Extended-PGD Model Reduction for Nonlinear Solid Mechanics Problems Involving Many Parameters

  • P. Ladevèze
  • Ch. Paillet
  • D. Néron
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 46)


Reduced models and especially those based on Proper Generalized Decomposition (PGD) are decision-making tools which are about to revolutionize many domains. Unfortunately, their calculation remains problematic for problems involving many parameters, for which one can invoke the “curse of dimensionality”. The paper starts with the state-of-the-art for nonlinear problems involving stochastic parameters. Then, an answer to the challenge of many parameters is given in solid mechanics with the so-called “parameter-multiscale PGD”, which is based on the Saint-Venant principle.


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© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.LMT (ENS Paris-Saclay, CNRS, Université Paris-Saclay)Cachan CedexFrance

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