Systems of Differential Algebraic Equations in Computational Electromagnetics
It provides a literature review for researchers in computational electromagnetics, but is incremental as it summarizes existing work without new results.
This paper surveys common formulations for simulating electromagnetic fields from space-discretized Maxwell's equations, focusing on their structural properties and differential-algebraic character quantified by the differential index concept.
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.