Accuracy and Limitations of the Resistor Network Used for Solving Laplace's and Poisson's Equations

Abstract

A resistor network developed for the solution of electron-optical problems is described. New, improved methods for simulating arbitrary boundary conditions with high accuracy are given. The sources of error are discussed. The error is defined by the dislocation of an equipotential, as determined with the network, from its correct position. It is measured in units of the distance between two nodes of the network, called an "interval." For a homogeneous field, the maximum error is below one hundredth of an interval. In most practical problems, the maximum error is well below one tenth of an interval.