DeepAI AI Chat
Log In Sign Up

Structure-preserving reduced-order modelling of Korteweg de Vries equation

04/18/2020
by   Bülent Karasözen, et al.
0

Computationally efficient, structure-preserving reduced-order methods are developed for the Korteweg de Vries (KdV) equations in Hamiltonian form. The KdV equation is discretized in space by finite differences. The resulting skew-gradient system of ordinary differential equations (ODEs) is integrated with the linearly implicit Kahan's method, which preserves the Hamiltonian approximately. We have shown, using proper orthogonal decomposition (POD), the Hamiltonian structure of the full-order model (FOM) is preserved by the reduced-order model (ROM). The quadratic nonlinear terms of the KdV equation are evaluated efficiently by the use of tensorial methods, clearly separating the offline-online cost of the FOMs and ROMs. The accuracy of the reduced solutions, preservation of the Hamiltonian, momentum and mass, and computational speed-up gained by ROMs are demonstrated for the one-dimensional KdV equation, coupled KdV equations and two-dimensional Zakharov-Kuznetzov equation with soliton solutions

READ FULL TEXT

page 1

page 2

page 3

page 4

11/02/2020

Structure-preserving reduced order modelling of thermal shallow water equation

Energy preserving reduced-order models are developed for the rotating th...
06/09/2020

Reduced order modelling of nonlinear cross-diffusion systems

In this work, we present a reduced-order model for a nonlinear cross-dif...
01/31/2022

Data-driven structure-preserving model reduction for stochastic Hamiltonian systems

In this work we demonstrate that SVD-based model reduction techniques kn...
11/29/2022

Data-driven identification of a 2D wave equation model with port-Hamiltonian structure

We consider a two-dimensional wave equation, for which the discretized v...
07/14/2022

Learning port-Hamiltonian systems – algorithms

In this article we study the possibilities of recovering the structure o...
09/23/2020

Port-Hamiltonian approximation of a nonlinear flow problem. Part I: Space approximation ansatz

This paper is on the systematic development of robust and online-efficie...
01/17/2020

Preservation of Equations by Monoidal Monads

If a monad T is monoidal, then operations on a set X can be lifted canon...