Approximation of constrained problems using the PGD method with application to pure Neumann problems

Kenan Kergrene; Serge Prudhomme; Ludovic Chamoin; Marc Laforest

doi:10.1016/j.cma.2016.12.023

Approximation of constrained problems using the PGD method with application to pure Neumann problems

Kenan Kergrene, Serge Prudhomme^*, Ludovic Chamoin, Marc Laforest

^*Corresponding author for this work

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

6 Scopus citations

Abstract

In this paper we introduce, analyze, and compare several approaches designed to incorporate a linear (or affine) constraint within the Proper Generalized Decomposition framework. We apply the considered methods and numerical strategies to two classes of problems: the pure Neumann case where the role of the constraint is to recover unicity of the solution; and the Robin case, where the constraint forces the solution to move away from the already existing unique global minimizer of the energy functional.

Original language	English (US)
Pages (from-to)	507-525
Number of pages	19
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	317
DOIs	https://doi.org/10.1016/j.cma.2016.12.023
State	Published - Apr 15 2017
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2016 Elsevier B.V.

Keywords

Constrained problem
Low-rank approximation
Mixed formulation
Model reduction
Proper Generalized Decomposition (PGD)
Tensor product approximation

ASJC Scopus subject areas

Computational Mechanics
Mechanics of Materials
Mechanical Engineering
General Physics and Astronomy
Computer Science Applications

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10.1016/j.cma.2016.12.023

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abstract = "In this paper we introduce, analyze, and compare several approaches designed to incorporate a linear (or affine) constraint within the Proper Generalized Decomposition framework. We apply the considered methods and numerical strategies to two classes of problems: the pure Neumann case where the role of the constraint is to recover unicity of the solution; and the Robin case, where the constraint forces the solution to move away from the already existing unique global minimizer of the energy functional.",

keywords = "Constrained problem, Low-rank approximation, Mixed formulation, Model reduction, Proper Generalized Decomposition (PGD), Tensor product approximation",

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

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doi = "10.1016/j.cma.2016.12.023",

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T1 - Approximation of constrained problems using the PGD method with application to pure Neumann problems

AU - Kergrene, Kenan

AU - Prudhomme, Serge

AU - Chamoin, Ludovic

AU - Laforest, Marc

PY - 2017/4/15

Y1 - 2017/4/15

N2 - In this paper we introduce, analyze, and compare several approaches designed to incorporate a linear (or affine) constraint within the Proper Generalized Decomposition framework. We apply the considered methods and numerical strategies to two classes of problems: the pure Neumann case where the role of the constraint is to recover unicity of the solution; and the Robin case, where the constraint forces the solution to move away from the already existing unique global minimizer of the energy functional.

AB - In this paper we introduce, analyze, and compare several approaches designed to incorporate a linear (or affine) constraint within the Proper Generalized Decomposition framework. We apply the considered methods and numerical strategies to two classes of problems: the pure Neumann case where the role of the constraint is to recover unicity of the solution; and the Robin case, where the constraint forces the solution to move away from the already existing unique global minimizer of the energy functional.

KW - Constrained problem

KW - Low-rank approximation

KW - Mixed formulation

KW - Model reduction

KW - Proper Generalized Decomposition (PGD)

KW - Tensor product approximation

UR - http://www.scopus.com/inward/record.url?scp=85009160767&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2016.12.023

DO - 10.1016/j.cma.2016.12.023

M3 - Article

AN - SCOPUS:85009160767

SN - 0045-7825

VL - 317

SP - 507

EP - 525

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

ER -

Approximation of constrained problems using the PGD method with application to pure Neumann problems

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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