%0 Journal Article
%T Approximated Lax Pairs for the Reduced Order Integration of Nonlinear Evolution Equations
%+ Numerical simulation of biological flows (REO)
%A Gerbeau, Jean-Frédéric
%A Lombardi, Damiano
%< avec comité de lecture
%Z RR-8454
%@ 0021-9991
%J Journal of Computational Physics
%I Elsevier
%V 265
%P 246-269
%8 2014-05-15
%D 2014
%Z 1401.4829
%R 10.1016/j.jcp.2014.01.047
%K Reduced Order Modeling
%K Lax Pair
%K KdV
%K FKPP
%Z Mathematics [math]/Numerical Analysis [math.NA]Journal articles
%X 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.
%G English
%2 https://inria.hal.science/hal-00933172/document
%2 https://inria.hal.science/hal-00933172/file/RR-8454.pdf
%L hal-00933172
%U https://inria.hal.science/hal-00933172
%~ UNIV-PARIS7
%~ UPMC
%~ CNRS
%~ INRIA
%~ INRIA-ROCQ
%~ INSMI
%~ LJLL
%~ INRIA_TEST
%~ TESTALAIN1
%~ INRIA2
%~ TDS-MACS
%~ UPMC_POLE_1
%~ SORBONNE-UNIVERSITE
%~ SU-SCIENCES
%~ SU-SCI
%~ UNIV-PARIS
%~ SU-TI
%~ ALLIANCE-SU