Reduced-Order Modeling based on Approximated Lax Pairs

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.

Cited by in corpus (3)

• Approximated Lax Pairs for the Reduced Order Integration of Nonlinear Evolution Equations
• $h$ and $hp$-adaptive Interpolation by Transformed Snapshots for Parametric and Stochastic Hyperbolic PDEs
• Transformed Snapshot Interpolation with High Resolution Transforms