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An a posteriori verification procedure for PGD reduced models

Abstract : Despite the important progress in computer sciences, the cost associated with the resolution of multi-parametric problems can be extremely prohibitive. This is especially important when dealing with problems depending on numerous parameters, as encountered in optimization studies which are becoming more and more mandatory for the design of new products. Reduced Order Modelling (ROM) are a good answer to circumvent this issue, usually called curse of dimensionality. However, the main drawback of ROM is the lack of a robust error estimator to measure the quality of the approximated solution, even if several a priori and a posteriori error estimators for them have already been proposed. This paper defines an a posteriori verification procedure that enables to control and certify PGD-based model reduction techniques, a particularly promising technique which is currently the subject of many research activities. Because of the absence of PGD’s error estimator in the literatures, such procedure is a first one. Using the concept of constitutive relation error, we show that we can get guaranteed global/goal-oriented error estimator taking both discretization and PGD truncation error into accounts. By splitting the errors sources, it also leads to a natural greedy adaptive strategy which can be driven in order to optimize the accuracy of PGD approximation. The key point of that method is the construction of an admissible solution by only post-processing the PGD one, allowing the reuse of classical constitutive relation error technique initially developed for the finite element methods. The focus of the talk is on two technical points: (i) construction of equilibrated fields required to compute guaranteed error bounds; (ii) error splitting and adaptive process when performing PGD-based model reduction.
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https://hal.archives-ouvertes.fr/hal-01216317
Contributor : Pierre-Eric Allier <>
Submitted on : Friday, October 16, 2015 - 9:44:25 AM
Last modification on : Tuesday, May 14, 2019 - 10:18:12 AM

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  • HAL Id : hal-01216317, version 1

Citation

Pierre-Eric Allier, Ludovic Chamoin, Pierre Ladevèze. An a posteriori verification procedure for PGD reduced models. Conférence Internationale de Géotechnique, des Ouvrages et Structures, May 2015, Cachan, France. ⟨hal-01216317⟩

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