Roger G. Ghanem

Learn More
The basic random variables on which random uncertainties can in a given model depend can be viewed as defining a measure space with respect to which the solution to the mathematical problem can be defined. This measure space is defined on a product measure associated with the collection of basic random variables. This paper clarifies the mathematical(More)
Olivier P. Le Maı̂tre,∗ Omar M. Knio,†,1 Habib N. Najm,‡ and Roger G. Ghanem§ ∗Centre d’Etudes de Mécanique d’Ile de France, Université d’Evry Val d’Essone, 40, rue du Pelvoux, 91020 Evry Cedex, France; †Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, Maryland 21218-2686; ‡Combustion Research Facility, Sandia National(More)
This paper gives an overview of the use of Polynomial Chaos expansions to represent stochastic processes in numerical simulations. Several methods are presented to perform arithmetic on, as well as to evaluate polynomial and non-polynomial functions of variables respresented with Polynomial Chaos expansions. These methods include Taylor series, a newly(More)
The particular properties of systems of linear equations arising in the context of the Stochastic Finite Element Method motivate the customization of existing iterative solution algorithms. The implementation described in this paper has aimed at optimizing data management, MAT-VEC operations and preconditioning strategies. It turns out that SFEM-systems can(More)
A spectral formalism has been developed for the “non-intrusive” analysis of parametric uncertainty in reacting-flow systems. In comparison to conventional Monte Carlo analysis, this method quantifies the extent, dependence, and propagation of uncertainty through the model system and allows the correlation of uncertainties in specific parameters to the(More)