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- Alireza Doostan, Houman Owhadi
- J. Comput. Physics
- 2011

Article history: Received 10 June 2010 Received in revised form 24 October 2010 Accepted 4 January 2011 Available online 9 January 2011

- Jerrad Hampton, Alireza Doostan
- J. Comput. Physics
- 2015

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

- Alireza Doostan, Gianluca Iaccarino
- J. Comput. Physics
- 2009

Uncertainty quantification schemes based on stochastic Galerkin projections, with global or local basis functions, and also stochastic collocation methods in their conventional form, suffer from the so called curse of dimensionality: the associated computational cost grows exponentially as a function of the number of random variables defining the underlying… (More)

We present the variational multiscale (VMS) method for partial differential equations (PDEs) with stochastic coefficients and source terms. We use it as a method for generating accurate coarse-scale solutions while accounting for the effect of the unresolved fine scales through a model term that contains a fine-scale stochastic Green’s function. For a… (More)

This paper demonstrates the use of polynomial chaos expansions (PCEs) for the nonlinear, non-Gaussian propagation of orbit state uncertainty. Using linear expansions in tensor-products of univariate orthogonal polynomial bases, PCEs approximate the stochastic solution of the ordinary differential equation describing the propagated orbit, and include… (More)

- Ji Peng, Jerrad Hampton, Alireza Doostan
- J. Comput. Physics
- 2014

- Tonkid Chantrasmi, Alireza Doostan, Gianluca Iaccarino
- J. Comput. Physics
- 2009

A novel uncertainty propagation method for problems characterized by highly non-linear or discontinuous system responses is presented. The approach is based on a Padé–Legendre (PL) formalism which does not require modifications to existing computational tools (nonintrusive approach) and it is a global method. The paper presents a novel PL method for… (More)

We present a numerical method to study convective heat transfer in a high Reynolds number incompressible flow around a cylinder subject to uncertain boundary conditions. We exploit the one-way coupling of the energy and momentum transport to derive a semi-intrusive uncertainty propagation scheme, which combines Galerkin and collocation approaches for… (More)

This paper presents the application of polynomial chaos (PC) to estimating the probability of collision between two spacecraft. Common methods of quantifying this probability for conjunction assessment use either Monte Carlo analyses or include simplifying assumptions to improve tractability. A PC expansion, or PCE, provides a means for approximating the… (More)