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

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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https://hal.archives-ouvertes.fr/hal-01216233
Contributor : Pierre-Eric Allier <>
Submitted on : Thursday, October 15, 2015 - 6:09:58 PM
Last modification on : Friday, May 24, 2019 - 5:29:35 PM

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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, ⟨10.1186/s40323-015-0038-4⟩. ⟨hal-01216233⟩

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