Operator splitting for semi-explicit differential-algebraic equations and port-Hamiltonian DAEs

TL;DR

This paper develops operator splitting methods tailored for coupled index-1 DAEs and port-Hamiltonian DAEs, leveraging their structural properties to improve numerical solution efficiency and accuracy.

Contribution

It introduces a novel splitting approach that respects the energy structure of port-Hamiltonian DAEs and coupled index-1 systems, with proven second-order convergence.

Findings

Numerical examples confirm second-order convergence.

Method effectively handles energy-conservative and dissipative parts.

Applicable to complex coupled DAE systems.

Abstract

Operator splitting methods allow to split the operator describing a complex dynamical system into a sequence of simpler subsystems and treat each part independently. In the modeling of dynamical problems, systems of (possibly coupled) differential-algebraic equations (DAEs) arise. This motivates the application of operator splittings which are aware of the various structural forms of DAEs. Here, we present an approach for the splitting of coupled index-1 DAE as well as for the splitting of port-Hamiltonian DAEs, taking advantage of the energy-conservative and energy-dissipative parts. We provide numerical examples illustrating our second-order convergence results.