Simulation of multi-dimensional non-gaussian non-stationary random fields

By Shigehiro Sakamoto, Roger G. Ghanem. 2002

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A multi‐scale spectral stochastic method for homogenization of multi‐phase periodic composites with random material properties (2010, methodology): “Sakamoto and Ghanem, almost at the same time utilized one-dimensional Hermite expansions, Karhunen–Loeve transform and Polynomial Chaos expansion to cast a second-order random process with given marginal probability density and correlation functions in the form of a Polynomial Chaos expansion [25, 2”
Fast Numerical Methods for Stochastic Computations: A Review (2009, background): “This remains an active research, see, for example, [32, 60, 61, 63, 70, 102].”
Numerical Methods and Smolyak Quadrature for Nonlinear Stochastic Partial Differential Equations (2003, unknown): “[43].”
Bridging the scales in nano engineering and science (2006, unknown): “The error due to uncertainty can be estimated by the statistical sampling of data and numerical experiments (Ghanem & Pellissetti, 2002; Sakamoto & Ghanem, 2002 ).”
High-Order Collocation Methods for Differential Equations with Random Inputs (2005, background): “, [23, 45, 58]) and is beyond the scope of this paper.”