An Efficient One-Step Leapfrog WCS-FDTD Method

For solving the electromagnetic problems with fine structures in two directions, this letter presents an efficient three-dimensional (3-D) one-step leapfrog weakly conditionally stable finite-difference time-domain (WCS-FDTD) method, in which the updating manner of field quantities is the same as that of the traditional FDTD method that electric and magnetic fields are calculated at every full time-step but interlaced half a step apart in both time and space. Furthermore, by introducing an auxiliary field variable group denoted by $m$ , the proposed algorithm is reformulated in a much simpler form with more concise right-hand sides for an efficient implementation. Compared to the original WCS scheme in Chen and Wang's work (IEEE Trans. Electromagn. Compat., vol. 49, no. 2, pp. 419–426, May 2007), the proposed method is more efficient while keeping the same numerical properties.