Differential forms provide an elegant formulation of electromagnetic field theory. Their geometric structure also leads to a self-consistent scheme for discretizing Maxwell’s equations in conducting media. This discretization, which is essentially a staggered-grid scheme, preserves differential operator identities, conservation laws, and physical boundary conditions.
The self-consistent scheme has been implemented in a code to model transient electromagnetic fields in a half-space with a step-function current excitation. For small conductivity contrasts results from the self-consistent scheme agree very well with results from a 3-D integral-equation code and from a staggered-grid finite-difference code. For high contrasts, though, the results from the integral-equation code differ. The difference may be a result of improper discretization of the integral equation.