Low-Frequency Electromagnetic Fields and Finite Element Method

  • Zhiguang ChengEmail author
  • Norio Takahashi (deceased)


Electromagnetic field analysis is the basis for solving the engineering coupled electromagnetic and thermal field problems. Based on the low-frequency Maxwell’s equations, some key problems concerning the formulations and numerical implementations of typical 3-D eddy current analysis methods, using different potential sets, such as A-V-A (or employing a reduced vector magnetic potential Ar to convert to Ar-V-Ar) and T-Ψ-Ψ, are briefly explained. Furthermore, the numerical solvers based on different potential sets have been developed by the author’s group and verified in the Testing Electromagnetic Analysis Methods (TEAM) benchmarking practices. In this chapter, the Galerkin weighted residual method, a key technique in numerical implementation, is elaborated, and the effectiveness of edge element, for example, in effectively reducing computational cost in industrial applications is discussed. Strengthening the theoretical basis of finite element analysis of electromagnetic fields and correctly understanding the significance of the combination of advanced numerical computation with accurate material property modeling will be more helpful in improving the effectiveness of modeling and simulation and further promoting the use of simulation in industrial applications.


Low-frequency electromagnetic field Finite element method Potential set Nodal element Edge element Galerkin weighted residual technique Formulation and implementation 



This work was supported in part by the Natural Science Foundation of China (no. 59277296 and no. 59924035). In particular, the author appreciates the support of the leaders concerned and thanks all the colleagues for joint development of 3-D eddy current field solvers for years.


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© Science Press, Beijing and Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Institute of Power Transmission and Transformation TechnologyBaobian ElectricBaodingChina
  2. 2.Okayama UniversityOkayamaJapan

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