Operator Splitting Based Dynamic Iteration for Linear Port-Hamiltonian Systems

TL;DR

This paper introduces a novel operator splitting-based dynamic iteration scheme for linear port-Hamiltonian systems, ensuring monotonic error reduction without stability constraints, applicable to multibody and electrical systems.

Contribution

It presents a new operator splitting-based dynamic iteration method specifically for linear port-Hamiltonian systems, with proven monotonic convergence and broad applicability.

Findings

Error decreases monotonically during iteration

Applicable to multibody systems and electrical networks

No stability conditions required for convergence

Abstract

A dynamic iteration scheme for linear differential-algebraic port-Hamil\-tonian systems based on Lions-Mercier-type operator splitting methods is developed. The dynamic iteration is monotone in the sense that the error is decreasing and no stability conditions are required. The developed iteration scheme is even new for linear port-Hamiltonian systems. The obtained algorithm is applied to multibody systems and electrical networks.