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 journalArticlepeer-review

5 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 languageEnglish (US)
Pages (from-to)507-525
Number of pages19
JournalComputer Methods in Applied Mechanics and Engineering
Volume317
DOIs
StatePublished - Apr 15 2017
Externally publishedYes

Bibliographical note

Funding Information:
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.

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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