In this paper, we study the class of linear elastodynamic problems with a ne parameter dependence using a goal-oriented approach by finite element (FE) and reduced basis (RB) methods. The main contribution of this paper is the "goal-oriented" proper orthogonal decomposition (POD)-Greedy sampling strategy within the RB approximation context. The proposed sampling strategy looks for the parameter points such that the output error approximation will be minimized by Greedy iterations. In estimating such output error approximation, the standard POD-Greedy algorithm is invoked to provide enriched RB approximations for the FE outputs. We propose a so-called "cross-validation" process to choose adaptively the dimension of the enriched RB space corresponding with the dimension of the RB space under consideration. Numerical results show that the new goal-oriented POD-Greedy sampling procedure with the cross-validation process improves signi ficantly the space-time output computations in comparison with the ones computed by the standard POD-Greedy algorithm. The method is thus ideally suited for repeated, rapid and reliable evaluations of input-output relationships in the space-time setting.
Research center :
Institute of Mechanics and Advanced Materials
Disciplines :
Mathematics Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Hoang, K. C.
Kerfriden, P.
Khoo, B. C.
Bordas, Stéphane ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit
External co-authors :
yes
Language :
English
Title :
An efficient goal-oriented sampling strategy using reduced basis method for parametrized elastodynamic problems
Publication date :
2015
Journal title :
Numerical Methods for Partial Differential Equations
ISSN :
1098-2426
Publisher :
John Wiley & Sons, Hoboken, United States - New Jersey
Special issue title :
MAFELAP 2013 Special Issue of Numerical Methods for Partial Differential Equations
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