Multiscale stochastic preconditioners in non-intrusive spectral projection


Journal Article

A preconditioning approach is developed that enables efficient polynomial chaos (PC) representations of uncertain dynamical systems. The approach is based on the definition of an appropriate multiscale stretching of the individual components of the dynamical system which, in particular, enables robust recovery of the unscaled transient dynamics. Efficient PC representations of the stochastic dynamics are then obtained through non-intrusive spectral projections of the stretched measures. Implementation of the present approach is illustrated through application to a chemical system with large uncertainties in the reaction rate constants. Computational experiments show that, despite the large stochastic variability of the stochastic solution, the resulting dynamics can be efficiently represented using sparse low-order PC expansions of the stochastic multiscale preconditioner and of stretched variables. The present experiences are finally used to motivate several strategies that promise to yield further advantages in spectral representations of stochastic dynamics. © 2011 Springer Science+Business Media, LLC.

Full Text

Duke Authors

Cited Authors

  • Alexanderian, A; Le Maître, OP; Najm, HN; Iskandarani, M; Knio, OM

Published Date

  • February 1, 2012

Published In

Volume / Issue

  • 50 / 2

Start / End Page

  • 306 - 340

International Standard Serial Number (ISSN)

  • 0885-7474

Digital Object Identifier (DOI)

  • 10.1007/s10915-011-9486-2

Citation Source

  • Scopus