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Error estimates for Galerkin reduced-order models of the semi-discrete wave equation

Published online by Cambridge University Press:  18 December 2013

D. Amsallem  and
U. Hetmaniuk
D. Amsallem
Affiliation:
Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305, USA.. amsallem@stanford.edu
U. Hetmaniuk
Affiliation:
Department of Applied Maths, University of Washington, Box 353925, Seattle, WA 98195-3925, USA.; hetmaniu@uw.edu
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Abstract

Galerkin reduced-order models for the semi-discrete wave equation, that preserve the second-order structure, are studied. Error bounds for the full state variables are derived in the continuous setting (when the whole trajectory is known) and in the discrete setting when the Newmark average-acceleration scheme is used on the second-order semi-discrete equation. When the approximating subspace is constructed using the proper orthogonal decomposition, the error estimates are proportional to the sums of the neglected singular values. Numerical experiments illustrate the theoretical results.

Keywords

Model order reductionproper orthogonal decompositionwave equation
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 48 , Issue 1 , January 2014 , pp. 135 - 163
Copyright
© EDP Sciences, SMAI 2013

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