ABSTRACT
Contrary to the finite-element method, the guiding principle of the finite-volume method, is not to arrive at piece-wise continuous approximations of the exact solutions but one is satisfied with a discretized representation of the exact solution at some discrete set of space-time points. In order to discuss the numerical consequences of the fact that the vector potential needs to be assigned to the links of the grid this chapter considers an example. It introduces a ghost field that needs to be added in order to avoid singular and/or non-square systems of equations. The chapter explains how one can exploit the gauge equations to reduce matrix fill-in in solving the full-wave Maxwell system in which the currents are self-consistently obtained from the field solutions. It then introduces a new gauge condition which is a variation of the Coulomb gauge condition.
