Operator splitting for coupled linear port-Hamiltonian systems

TL;DR

This paper develops operator splitting algorithms for coupled linear port-Hamiltonian systems that preserve their structure, are second-order convergent, and demonstrate improved efficiency over traditional methods in numerical experiments.

Contribution

The paper introduces structure-preserving, second-order convergent operator splitting algorithms specifically designed for coupled linear port-Hamiltonian systems, exploiting scalar coupling and multirate potential.

Findings

Algorithms preserve dissipative structure

Second-order convergence achieved

Numerical results show improved efficiency

Abstract

Operator splitting methods tailored to coupled linear port-Hamiltonian systems are developed. We present algorithms that are able to exploit scalar coupling, as well as multirate potential of these coupled systems. The obtained algorithms preserve the dissipative structure of the overall system and are convergent of second order. Numerical results for coupled mass-spring-damper chains illustrate the computational efficiency of the splitting methods compared to a straight-forward application of the implicit midpoint rule to the overall system.