Recent years have witnessed considerable research activity in the application of digital-computer methods for the determination of the electromagnetic fields in electrical devices through the solution of Maxwell's equations, while taking full account of the magnetic saturation. Slow rate of convergence towards a meaningful solution and consequent demand for prohibitively large computer time are some of the chief drawbacks of the numerical iterative procedures. Many efforts have been made to find satisfactory methods of accelerating the convergence and thereby minimize the computer time needed for the solution. Various methods such as application of relaxation factors, block-relaxation procedures; and alternating-direction iterative techniques have been developed. It is the purpose of this paper to present a new method of computing an appropriate optimum relaxation factor for the reluctivity at each grid point (in 2-dimensions) or lattice point (in 3-dimensions) depending on the value of the local flux density and its location on the magnetization characteristic.


Author's manuscript; originally published in IEEE Transactions on Magnetics, Vol. MAG-12, No 6, pp.1042-1044, November 1976.


electrical devices, iterative solutions, Maxwell's equations, digital computer methods, local flux density, optimum relaxation factors, reluctivity

Subject Categories

Magnetic fields, Electromagnetic fields


Electromagnetics and photonics



Publication Date


Rights Information

(c) 1976 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.

Rights Holder


Click button above to open, or right-click to save.