Further Reinterpretation of Multi-Stage Implicit FDTD Schemes

This communication presents further reinterpretation of multi-stage implicit finite-difference time-domain (FDTD) schemes. The equivalence of several multi-stage split-step (SS) schemes is shown based on amplification matrices and power property of eigenvalues in dispersion relations. In doing so, the explicit expressions for dispersion relations need not be derived, thus amenable to 3D and generalized multi-stage SS schemes conveniently. The improvement of temporal accuracy for generalized multi-stage SS schemes using generalized input and output processing matrices is also provided. It is further shown that the SS, alternating-direction-implicit (ADI) as well as the recently proposed divergence-preserving (DP) ADI schemes can be interpreted based on the more concise matrix exponential.