Accelerating the magnetic field iterative solutions

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.