Recursive low-rank approximation and model reduction of second-order systems

TL;DR

This paper adapts low-rank approximation techniques from first-order to second-order systems, ensuring structure preservation and demonstrating effectiveness through numerical benchmarks.

Contribution

It introduces a method to extend low-rank approximation techniques to second-order systems while maintaining their physical structure.

Findings

Reduced models preserve second-order structure.

Numerical simulations confirm approximation quality.

Method applicable to benchmark examples.

Abstract

We present an adaptation of two recent low-rank approximation technique proposed for first-order model reduction systems to the second-order systems. The resulting reduced order models are guaranteed to keep the second order structure which has a physical meaning. The quality of the approximation is shown using numerical simulations on benchmark examples.