%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