Solution of 2-dimensional field problems by boundary relaxation

Abstract

A numerical method is described for solution of 2-dimensional electric- and magnetic-field problems of the exterior type. Such problems are temporarily converted into interior problems by defining an arbitrary closed boundary, and then improving field values on the boundary iteratively, until a solution valid both within and without the artificial boundary is obtained. Within the boundary, the solution is found at a finite number of points, by any of the well known finite-difference methods. The final result is independent of the choice of artificial boundary, and corresponds exactly to the solution that would be obtained by applying finite-difference techniques to an infinite array of points. An empirical study of the convergence properties of this process is described, and typical computing speeds are indicated. Use of this method is illustrated by a variety of simple problems.