Structure-preserving model reduction for dynamical systems with a first integral

TL;DR

This paper introduces new structure-preserving model reduction methods for large dynamical systems with a first integral, ensuring the reduced models retain key properties and improve computational efficiency.

Contribution

The paper presents novel model reduction techniques that preserve the first integral in dynamical systems, enhancing accuracy and stability over existing methods.

Findings

Reduced models preserve the first integral.

Numerical experiments show improved stability.

Energy-preserving integrators enhance performance.

Abstract

Since the expense of the numerical integration of large scale dynamical systems is often computationally prohibitive, model reduction methods, which approximate such systems by simpler and much lower order ones, are often employed to reduce the computational effort. In this paper, for dynamical systems with a first integral, new structure-preserving model reduction approaches are presented that yield reduced-order systems while preserving the first integral. We apply energy-preserving integrators to the reduced-order systems and show some numerical experiments that demonstrate the favourable behaviour of the proposed approaches.