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Application of local improvements to reduced-order models to sampling methods for nonlinear PDEs with noise

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Pages 870-880 | Received 12 Feb 2015, Accepted 14 Jun 2016, Published online: 16 Mar 2017
 

ABSTRACT

In this work, we extend upon the results of Raissi and Seshaiyer [A multi-fidelity stochastic collocation method for parabolic partial differential equations with random input data, Int. J. Uncertain. Quantif. 4(3) (2014), pp. 225–242]. In Raissi and Seshaiyer (2014), the authors propose to use deterministic model reduction techniques to enhance the performance of sampling methods like Monte-Carlo or stochastic collocation. However, in order to be able to apply the method proposed in Raissi and Seshaiyer (2014) to non-linear problems a crucial step needs to be taken. This step involves local improvements to reduced-order models. This paper is an illustration of the importance of this step. Local improvements to reduced-order models are achieved using sensitivity analysis of the proper orthogonal decomposition.

2010 MSC Subject Classifications:

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. The expert reader will notice that the term k=1dξkhk(t) approximates W˙(t), where W(t) is a Brownian motion.

2. Please refer to pages 10–11 of [Citation21] for a more detailed exposure.

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