Article (Scientific journals)
An efficient goal-oriented sampling strategy using reduced basis method for parametrized elastodynamic problems
Hoang, K. C.; Kerfriden, P.; Khoo, B. C. et al.
2015In Numerical Methods for Partial Differential Equations, 31 (2), p. 575-608
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Keywords :
goal-oriented; wave equation; space-time domain; goal-oriented asymptotic error; goal-oriented POD–Greedy algorithm; reduced basis method; model reduction
Abstract :
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
Volume :
31
Issue :
2
Pages :
575-608
Peer reviewed :
Peer Reviewed verified by ORBi
Focus Area :
Computational Sciences
European Projects :
FP7 - 279578 - REALTCUT - Towards real time multiscale simulation of cutting in non-linear materials with applications to surgical simulation and computer guided surgery
Name of the research project :
RealTCut
Funders :
FP7
CE - Commission Européenne [BE]
Commentary :
cited By 0 Scopus
Available on ORBilu :
since 16 November 2016

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