Ingredients for a general purpose stochastic finite elements implementation

Abramowitz, 1964

Cameron, 1947, The orthogonal development of nonlinear functionals in series of Fourier-Hermite functionals, Ann. Math., 48, 385, 10.2307/1969178

Cannon, 1977, Galerkin procedures for systems of parabolic partial differential equations related to the transmission of nerve impulses, 24

Dobrushin, 1971, Polynomials in linear random functions, Russian Math. Surveys, 32, 71, 10.1070/RM1977v032n02ABEH001618

Dunford, 1958

Ghanem, 1991

Ghanem, 1996, Numerical solution of spectral stochastic finite element systems, Comp. Methods Appl. Mech. Engrg., 129, 289, 10.1016/0045-7825(95)00909-4

Ghanem, 1996, Stochastic finite element analysis of randomly layered media, J. Engrg. Mech., 122, 361, 10.1061/(ASCE)0733-9399(1996)122:4(361)

Ghanem, 1998, Adaptive polynomial chaos simulation applied to statistics of extremes in nonlinear random vibration, Prob. Engrg. Mech., 13, 125, 10.1016/S0266-8920(97)00020-9

R. Ghanem, Hybrid stochastic finite elements: coupling of spectral expansions with Monte Carlo simulations, J. Appl. Mech., to appear.

Ghanem, 1998, Probabilistic characterization of transport in heterogeneous porous media, Comp. Methods Appl. Mech. Engrg., 158, 199, 10.1016/S0045-7825(97)00250-8

Ghanem, 1998, A new implementation of the spectral stochastic finite element method for stochastic constitutive relations

Janson, 1997

Kallianpur, 1970, The role of reproducing kernel Hilbert spaces in the study of Gaussian processes, Vol. 2, 49

Kallianpur, 1972, Homogeneous chaos expansions, 230

Kree, 1971, Equations lineaires a coefficients aleatoires, Instituto Nazionale di Alta Mathematica, Vol. VII, 515

Kree, 1995, Functional analysis in stochatsic modelling

Loeve, 1977

MacKay, 1979, A comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, 21, 239

Malliavin, 1997

Murray, 1936, On rings of operators, Ann. Math., 37, 116, 10.2307/1968693

Obata, 1991

Pastur, 1991

Pradlwarter, 1996, On advanced procedures in stochastic structural dynamics, J. Nonlinear Mech.

Segall, 1976, Orthogonal functionals of independent-increment processes, IEEE, Trans. Information Theory IT, 22, 287, 10.1109/TIT.1976.1055560

Skorohod, 1984

Thompson, 1992

Wick, 1950, The evaluation of the collision matrix, Phys. Rev., 80, 268, 10.1103/PhysRev.80.268

Wiener, 1938, The homogeneous chaos, Am. J. Math., 60, 897, 10.2307/2371268

1982

Wintner, 1943, The discrete chaos, Am. J. Math., 65, 279, 10.2307/2371816