N. Wiener, The Homogeneous Chaos, American Journal of Mathematics, vol.60, issue.4, pp.897-936, 1938.
DOI : 10.2307/2371268

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

M. Shinozuka and F. Yamakasi, Stochastic finite element analysis: an introduction. Stochastic Structural Dynamics, Progress in Therory and Applications, pp.241-291, 1988.

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

M. T. Reagan, H. N. Najm, R. G. Ghanem, and O. M. Knio, Uncertainty quantification in reacting-flow simulations through non-intrusive spectral projection, Combustion and Flame, vol.132, issue.3, pp.545-555, 2003.
DOI : 10.1016/S0010-2180(02)00503-5

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

R. Gagnaire, Contribution à la modélisation numérique en électromagnétisme statique stochastique, Thèse de doctorat, Arts et Métier ParisTech, 2008.

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

A. Clement, Elément finis étendu pour calculer de structures à géométrie aléatoire : application à la pris en compte de la corrosion de structures en région littorale, Thèse de doctorat de l'université de Nantes, 2008.

I. Tsukerman, Computational Methods for Nanoscale Apllications. Nanostructure science and technology, 2008.
DOI : 10.1007/978-0-387-74778-1

S. Clenet, N. Ida, R. Gaignaire, and O. Moreau, Solution of Dual Stochastic Static Formulations Using Double Orthogonal Polynomials, IEEE Transactions on Magnetics, vol.46, issue.8, pp.3543-3546, 2010.
DOI : 10.1109/TMAG.2010.2044767

R. H. Cameron and W. T. Martin, The orthogonal development of non linear functionals in series of

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

URL : http://www.dtic.mil/get-tr-doc/pdf?AD=ADA460654

G. Blattman and B. Sudret, Sparse polynomial chaos expansions and adaptive stochastic finite elements using a regression approach, Comptes Rendus M??canique, vol.336, issue.6, pp.516-523, 2008.
DOI : 10.1016/j.crme.2008.02.013

K. Beddek, S. Clénet, O. Moreau, V. Costan, Y. L. Menach et al., Adaptive method for Non-Intrusive Spectral Projection ? Application on Eddy Current Non Destructive Testing, Compumag, 2011.
DOI : 10.1109/tmag.2011.2175204

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

S. Clenet and N. Ida, Error estimation in a stochastic finite element method in electrokinetics, International Journal for Numerical Methods in Engineering, vol.26, issue.2
DOI : 10.1002/nme.2394

T. Henneron, Y. Le-menach, F. Piriou, O. Moreau, S. Clenet et al., Source Field Computation in NDT Applications, IEEE Transactions on Magnetics, vol.43, issue.4, pp.1785-1788, 2007.
DOI : 10.1109/TMAG.2007.892522

P. Dular, W. Legros, and A. Nicolet, Coupling of local and global quantities in various finite element formulations and its application to electrostatics, magnetostatics and magnetodynamics, IEEE Transactions on Magnetics, vol.34, issue.5, pp.3078-3081, 1998.
DOI : 10.1109/20.717720

S. Clenet, Contribution à la modélisation numérique en électromagnétisme statique, HDR, université des sciences et technologies de Lille, 2001.

T. Henneron, Contribution à la prise en compte des Grandeurs Globales dans les Problèmes d'Electromagnétisme résolus avec la Méthode des Eléments Finis, Thèse de doctorat, U.S.T.L, 2004.

A. Bossavit, Whitney forms: a class of finite elements for three-dimensional computations in electromagnetism, IEE Proceedings A Physical Science, Measurement and Instrumentation, Management and Education, Reviews, vol.135, issue.8
DOI : 10.1049/ip-a-1.1988.0077

S. P. Huang, S. T. Quek, and K. K. Phoon, Convergence study of the truncated Karhunen???Loeve expansion for simulation of stochastic processes, International Journal for Numerical Methods in Engineering, vol.8, issue.9, pp.1029-1043, 2001.
DOI : 10.1002/nme.255

J. C. Helton and F. J. Davis, Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems, Reliability Engineering & System Safety, vol.81, issue.1, pp.23-69, 2003.
DOI : 10.1016/S0951-8320(03)00058-9

B. Sudret, Uncertainty propagation and sensitivity analysis in mechanical models contribution to structural reliability and stochastic spectral method, 2007.

