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    On a Goal-Oriented Version of the Proper Generalized Decomposition Method

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    Type
    Article
    Authors
    Kergrene, Kenan
    Chamoin, Ludovic
    Laforest, Marc
    Prudhomme, Serge
    KAUST Grant Number
    CRG3
    OCRF-2014-CRG
    Date
    2019-02-11
    Permanent link to this record
    http://hdl.handle.net/10754/668693
    
    Metadata
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    Abstract
    In this paper, we introduce, analyze, and numerically illustrate a goal-oriented version of the Proper Generalized Decomposition method. The objective is to derive a reduced-order formulation such that the accuracy in given quantities of interest is increased when compared to a standard Proper Generalized Decomposition method. Traditional goal-oriented methods usually compute the solution of an adjoint problem following the calculation of the primal solution for error estimation and adaptation. In the present work, we propose to solve the adjoint problem first, based on a reduced approach, in order to extract estimates of the quantities of interest and use this information to constrain the reduced primal problem. The resulting reduced-order constrained solution is thus capable of delivering more accurate estimates of the quantities of interest. The performance of the proposed approach is illustrated on several numerical examples.
    Citation
    Kergrene, K., Chamoin, L., Laforest, M., & Prudhomme, S. (2019). On a Goal-Oriented Version of the Proper Generalized Decomposition Method. Journal of Scientific Computing, 81(1), 92–111. doi:10.1007/s10915-019-00918-1
    Sponsors
    SP is grateful for the support by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada. He also acknowledges the support by KAUST under Award Number OCRF-2014-CRG3-2281. Moreover, the authors gratefully acknowledge Olivier Le Maître for fruitful discussions on the subject.
    Publisher
    Springer Nature
    Journal
    Journal of Scientific Computing
    DOI
    10.1007/s10915-019-00918-1
    Additional Links
    http://link.springer.com/10.1007/s10915-019-00918-1
    ae974a485f413a2113503eed53cd6c53
    10.1007/s10915-019-00918-1
    Scopus Count
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