An equation-free, multiscale approach to uncertainty quantification

Dongbin Xiu, Yannis Kevrekidis, Roger Ghanem

Research output: Contribution to journalArticle

34 Scopus citations

Abstract

An equation-free, multiscale computational method to uncertainty quantification (UQ) that combines sampling methods with nonsampling methods is proposed. The method uses short bursts of appropriately initialized sampling runs to estimate quantities arising in Stochastic Galerkin (SG) methods. The method is also used to integrate the nonlinear dynamical equations in SG projections and present computations of their fixed points and limit cycles. The fixed-point of the system are computed through short bursts of dynamic simulation, combining it with matrix-free techniques of iterative linear algebra. The method also combines the simplicity of MC simulations with the power and convergence of nonsampling generalized polynomial chaos (gPC) representations.

Original languageEnglish (US)
Pages (from-to)16-23
Number of pages8
JournalComputing in Science and Engineering
Volume7
Issue number3
DOIs
StatePublished - May 1 2005

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Engineering(all)

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