Recent years have witnessed considerable research activity in the application of digital-computer methods for the determination of the electromagnetic fields in electrical machinery through the solution of Maxwell's equations, while taking full account of the magnetic saturation. Two distinct numerical approaches are evident in the literature: Finite-Difference Method and Finite Element Method. The author has presented in the recent years a finite-difference formulation for 3-dimensional numerical solutions of the nonlinear electromagnetic field problems in terms of potential functions, and has applied for the analysis of the end-zone fields of aerospace homopolar alternators and solid-rotor induction motors. The present work is directed towards the finite-element formulation for the numerical solution problems. A variational principle is developed here utilizing the vector potential concept. The approach is based on variational methods in which a corresponding energy functional for the nonlinear case is minimized over the entire region. The minimization is performed by means of the finite-element method and the resulting set of nonlinear algebraic equations is solved through iterative schemes.


Author's manuscript; originally published in IEEE Transactions on Magnetics, Vol. MAG-12, No. 6, pp. 1045-46, Nov 1976.


magnetostatic field computation, digital computer methods, electrical machinery, Maxwell's equations, FEA, FEM, aerospace homopolar alternators, solid rotor induction motors, magnetic saturation

Subject Categories

Electromagnetic fields, Finite element method, Finite differences


Electromagnetics and photonics



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