Approximated Lax Pairs for the Reduced Order Integration of Nonlinear Evolution Equations

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, called ALP, is proposed to solve nonlinear evolution partial differential equations. It is based on approximations of generalized Lax pairs. Contrary to other reduced-order methods, like Proper Orthogonal Decomposition, the basis on which the solution is searched for evolves in time according to a dynamics specific to the problem. It is therefore well-suited to solving problems with progressive front or wave propagation. Another difference with other reduced-order methods is that it is not based on an off-line / on-line strategy. Numerical examples are shown for the linear advection, KdV and FKPP equations, in one and two dimensions.
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Jean-Frédéric Gerbeau, Damiano Lombardi. Approximated Lax Pairs for the Reduced Order Integration of Nonlinear Evolution Equations. Journal of Computational Physics, Elsevier, 2014, 265, pp.246-269. ⟨10.1016/j.jcp.2014.01.047⟩. ⟨hal-00933172⟩

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