Reduced-Order Modeling based on Approximated Lax Pairs
Numerical Analysis
2012-11-20 v1
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.
Cite
@article{arxiv.1211.4153,
title = {Reduced-Order Modeling based on Approximated Lax Pairs},
author = {Jean-Frédéric Gerbeau and Damiano Lombardi},
journal= {arXiv preprint arXiv:1211.4153},
year = {2012}
}