研究目的
Investigating the structural properties of various formulations for the simulation of electromagnetic fields derived from Maxwell’s equations, with a focus on their differential-algebraic character and differential index.
研究成果
The paper concludes with a discussion on various formulations for low and high-frequency problems in computational electromagnetics, highlighting that most formulations lead to systems of low DAE index (≤2). It emphasizes the mitigation of index-2 problems in A–φ-potential formulation with a Coulomb gauge through reformulation based on Lorenz’ gauge.
研究不足
The paper focuses on theoretical analysis and does not address specific technical constraints or optimization areas for experimental setups.
1：Experimental Design and Method Selection:
The paper reviews classical formulations for simulating electromagnetic fields derived from Maxwell’s equations, focusing on their structural properties and differential-algebraic character.
2：Sample Selection and Data Sources:
The study is theoretical, focusing on the analysis of differential-algebraic equations (DAEs) in computational electromagnetics.
3：List of Experimental Equipment and Materials:
Not applicable as the study is theoretical.
4：Experimental Procedures and Operational Workflow:
The paper discusses the spatial discretisation of Maxwell’s equations using the finite element method and the finite integration technique, and analyzes the resulting DAEs.
5：Data Analysis Methods:
The differential index concept is used to quantify the difficulty of the numerical time-domain solution of the DAEs.
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