L. M. Arriola and J. M. Hyman, Being sensitive to uncertainty,
Comput. Sci. Engrg. 9(2):10-20, 2007.
G. Lin, X. Wan, C.-H. Su, and G. E. Karniadakis, Stochastic computational
fluid dynamics, Comput. Sci. Engrg. 9(2):21-29, 2007.
D. M. Tartakovsky and D. B. Xiu, Stochastic modeling of complex systems,
Comput. Sci. Engrg. 9(2):8-9, 2007.
N. Zabaras and S. Sankaran, An information-theoretic approach to
stochastic materials modeling, Comput. Sci. Engrg. 9(2):30-39, 2007
Research Papers and Monographs
S. Acharjee and N. Zabaras, A non-intrusive stochastic Galerkin
approach for modeling uncertainty propagation in deformation processes,
Computers and Structures, 85:244-254, 2007.
S. Acharjee and N. Zabaras, Uncertainty propagation in finite
deformations – A spectral stochastic Lagrangian approach,
Comput. Meth. Appl. Mech. Engrg., 195:2289-2312, 2006.
L. A. Bergman, B. F. Spencer, and S. F. Wojtkiewicz, A
state-of-the-art report on computational stochastic mechanics,
Probabilistic Engrg. Mech., 12(4):197-321, 1997.
R. H. Cameron and W. T. Martin, The orthogonal development of
non-linear functionals in series of Fourier-Hermite functionals,
Ann. Math., 48:385-392, 1947.
B. J. Debusschere, H. N. Najm, P. P. Pebay, O. M. Knio, R. G. Ghanem,
and O. P. Le Maitre, Numerical challenges in the use of polymomial
chaos representations for stochastic processes, SIAM J. Sci. Comput.,
26:698-719, 2004.
B. DeVolder, J. Glimm, Y. Kang, Y. Lee, K. Pao, D. H. Sharp and K. Ye,
Uncertainty quantification for multiscale simulations, J. Fluids
Engrg., 124:29-41, 2002.
R. G. Ghanem, Ingredients for a general purpose stochastic finite
elements formulation, Comput. Meth. Appl. Mech. Engrg., 168:19-34,
1999.
R. G. Ghanem and P. Spanos, Stochastic Finite Elements: A Spectral
Approach, Springer, 1991 (Dover reprint, 2002).
R. G. Ghanem and S. F. Wojtkiewicz, editors, Special Issue on
uncertainty quantification, SIAM J. Sci. Comput. 26(2):359-735, 2004.
J. Glimm and D. H. Sharp, Stochastic methods for the prediction of
complex multiscale phenomena, Q. Appl. Math., 56:741-765, 1998.
J. Glimm and D. H. Sharp, Prediction and the quantification of
uncertainty, Physica D, 133: 152-170, 1999.
I. Hlavacek, J. Chleboun, and I. Babuska, Uncertain Input Data Problems
and the Worst Scenario Method, Elsevier, 2004.
J. Oakley and A. O'Hagan, Bayesian inference for the uncertainty
distribution of computer model outputs, Biometrika 89:769-784, 2002.
W. L. Oberkampf, J. C. Helton, C. A. Joslyn, S. F. Wojtkiewicz, and
S. Ferson, Uncertainty in system response given uncertain parameters,
Reliability Engineering and System Safety 85:11-19, 2004.
W. L. Oberkampf, T. G. Trucano and C. Hirsch, Verification, validation,
and predictive capability in computational engineering and physics,
Appl. Mech. Rev., 57:345-384, 2004.
M. T. Reagan, H. N. Najm, P. P. Pebay, O. M. Knio and R. G. Ghanem,
Quantifying uncertainty in chemical systems modeling, Internat. J.
Chem. Kinetics, 37:368-386, 2005.
W. Schoutens, Stochastic Processes and Orthogonal Polynomials,
Springer, 2000.
C. Soize and R. Ghanem, Physical systems with random uncertainties:
Chaos representations with arbitrary probability measure, SIAM J.
Sci. Comput. 26:395-410, 2004.
D. B. Xiu and G. E. Karniadakis, The Wiener-Askey polynomial chaos for
stochastic differential equations, SIAM J. Sci. Comput. 24:619-644, 2002.
D. B. Xiu and G. E. Karniadakis, Modeling uncertainty in flow simulations
via generalized polynomial chaos, J. Comput. Physics, 187:137-167, 2003.
D. B. Xiu, C.-H. Lucor and G. E. Karniadakis, Stochastic modeling of
flow-structure interactions using generalized polynomial chaos, J.
Fluids Engrg. 124:51-59, 2002.
X. Wan and G. E. Karniadakis, An adaptive multi-element generalized
polynomial chaos method for stochastic differential equations,
J. Comput. Phys. 209:617-642, 2005.
X. Wan and G. E. Karniadakis, Beyond Wiener-Askey expansions: handling
arbitrary PDFs, SIAM J. Sci. Comput. 28:455-464, 2006.
X. Wan and G. E. Karniadakis, Multi-element generalized polynomial
chaos for arbitrary probability measures, SIAM J. Sci. Comput.
28:901-928, 2006.
J. Wang and N. Zabaras, Hierarchical Bayesian models for inverse
problems in heat conduction, Inverse Problems 21:183-206, 2005.
N. S. Wiener, The homogeneous chaos, Amer. J. Math., 60:897-936, 1938.
