Discrete formulation of Maxwell equations

Abstract

The simplest possible discretization of the Maxwell equations is described. Unlike most discretizations, it preserves the symmetries and conservation laws that make electrodynamics an elegant and appealing subject. It is suitable for undergraduate courses in electromagnetic theory but also surprisingly competitive with analytical techniques for problems with low symmetry (i.e., most practical problems). It is argued that a discrete approach is a more natural way to introduce a field theory than the traditional continuum approach.