I. Tsukerman, Accurate computation of 'ripple solutions' on moving finite element meshes, IEEE Transactions on Magnetics, vol.31, issue.3, pp.1472-1475, 1995.
DOI : 10.1109/20.376307

A. Nouy, A. Clément, F. Schoefs, and N. Moes, 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.51-52, 2008.
DOI : 10.1016/j.cma.2008.06.010

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

A. Nouy, Contributions à la quantification et à la propagation des incertitudes en mécanique numérique, HDR université de Nantes, 2008.

N. Moës, M. Cloirec, P. Cartraud, and J. F. Remacle, A computational approach to handle complex microstructure geometries, Computer Methods in Applied Mechanics and Engineering, vol.192, issue.28-30, pp.28-30, 2003.
DOI : 10.1016/S0045-7825(03)00346-3

D. H. Mac, S. Clenet, J. C. Mipo, and O. Moreau, Solution of Static Field Problems With Random Domains, IEEE Transactions on Magnetics, vol.46, issue.8
DOI : 10.1109/TMAG.2010.2045358

URL : https://hal.archives-ouvertes.fr/hal-00857180

D. H. Mac, S. Clenet, and J. C. Mipo, Transformation Methods for Static Field Problems With Random Domains, IEEE Transactions on Magnetics, vol.47, issue.5, pp.1446-1449, 2011.
DOI : 10.1109/TMAG.2010.2096460

URL : https://hal.archives-ouvertes.fr/hal-00857179

D. H. Mac, S. Clenet, and J. C. Mipo, Calculation of field distribution in electromagnetic problems with random domains, IET 8th International Conference on Computation in Electromagnetics (CEM 2011), 2011.
DOI : 10.1049/cp.2011.0014

E. Parzen, On Estimation of a Probability Density Function and Mode, The Annals of Mathematical Statistics, vol.33, issue.3, pp.1065-1076, 1962.
DOI : 10.1214/aoms/1177704472

I. Babuska, R. Tempone, and G. E. Zouraris, Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations, SIAM Journal on Numerical Analysis, vol.42, issue.2, pp.800-825, 2004.
DOI : 10.1137/S0036142902418680

C. Soize, Probabilités et modélisation des incertitudes, 2008.

M. Ferrari and S. Bellini, Importance sampling simulation of turbo product codes, ICC 2001. IEEE International Conference on Communications. Conference Record (Cat. No.01CH37240), pp.2773-2777, 2001.
DOI : 10.1109/ICC.2001.936655

O. Le-maitre, O. Knio, H. Najm, and R. Ghanem, Adaptive multi-wavelets decomposition for stochastic processes, International Conference on Spectral and High Order Methods (ICOSAHOM) 2004, 2004.

T. T. Soong, Random Differential Equations in Science and Engineering, Journal of Applied Mechanics, vol.41, issue.4, 1973.
DOI : 10.1115/1.3423466

C. Papadimitriou, L. S. Katafygiotis, and J. L. Beck, Approximate analysis of response variability of uncertain linear systems, Probabilistic Engineering Mechanics, vol.10, issue.4, pp.251-64, 1995.
DOI : 10.1016/0266-8920(95)00020-8

J. D. Collins and W. T. Thomson, The eigenvalue problem for structural systems with statistical properties, AIAA Journal, vol.7, issue.4, pp.642-648, 1969.

R. C. Micaletti, A. S. Cakmak, S. R. Nielsen, and H. U. Koyluglu, A solution method for linear and geometrically nonlinear MDOF systems with random properties subject to random excitation, Probabilistic Engineering Mechanics, vol.13, issue.2, pp.85-95, 1998.
DOI : 10.1016/S0266-8920(97)00012-X

E. Vanmarcke and M. Grigoriu, Stochastic Finite Element Analysis of Simple Beams, Journal of Engineering Mechanics, vol.109, issue.5, pp.1203-1214, 1983.
DOI : 10.1061/(ASCE)0733-9399(1983)109:5(1203)

V. Papadopoulos and M. Papadrakakis, Stochastic finite element-based reliability analysis of space frames, Probabilistic Engineering Mechanics, vol.13, issue.1, pp.53-65, 1998.
DOI : 10.1016/S0266-8920(97)00007-6

L. A. Zadeh, Fuzzy sets, Information and Control, vol.8, issue.3, pp.338-353, 1965.
DOI : 10.1016/S0019-9958(65)90241-X

L. A. Zadeh, K. S. Fu, K. Tanaka, and M. Shimura, Fuzzy Sets and Their Applications to Cognitive and Decision Processes, 1975.

