Calculation of electric fields by digital computer

Abstract

Laplacian electric-field distributions are usually obtained with the aid of an electrolytic tank or other analogue means. Alternatively, it is possible to investigate such fields using numerical methods. The paper describes a method by which finite-difference equations are set up, for multidielectric fields in two dimensions or in three dimensions with at least one axis of symmetry, from the fundamental Laplace equation. Because these finite-difference equations are solved by an exact noniterative method, it is possible to cover any range of permittivities and boundary shapes. The accuracy of the computer results is governed by the accuracy of the difference equations, which depends on the fineness of the grid used to cover the field. Results from extensive validation studies are reported, and comparisons are made with results obtained using other techniques.