Header

UZH-Logo

Maintenance Infos

Model order reduction for parametrized nonlinear hyperbolic problems as an application to uncertainty quantification


Crisovan, R; Torlo, D; Abgrall, Rémi; Tokareva, S (2019). Model order reduction for parametrized nonlinear hyperbolic problems as an application to uncertainty quantification. Journal of Computational and Applied Mathematics, 348:466-489.

Abstract

In this work, we present a model order reduction (MOR) technique for hyperbolic conservation laws with applications in uncertainty quantification (UQ). The problem consists of a parametrized time dependent hyperbolic system of equations, where the parameters affect the initial conditions and the fluxes in a non- linear way. The procedure utilized to reduce the order is a combination of a Greedy algorithm in the parameter space, a proper orthogonal decomposition (POD) in time and empirical interpolation method (EIM) to deal with non-linearities (Drohmann, 2012). We provide under some hypothesis an error bound for the reduced solution with respect to the high order one. The algorithm shows small errors and savings of the computational time up to 90% in the UQ simulations, which are performed to validate the algorithm.

Abstract

In this work, we present a model order reduction (MOR) technique for hyperbolic conservation laws with applications in uncertainty quantification (UQ). The problem consists of a parametrized time dependent hyperbolic system of equations, where the parameters affect the initial conditions and the fluxes in a non- linear way. The procedure utilized to reduce the order is a combination of a Greedy algorithm in the parameter space, a proper orthogonal decomposition (POD) in time and empirical interpolation method (EIM) to deal with non-linearities (Drohmann, 2012). We provide under some hypothesis an error bound for the reduced solution with respect to the high order one. The algorithm shows small errors and savings of the computational time up to 90% in the UQ simulations, which are performed to validate the algorithm.

Statistics

Citations

Dimensions.ai Metrics
3 citations in Web of Science®
2 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

0 downloads since deposited on 30 Apr 2019
1 download since 12 months

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Applied Mathematics, Computational Mathematics
Language:English
Date:1 March 2019
Deposited On:30 Apr 2019 15:16
Last Modified:25 Sep 2019 00:06
Publisher:Elsevier
ISSN:0377-0427
OA Status:Closed
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1016/j.cam.2018.09.018
Project Information:
  • : FunderSNSF
  • : Grant ID200021_153604
  • : Project TitleHigh fidelity simulation for compressible material

Download

Closed Access: Download allowed only for UZH members