Proper Generalized Decomposition computational methods on a benchmark problem : introducing a new strategy based on Constitutive Relation Error minimization

Pierre-Eric Allier 1 Ludovic Chamoin 1, 2 Pierre Ladevèze 1
2 MATHERIALS - MATHematics for MatERIALS
ENPC - École des Ponts ParisTech, CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique, Inria Paris-Rocquencourt
Abstract : First, the effectivity of classical Proper Generalized Decomposition (PGD) computational methods is analyzed on a one dimensional transient diffusion benchmark problem, with a moving load. Classical PGD methods refer to Galerkin, Petrov–Galerkin and Minimum Residual formulations. A new and promising PGD computational method based on the Constitutive Relation Error concept is then proposed and provides an improved, immediate and robust reduction error estimation. All those methods are compared to a reference Singular Value Decomposition reduced solution using the energy norm. Eventually, the variable separation assumption itself (here time and space) is analyzed with respect to the loading velocity.
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Advanced Modeling and Simulation in Engineering Sciences, SpringerOpen, 2015, 2 (17), 〈10.1186/s40323-015-0038-4〉
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https://hal.archives-ouvertes.fr/hal-01241744
Contributeur : Ludovic Chamoin <>
Soumis le : jeudi 10 décembre 2015 - 23:02:30
Dernière modification le : samedi 23 mars 2019 - 01:29:32

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Pierre-Eric Allier, Ludovic Chamoin, Pierre Ladevèze. Proper Generalized Decomposition computational methods on a benchmark problem : introducing a new strategy based on Constitutive Relation Error minimization. Advanced Modeling and Simulation in Engineering Sciences, SpringerOpen, 2015, 2 (17), 〈10.1186/s40323-015-0038-4〉. 〈hal-01241744〉

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