.607-616, 2000.
DOI : 10.1016/S0965-9978(00)00034-X

I. Ramière, P. Angot, and M. Et-belliard, A fictitious domain approach with spread interface for elliptic problems with general boundary conditions, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.4-6, pp.4-6766, 2007.
DOI : 10.1016/j.cma.2006.05.012

I. Ramière, P. Angot, and M. Et-belliard, A general fictitious domain method with immersed jumps and multilevel nested structured meshes, Journal of Computational Physics, vol.225, issue.2, pp.1347-1387, 2007.
DOI : 10.1016/j.jcp.2007.01.026

F. Riesz and B. Et-sz.-nagy, Functional Analysis, p.147, 1990.

A. Sarkar, N. Benabbou, and R. Et-ghanem, Domain decomposition of stochastic PDEs: Theoretical formulations, International Journal for Numerical Methods in Engineering, vol.31, issue.4, pp.689-701, 2009.
DOI : 10.1002/nme.2431

G. Shafer, A mathematical theory of evidence, 1976.

B. F. Smith, F. E. Bjorstad, and W. Et-gropp, Domain Decomposition, p.27, 1996.
DOI : 10.1007/978-3-540-70529-1_411

S. A. Smolyak, Quadrature and interpolation formulas for tensor products of certain classes of functions, Sov. Math. Dokl, vol.3, pp.240-243, 1963.

C. Soize, Non-Gaussian positive-definite matrix-valued random fields for elliptic stochastic partial differential operators, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.1-3, pp.1-326, 2006.
DOI : 10.1016/j.cma.2004.12.014

URL : https://hal.archives-ouvertes.fr/hal-00686157

P. Sonneveld, CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems, SIAM Journal on Scientific and Statistical Computing, vol.10, issue.1, pp.36-52, 1989.
DOI : 10.1137/0910004

F. D. Steger and J. Et-benek, A chimera grid scheme, in advances in grid generation, ASME FED, vol.5, p.34, 1983.

E. Stein and S. Et-ohnimus, Coupled model-and solution-adaptivity in the finite-element method. omputer Methods in Applied Mechanics and En-gineering, pp.327-350, 1997.

H. A. Vorst, Iterative Krylov Methods for Large Linear Systems, 2003.

G. J. Wagner and W. K. Et-liu, Coupling of atomistic and continuum simulations using a bridging scale decomposition, Journal of Computational Physics, vol.190, issue.1, pp.249-274, 2003.
DOI : 10.1016/S0021-9991(03)00273-0

B. I. Wohlmuth, Discretization methods and iterative solvers based on domain decomposition, p.41, 2001.
DOI : 10.1007/978-3-642-56767-4

S. Xiao and T. Et-belytschko, Fast numerical methods for stochastic computations : a review, Comm. Comput. Phys, vol.193, pp.17-201645, 2004.

D. Xiu, Fast numerical methods for stochastic computations : a review, Comm. Comput. Phys, vol.5, pp.242-272, 2009.

D. Xiu and G. E. Et-karniadakis, The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations, SIAM Journal on Scientific Computing, vol.24, issue.2, pp.619-644, 2002.
DOI : 10.1137/S1064827501387826

D. Xiu and D. M. Et-tartakovsky, Numerical Methods for Differential Equations in Random Domains, SIAM Journal on Scientific Computing, vol.28, issue.3, pp.1167-1185, 2006.
DOI : 10.1137/040613160

J. Xu, Iterative Methods by Space Decomposition and Subspace Correction, SIAM Review, vol.34, issue.4, pp.581-613, 1992.
DOI : 10.1137/1034116

J. Xu and J. Et-zou, Some Nonoverlapping Domain Decomposition Methods, SIAM Review, vol.40, issue.4, pp.857-914, 1998.
DOI : 10.1137/S0036144596306800

X. F. Xu, A multiscale stochastic finite element method on elliptic problems involving uncertainties, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.25-28, pp.2723-2736, 2007.
DOI : 10.1016/j.cma.2007.02.002

X. F. Xu, X. Chen, and L. Et-shen, A Green-function-based multiscale method for uncertainty quantification of finite body random heterogeneous materials, Computers & Structures, vol.87, issue.21-22, pp.1416-1426, 2009.
DOI : 10.1016/j.compstruc.2009.05.009

L. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, vol.1, issue.1, pp.3-28, 1978.
DOI : 10.1016/0165-0114(78)90029-5