Design of optimized FDTD schemes for the accurate solution of electromagnetic problems

In this paper, we develop a set of two-dimensional finite-difference time-domain (FDTD) schemes, capable of minimizing dispersion errors according to problem-related requirements. Their performance is optimized within either a narrow or wide frequency band, by requiring the minimization of an error estimator at selected frequency points. By properly utilizing a series expansion of the estimator, accuracy improvement is ensured regardless of the propagation angle. Contrary to standard FDTD approaches, the design procedure is proven to efficiently exploit the potential of higher order operators, as the developed techniques attain significantly lower error levels, at no or low additional computational cost