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hal-00752810, version 1

Reduced-Order Modeling based on Approximated Lax Pairs

Jean-Frédéric Gerbeau (, http://www-rocq.inria.fr/who/Jean-Frederic.Gerbeau/) 1, Damiano Lombardi () 1

N° RR-8137 (2012)

Abstract: A reduced-order model algorithm, based on approximations of Lax pairs, is proposed to solve nonlinear evolution partial differential equations. Contrary to other reduced-order methods, like Proper Orthogonal Decomposition, the space where the solution is searched for evolves according to a dynamics specific to the problem. It is therefore well-suited to solving problems with progressive waves or front propagation. Numerical examples are shown for the KdV and FKPP (nonlinear reaction diffusion) equations, in one and two dimensions.

  • 1:  REO (INRIA Paris-Rocquencourt)
  • INRIA – Laboratoire Jacques-Louis Lions – Université Pierre et Marie Curie (UPMC) - Paris VI
  • Domain : Mathematics/Numerical Analysis
  • Keywords : Reduced Order Modeling – Lax Pair – Scattering Transform – KdV – FKPP
  • Internal note : RR-8137
 
  • hal-00752810, version 1
  • oai:hal.inria.fr:hal-00752810
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  • Submitted on: Friday, 16 November 2012 15:01:27
  • Updated on: Saturday, 17 November 2012 21:12:02