Numerical Calculations of Three-Dimensional Magnetic Fields Using SER

Abstract
A technique for improving the rate of convergence of the solution of field problems by the method of finite differences called SER (successive extrapolated relaxation) has been developed. Sufficient saving in computing time is obtained by the method so that it is feasible to solve three‐dimensional field problems. This method uses conventional overrelaxation for every three iterations and then extrapolates simultaneously to the solution using a modification of Aitken's formula. In this paper, this method is applied to obtain the field in three dimensions from “T bar” circuits used for propagating magnetic bubbles. Symmetry considerations have been used so that the analysis is required over only one half of the propagating period. The permalloy circuit is idealized for these calculations.