A Port-Hamiltonian System Perspective on Electromagneto-Quasistatic Field Formulations of Darwin-Type

TL;DR

This paper analyzes electromagneto-quasistatic field formulations, specifically Darwin-type models, within the port-Hamiltonian system framework, demonstrating their stability and energy conservation properties based on the chosen gauge equations.

Contribution

It introduces a port-Hamiltonian perspective to EMQS formulations, showing how certain gauge choices lead to stable, energy-conserving models.

Findings

Port-Hamiltonian structure ensures numerical stability.

Certain gauge choices yield energy conservation.

Framework unifies EMQS models under a common stability analysis.

Abstract

Electromagneto-quasistatic (EMQS) field formulations are often dubbed as Darwin-type field formulations which approximate the Maxwell equations by neglecting radiation effects while modelling resistive, capacitive, and inductive effects. A common feature of EMQS field models is the Darwin-Amp\'ere equation formulated with the magnetic vector potential and the electric scalar potential. EMQS field formulations yield different approximations to the Maxwell equations by choice of additional gauge equations. These EMQS formulations are analyzed within the port-Hamiltonian system (PHS) framework. It is shown via the PHS compatibility equation that formulations based on the combination of the Darwin-Amp\'ere equation and the full Maxwell continuity equation yield port-Hamiltonian systems implying numerical stability and specific EMQS energy conservation.