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- Christian Soize, Roger G. Ghanem
- SIAM J. Scientific Computing
- 2004

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, Habib N. Najm, Roger G. Ghanem
- 2001

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)

- Bert J. Debusschere, Habib N. Najm, Philippe P. Pébay, Omar M. Knio, Roger G. Ghanem, Olivier P. Le Maître
- SIAM J. Scientific Computing
- 2004

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)

- Manuel F. Pellissetti, Roger G. Ghanem
- 2000

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)

- Roger G. Ghanem
- 1999

The spectral formulation of the stochastic finite-element method is applied to the problem of heat conduction in a random medium. Specifically, the conductivity of the medium, as well as its heat capacity are treated as uncorrelated random processes with spatial random fluctuations. Using the spectral stochastic finiteelement method, this paper analyzes the… (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)

- Roger G. Ghanem
- 1998

The mechanics of transport and ow in a random porous medium are addressed in this paper. The hydraulic properties of the porous medium are modeled as spatial random processes. The random aspect of the problem is treated by introducing a new dimension along which spectral approximations are implemented. Thus, the hydraulic processes are discretized using the… (More)

- Roger G. Ghanem, Alireza Doostan
- J. Comput. Physics
- 2006

- Roger G. Ghanem
- 1998

This study is concerned with developing a two-dimensional multiphase model that simulates the movement of NAPL in heterogeneous aquifers. Heterogeneity is dealt with in a probabilistic sense by modeling the intrinsic permeability of the porous medium as a stochastic process. The deterministic nite element method is used to spatially discretize the… (More)

- M. Arnst, Roger G. Ghanem, Christian Soize
- J. Comput. Physics
- 2010