Improved Unconditionally Stable FDTD Method for 3-D Wave-Propagation Problems

The findings of this paper prove that the direct implementation of fourth-order operators in the alternating-direction-implicit finite-difference time-domain algorithm is not the most consistent way to improve its accuracy. Instead of applying the standard expressions, a methodology that exploits the scheme's dispersion relation is introduced, so that space-time errors are balanced as equally as possible. After applying a matching-terms approach, new operator coefficients are extracted that depend on cell shape and time-step size. The resulting scheme offers an order of magnitude smaller error over practically all frequencies of interest, verifying the successful implementation of dispersion-reducing practices in this unconditionally stable technique.