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

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...

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Bibliographic Details
Published in:Advanced modeling and simulation in engineering sciences 2015-07, Vol.2 (1), Article 17
Main Authors: Allier, Pierre-Eric, Chamoin, Ludovic, Ladevèze, Pierre
Format: Article
Language:English
Subjects:
Classical and Continuum Physics
Computational Science and Engineering
Engineering
Mechanics
Physics
Research Article
Structural mechanics
Theoretical and Applied Mechanics
Verification and validation for and with reduced order modeling
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Summary: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.
ISSN:2213-7467
2213-7467
DOI:10.1186/s40323-015-0038-4