Introduction

  • Francisco Chinesta
  • Roland Keunings
  • Adrien Leygue
Chapter
Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)

Abstract

This chapter summarizes several recurrent issues related to efficient numerical simulations of problems encountered in engineering sciences. In order to alleviate such issues, model reduction techniques constitute an appealing alternative to standard discretization techniques. First, reduction techniques based on Proper Orthogonal Decompositions are revisited. Their use is illustrated and discussed, suggesting the interest of a priori separated representations which are at the heart of the Proper Generalized Decomposition (PGD). The main ideas behind the PGD are described, underlying its potential for addressing standard computational mechanics models in a non-standard way, within a new computational engineering paradigm. The chapter ends with a brief overview of some recent PGD applications in different areas, proving the potentiality of this novel technique.

Keywords

Inverse analysis Model Order Reduction Multidimensional models Optimization Parametric solutions Proper Generalized Decomposition Proper Orthogonal Decomposition Real time Separated representations Shape optimization Simulation based control Simulation Based Engineering Virtual charts 

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Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Francisco Chinesta
    • 1
  • Roland Keunings
    • 2
  • Adrien Leygue
    • 1
  1. 1.GeM UMR CNRSEcole Centrale de NantesNantes Cedex 3France
  2. 2.Applied MathematicsUniversité catholique de LouvainLouvain-la-NeuveBelgium

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