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Model reduction using $L^1$ -norm minimization as an application to nonlinear hyperbolic problems


Abgrall, Rémi; Crisovan, R (2018). Model reduction using $L^1$ -norm minimization as an application to nonlinear hyperbolic problems. International Journal for Numerical Methods in Fluids, 87(12):628-651.

Abstract

We are interested in the model reduction techniques for hyperbolic problems, particularly in fluids. This paper, which is a continuation of an earlier paper of Abgrall et al, proposes a dictionary approach coupled with an L1 minimization approach. We develop the method and analyze it in simplified 1‐dimensional cases. We show in this case that error bounds with the full model can be obtained provided that a suitable minimization approach is chosen. The capability of the algorithm is then shown on nonlinear scalar problems, 1‐dimensional unsteady fluid problems, and 2‐dimensional steady compressible problems. A short discussion on the cost of the method is also included in this paper.

Abstract

We are interested in the model reduction techniques for hyperbolic problems, particularly in fluids. This paper, which is a continuation of an earlier paper of Abgrall et al, proposes a dictionary approach coupled with an L1 minimization approach. We develop the method and analyze it in simplified 1‐dimensional cases. We show in this case that error bounds with the full model can be obtained provided that a suitable minimization approach is chosen. The capability of the algorithm is then shown on nonlinear scalar problems, 1‐dimensional unsteady fluid problems, and 2‐dimensional steady compressible problems. A short discussion on the cost of the method is also included in this paper.

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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:Mechanical Engineering, Mechanics of Materials, Applied Mathematics, Computational Mechanics, Computer Science Applications
Language:English
Date:1 December 2018
Deposited On:17 Jan 2019 07:29
Last Modified:24 Sep 2019 23:30
Publisher:Wiley-Blackwell Publishing, Inc.
ISSN:0271-2091
OA Status:Closed
Publisher DOI:https://doi.org/10.1002/fld.4507
Project Information:
  • : FunderSNSF
  • : Grant ID200021_153604
  • : Project TitleHigh fidelity simulation for compressible material

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