A more practical approach is to integrate Maxwell's equations in the time-domain using finite differences. This approach eliminates the large system of frequency-domain equations and yields a simple, fast algorithm that is well suited to pipelined or parallel computer architectures. There are two standard methods for spatial discretization of Maxwell's equations, finite differences and finite elements. Finite differences 3 are the oldest and the most efficient for structurally simple models. Finite elements are newer and better suited to structurally complex models, but increase the floating point operation count.
Speed turns out to be a secondary issue in most cases.
A critical issue for discrete solvers is grid truncation error caused by spurious reflections at the model's artificial boundaries. Radiation conditions are necessary to reduce this error. In time-domain analysis these are usually local relations among nodal boundary values derived from the paraxial wave equation 4 . However, higher order implementations tend to degrade in 3D vector domains. Also, the local phase velocity is required.