Since 1990, as computer resources have made it possible, interest in space-grid solvers for Maxwell's equations has exploded in the electromagnetic engineering community. Taflove was somewhat ahead of the curve in this trend, having pioneered such methods starting in 1972. These formulations use PDEs instead of integral equations, avoiding the dense matrices that the IE approach requires. The space-grid methods can more readily model complex material properties and inhomogeneities that determine the electromagnetic response of a structure, reducing the specification of a new structure to a problem of mesh generation rather than one of reformulating the underlying integral equation.

A major theme of this article is that such PDE solvers, especially when formulated in the time domain to incorporate nonlinear and dispersive effects over extremely large instantaneous bandwidths, are having a strong positive impact in two core areas of electrical engineering--electronic circuits, and optics--that have not been traditionally associated with rigorous electromagnetic field theory. To pursue this theme, Taflove summarizes some current highlights in finite-difference time-domain (FD-TD) electromagnetic wave modeling, ranging from the traditional application of military aircraft radar scattering to a novel application, the development of subpicosecond photonic switches. Such computed solutions to Maxwell's equations are leading to science and engineering advances that are particularly relevant in today's world.