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Computational Mechanics

, Volume 54, Issue 6, pp 1529–1539 | Cite as

Virtual charts of solutions for parametrized nonlinear equations

  • Matthieu Vitse
  • David Néron
  • Pierre-Alain Boucard
Original Paper

Abstract

During many decades, engineers relied on experimental abaci to design and optimize mechanical structures. Virtual charts are based on numerical computations and aim at making the design and optimization of structures faster and cheaper as it requires less (or no) experimentation. The parametric problems are solved offline and the associated charts are used for online design. However, in this context, the cost associated to the resolution of parametric problems can be extremely prohibitive. Model reduction techniques are an answer to circumvent this issue. This paper provides the developments of an algorithm for solving nonlinear parametric problems, based on the LATIN method for the treatment of the nonlinear aspects and the PGD for the parameter dependency. A full time–space-parameter decomposition of the solution is introduced into the LATIN algorithm, numerical examples on academic problems are given so as to point out the advantages of this extension and leads on possible improvements to the strategy are given.

Keywords

Nonlinear problems Reduced order modeling Proper generalized decomposition Parametric problems LATIN solver 

Notes

Acknowledgments

This work carried out under the SINAPS@ project benefited French funding managed by the National Research Agency under the program “Future Investment” (SINAPS@ Reference No. ANR-11-RSNR-0022).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Matthieu Vitse
    • 1
  • David Néron
    • 1
  • Pierre-Alain Boucard
    • 1
  1. 1.LMT Cachan (ENS Cachan/CNRS/PRES UniverSud Paris)Cachan CedexFrance

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