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

  • Kenan Kergrene
  • Ludovic Chamoin
  • Marc Laforest
  • Serge PrudhommeEmail author


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.


Model reduction Quantities of interest Constrained problem Mixed formulation Penalization Lagrange multiplier 



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.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Kenan Kergrene
    • 1
  • Ludovic Chamoin
    • 2
  • Marc Laforest
    • 1
  • Serge Prudhomme
    • 1
    Email author
  1. 1.Département de mathématiques et de génie industrielPolytechnique MontréalMontréalCanada
  2. 2.LMT ENS Paris-Saclay/CNRS/Université Paris-SaclayCachanFrance

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