Domain Decomposition Methods -Algorithms and Theory, Theory, vol.34, p.27, 2005. ,
DOI : 10.1007/b137868
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
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. ,
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
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
Multiscale mechanical problems : the Arlequin method, C. R. Acad. Sci. Paris, Série IIb, vol.326, pp.899-904, 1998. ,
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
Convex models of uncertainty in applied mechanics, p.11, 1990. ,
Stochastic finite elements : intrusive and nonintrusive methods for reliability analysis, Thèse de doctorat, p.14, 2005. ,
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
Solutions to Stochastic Partial Differential Equations as Elements of Tensor Product Spaces, Thèse de doctorat, p.17, 2000. ,
Algorithms for Numerical Analysis in High Dimensions, SIAM Journal on Scientific Computing, vol.26, issue.6, pp.2133-2159, 2005. ,
DOI : 10.1137/040604959
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
Analyse fonctionnelle : théorie et applications, p.17, 1983. ,
Numerical solution of partialdifferential equations in random domains : An application to wind engineering, Communications in computational physics, vol.5, pp.2-4515, 2008. ,
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
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
Domain decomposition algorithms, Acta Numerica, pp.61-143, 1994. ,
DOI : 10.1016/0041-5553(78)90012-5
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
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
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
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 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
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
Whys and hows in uncertainty modelling-probability , fuzziness, and anti-optimization, 1999. ,
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
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
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. ,
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
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
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
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
Handbook of stochastic methods, 1985. ,
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
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
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
Stochastic finite elements : a spectral approach, p.19, 1991. ,
DOI : 10.1007/978-1-4612-3094-6
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
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
Tensor Spaces and Numerical Tensor Calculus, de Series in Computational Mathematics, pp.79-84, 2012. ,
DOI : 10.1007/978-3-642-28027-6
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
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
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
Numerical methods and Smolyak quadrature for nonlinear stochastic partial differential equations, SIAM J. Sci. Comput, vol.83, p.14, 2003. ,
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
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
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
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
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
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
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
Probability Theory. I, fourth edition, Graduate Texts in Mathematics, vol.45, p.11, 1977. ,
Probability Theory. II, fourth edition, Graduate Texts in Mathematics, vol.46, p.11, 1978. ,
Méthodes numériques et modélisation pour certains problèmes multi-échelles. Habilitation à diriger des recherches, pp.31-32, 2010. ,
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
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
Spectral Methods for Uncertainty Quantification With Applications to Computational Fluid Dynamics . Scientific Computation, p.12, 2010. ,
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. ,
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
Stochastic finite elements : Computational approaches to stochastic partial differential equations. Zamm-Zeitschrift Fur, pp.849-873, 2008. ,
DOI : 10.1002/zamm.200800095
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
The partition of unity method : basic theory and applications, Computer Methods in Applied Mechanics and Engineering, vol.39, pp.289-314, 1996. ,
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
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 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
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
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 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
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
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
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
Constrained tensor product approximations based on penalized best approximations, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00577942
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
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
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
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
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
Functional Analysis, p.147, 1990. ,
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
A mathematical theory of evidence, 1976. ,
Domain Decomposition, p.27, 1996. ,
DOI : 10.1007/978-3-540-70529-1_411
Quadrature and interpolation formulas for tensor products of certain classes of functions, Sov. Math. Dokl, vol.3, pp.240-243, 1963. ,
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
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
A chimera grid scheme, in advances in grid generation, ASME FED, vol.5, p.34, 1983. ,
Coupled model-and solution-adaptivity in the finite-element method. omputer Methods in Applied Mechanics and En-gineering, pp.327-350, 1997. ,
Iterative Krylov Methods for Large Linear Systems, 2003. ,
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
Discretization methods and iterative solvers based on domain decomposition, p.41, 2001. ,
DOI : 10.1007/978-3-642-56767-4
Fast numerical methods for stochastic computations : a review, Comm. Comput. Phys, vol.193, pp.17-201645, 2004. ,
Fast numerical methods for stochastic computations : a review, Comm. Comput. Phys, vol.5, pp.242-272, 2009. ,
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
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
Iterative Methods by Space Decomposition and Subspace Correction, SIAM Review, vol.34, issue.4, pp.581-613, 1992. ,
DOI : 10.1137/1034116
Some Nonoverlapping Domain Decomposition Methods, SIAM Review, vol.40, issue.4, pp.857-914, 1998. ,
DOI : 10.1137/S0036144596306800
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
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
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