Discretization of Dirac systems and port-Hamiltonian systems: the role of the constraint algorithm

TL;DR

This paper develops discretization methods for Dirac and port-Hamiltonian systems using retraction and discretization maps, integrating these with constraint algorithms to improve numerical simulation of implicit differential equations.

Contribution

It introduces a novel discretization approach for Dirac structures and port-Hamiltonian systems, combining geometric methods with constraint algorithms.

Findings

Effective discretization techniques for Dirac structures

Numerical integrators for port-Hamiltonian systems

Unified framework for discretization and constraints

Abstract

We study the discretization of (almost-)Dirac structures using the notion of retraction and discretization maps on manifolds. Additionally, we apply the proposed discretization techniques to obtain numerical integrators for port-Hamiltonian systems and we discuss how to merge the discretization procedure and the constraint algorithm associated to systems of implicit differential equations.