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

Kenan Kergrene; Ludovic Chamoin; Marc Laforest; Serge Prudhomme

doi:10.1007/s10915-019-00918-1

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

Kenan Kergrene, Ludovic Chamoin, Marc Laforest, Serge Prudhomme

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

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.

Original language	English (US)
Pages (from-to)	92-111
Number of pages	20
Journal	Journal of Scientific Computing
Volume	81
Issue number	1
DOIs	https://doi.org/10.1007/s10915-019-00918-1
State	Published - Feb 11 2019
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2021-04-13
Acknowledged KAUST grant number(s): CRG3, OCRF-2014-CRG
Acknowledgements: 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

ASJC Scopus subject areas

Computational Theory and Mathematics
Theoretical Computer Science
Software
General Engineering

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10.1007/s10915-019-00918-1

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title = "On a Goal-Oriented Version of the Proper Generalized Decomposition Method",

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.",

author = "Kenan Kergrene and Ludovic Chamoin and Marc Laforest and Serge Prudhomme",

note = "KAUST Repository Item: Exported on 2021-04-13 Acknowledged KAUST grant number(s): CRG3, OCRF-2014-CRG Acknowledgements: 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 Ma{\^i}tre for fruitful discussions on the subject. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

year = "2019",

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doi = "10.1007/s10915-019-00918-1",

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AU - Kergrene, Kenan

AU - Chamoin, Ludovic

AU - Laforest, Marc

AU - Prudhomme, Serge

N1 - KAUST Repository Item: Exported on 2021-04-13 Acknowledged KAUST grant number(s): CRG3, OCRF-2014-CRG Acknowledgements: 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. This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2019/2/11

Y1 - 2019/2/11

N2 - 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.

AB - 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.

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JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

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

Abstract

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