Systems of Differential Algebraic Equations in Computational Electromagnetics

TL;DR

This paper surveys various differential algebraic equation formulations derived from Maxwell's equations for electromagnetic simulation, focusing on their structural properties and differential index to understand their mathematical characteristics.

Contribution

It provides a comprehensive literature review of classical formulations in computational electromagnetics emphasizing their differential-algebraic structure and properties.

Findings

Different formulations vary in phenomena considered and variables discretized.

The differential index concept helps quantify the algebraic complexity.

Structural properties influence the choice of numerical methods.

Abstract

Starting from space-discretisation of Maxwell's equations, various classical formulations are proposed for the simulation of electromagnetic fields. They differ in the phenomena considered as well as in the variables chosen for discretisation. This contribution presents a literature survey of the most common approximations and formulations with a focus on their structural properties. The differential-algebraic character is discussed and quantified by the differential index concept.