Advanced Topics

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

Abstract

This chapter addresses some advanced topics whose development remains work in progress. The first topic concerns the efficient treatment of non-linear models where standard strategies can fail for high-dimensional problems. The second topic concerns the use of advective stabilization when the involved fields are approximated in a separated form. Finally, we introduce a discrete form of the PGD solver, the one that we consider in computer implementations, that is then extended for considering a separated representation constructor based on residual minimization. Residual minimization is particularly suitable for addressing non-symmetric differential operators, for which the standard procedure described in the previous chapters can be inefficient (slow convergence and non-optimal representations).

Keywords

Advection-Diffusion equation Discrete representation Nonlinear models Residual minimization 

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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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