Asynchronous time integration for polynomial chaos expansion of uncertain periodic dynamics
type: Item
instance of: scholarly article
title: Asynchronous time integration for polynomial chaos expansion of uncertain periodic dynamics
zbMATH Open document ID: 1198.37072
author: O. Le Maître
author: L. Mathelin
author: Omar M. Knio
author: M. Yousuff Hussaini
published in: Discrete and Continuous Dynamical Systems
publication date: 2010-06-23T00:00:00Z
review text: In this work quantifying the uncertainty associated with time dependent physical systems involving random parameters is explored. The simulation of such systems requires the basis dimension and computational resources for long time integration. This paper proposed the development of a computational approach based on a reformulation of the problem. Two variants of this approach are considered and evaluated. The first relies on an explicit expression to some distance between the corresponding solution on a reference deterministic system. The second variant achieves the same objective by concepts from optimal control theory, and yields more precise estimates at the price of a higher CPU cost, that is more appropriate for uncertain systems. As examples, the method applied to the case of a linear oscillator with uncertain properties, and to a stiff nonlinear chemical system involving uncertain reaction constants or rates. The tests show that the effectiveness of the proposed approaches, where the topology of the limit cycle does not change when the uncertain system parameters vary.
reviewed by: Gasanbek T. Arazov
Mathematics Subject Classification ID: 37F10
zbMATH DE Number: 5725460
zbMATH Keywords: dynamical systems
zbMATH Keywords: uncertainty
zbMATH Keywords: polynomial chaos
MaRDI profile type: Publication
full work available at URL: dcds.2010.28.199
OpenAlex ID: W2029289838
DOI: 10.3934/DCDS.2010.28.199
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description: scientific article; zbMATH DE number 5725460