High accuracy solution of Maxwell’s equations using nonstandard finite differences

We introduce a new finite-difference time-domain algorithm to directly solve Maxwell’s equations based on nonstandard finite differences. This algorithm is some 10,000 times more accurate than the standard one on a coarse grid. Although computational load per grid point is greater, it is more than offset by a large reduction in the total number of grid points needed to solve a given problem. In addition, algorithm stability is greater, so that the number of iterations needed is also reduced. While optimum performance is achieved at a fixed frequency, the accuracy is still higher than that of the standard algorithm over moderate bandwidths. The algorithm is implemented in Fortran 90 and can easily model spatially variant media and irregular boundaries. By displaying one or more fields per wave period we obtain on-line movielike visualizations of the electromagnetic fields while the computation is running. © 1997 American Institute of Physics.