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Reduced-Order Modeling based on Approximated Lax Pairs

Jean-Frédéric Gerbeau 1 Damiano Lombardi 1 
1 REO - Numerical simulation of biological flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6
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.
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Submitted on : Friday, November 16, 2012 - 3:01:27 PM
Last modification on : Wednesday, October 26, 2022 - 8:16:25 AM
Long-term archiving on: : Saturday, December 17, 2016 - 11:49:09 AM


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  • HAL Id : hal-00752810, version 1
  • ARXIV : 1211.4153


Jean-Frédéric Gerbeau, Damiano Lombardi. Reduced-Order Modeling based on Approximated Lax Pairs. [Research Report] RR-8137, INRIA. 2012, pp.21. ⟨hal-00752810⟩



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