S. Medasani, J. Kim, and R. Krishnapuram, An overview of membership function generation techniques for pattern recognition, International Journal of Approximate Reasoning, vol.19, issue.3-4, pp.3-4, 1998.
DOI : 10.1016/S0888-613X(98)10017-8

A. L. Medaglia, S. C. Fang, H. L. Nuttle, and J. R. Wilson, An efficient and flexible mechanism for constructing membership functions, European Journal of Operational Research, vol.139, issue.1, pp.84-95, 2001.
DOI : 10.1016/S0377-2217(01)00157-6

B. Möller, M. Beer, W. Graf, and J. U. Sickert, Fuzzy finite element method and its application. Trends in computational structural mechanics, 2001.

D. Moens and M. Hanss, Non-probabilistic finite element analysis for parametric uncertainty treatment in applied mechanics: Recent advances, Finite Elements in Analysis and Design, vol.47, issue.1, pp.4-16, 2011.
DOI : 10.1016/j.finel.2010.07.010

S. Valiappan and T. D. Pham, Elasto-plastic finite element analysis with fuzzy parameters, International Journal for Numerical Methods in Engineering, vol.20, issue.4, pp.531-548, 1995.
DOI : 10.1002/nme.1620380403

P. Billingsley, Probability and Measure, 1986.

E. Castillo, J. M. Sarabia, C. Solares, and P. Gomez, Uncertainty analyses in fault trees and Bayesian networks using FORM/SORM methods, Reliability Engineering & System Safety, vol.65, issue.1, pp.29-40, 1999.
DOI : 10.1016/S0951-8320(98)00083-0

T. Haukaas and A. D. Kiureghian, Strategies for finding the design point in non-linear finite element reliability analysis, Probabilistic Engineering Mechanics, vol.21, issue.2, pp.133-147, 2006.
DOI : 10.1016/j.probengmech.2005.07.005

A. D. Kiureghian, T. Haukaas, and K. Fujimura, Structural reliability software at the University of California, Berkeley, Structural Safety, vol.28, issue.1-2, pp.1-2, 2006.
DOI : 10.1016/j.strusafe.2005.03.002

Y. G. Zhao and T. Ono, A general procedure for first/second-order reliability method (form/sorm) Structural Safety, pp.95-112, 1999.
DOI : 10.1016/s0167-4730(99)00008-9

W. Prager and J. L. Synge, Approximations in elasticity based on the concept of function space, Quarterly of Applied Mathematics, vol.5, issue.3, pp.241-269, 1947.
DOI : 10.1090/qam/25902

J. F. Le and . Gall, Intégration, probabilités et processus aléatoires

I. Tsukerman, A general accuracy criterion for finite element approximation, IEEE Transactions on Magnetics, vol.34, issue.5, 1998.
DOI : 10.1109/20.717557

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

T. W. Preston, A. B. Reece, and P. S. Sangha, Induction motor analysis by time-stepping techniques, IEEE Transactions on Magnetics, vol.24, issue.1, pp.471-474, 1988.
DOI : 10.1109/20.43959

B. Boualem, Contribution à la modélisation des systèmes électrotechnique à l'aide des formulations en potentiels: application à la machine asynchrone, Thèse de doctorat, 1997.

B. Sudret, Global sensitivity analysis using polynomial chaos expansions, Reliability Engineering & System Safety, vol.93, issue.7, pp.964-979, 2008.
DOI : 10.1016/j.ress.2007.04.002

URL : https://hal.archives-ouvertes.fr/hal-01432217

R. Ramarotafika, Modélisation stochastique de la loi de comportement des matériaux ferromagnétiques, application sur les machines électriques, Thèse de doctorat, Arts et Métiers ParisTech-2012

A. Nouy, M. Chevreuil, and E. 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, pp.45-46, 2011.
DOI : 10.1016/j.cma.2011.07.002

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

P. S. Mohan, P. B. Nair, and A. J. 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

URL : http://eprints.soton.ac.uk/204239/1/Stochastic_projection_schemes_for_deterministic_linear_elliptic_partial_differential_equations_on_random_domains.pdf