HIGH-ACCURACY SOLUTION OF MAXWELLS 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. Th is algorithm is some 10,000 times more accurate than the standard one on a coarse grid. Although computational load per grid point is greate r, 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 st ability is greater, so that the number of iterations needed is also re duced. While optimum performance is achieved at a fixed frequency, the accuracy is still higher than that of the standard-algorithm over mod erate bandwidths. The algorithm is implemented in Fortran 90 and can e asily model spatially variant media and irregular boundaries. By displ aying one. or more fields per wave period we obtain on-line movielike visualizations of the electromagnetic fields while the computation is running. (C) 1997 American Institute of Physics.