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

D. Amsallem; U. Hetmaniuk

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2014)

  • Volume: 48, Issue: 1, page 135-163
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Amsallem, D., and Hetmaniuk, U.. "Error estimates for Galerkin reduced-order models of the semi-discrete wave equation." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 48.1 (2014): 135-163. <http://eudml.org/doc/273305>.

@article{Amsallem2014,
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.},
author = {Amsallem, D., Hetmaniuk, U.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {model order reduction; proper orthogonal decomposition; wave equation; Galerkin reduced-order models; Newmark schemes; second-order structure preservation; convergence acceleration; semidiscretization; error estimates; numerical experiments},
language = {eng},
number = {1},
pages = {135-163},
publisher = {EDP-Sciences},
title = {Error estimates for Galerkin reduced-order models of the semi-discrete wave equation},
url = {http://eudml.org/doc/273305},
volume = {48},
year = {2014},
}

TY - JOUR
AU - Amsallem, D.
AU - Hetmaniuk, U.
TI - Error estimates for Galerkin reduced-order models of the semi-discrete wave equation
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2014
PB - EDP-Sciences
VL - 48
IS - 1
SP - 135
EP - 163
AB - 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.
LA - eng
KW - model order reduction; proper orthogonal decomposition; wave equation; Galerkin reduced-order models; Newmark schemes; second-order structure preservation; convergence acceleration; semidiscretization; error estimates; numerical experiments
UR - http://eudml.org/doc/273305
ER -

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