Computing electrical potential in unbounded two‐dimensional regions

Abstract

Finite difference and finite element methods have serious limitations when applied to unbounded regions. This paper describes a hybrid method which uses a conformal transformation to map the original boundaries, including those at infinity, to a bounded region and only then applies a numerical method based on finite differences or finite elements when no direct solution is obvious. Testing this approach by means of examples for which exact solutions are obtainable, the hybrid method is applied to determine the electrical potential at specific points in the field of a capacitor with long plates that in their cross‐sectional view are parallel to each other, and in the field of a microstrip line at some distance from it. In both the cases, the results are in agreement with analytically derived results. The method is simple, readily applied by undergraduate students, yet accurate and thus of use in professional engineering work as well.