A leapfrog formulation of the 3D ADI-FDTD algorithm

We introduce a new, alternative form of the 3D alternating direction implicit finite-difference time-domain (ADI-FDTD) algorithm that has a number of attractive properties for electromagnetic simulation. We obtain a leapfrog form of the time advance equations, where the E- and H- fields are staggered at half-integer and integer time steps respectively, that preserves the unconditional stability of the ADI-FDTD method. The resulting equations resemble the explicit leapfrog FDTD method, but the field update equations are modified to include the solution of sets of tridiagonal equations at each step, similar to the original ADI-FDTD scheme, so that the scheme is not constrained by the Courant-Friedrichs-Lewy (CFL) limit. The algorithm is simpler than the ADI-FDTD method but algebraically equivalent, allowing a reduction in computation to achieve the same numerical solution. We discuss the advantages of the formulation over the original FDTD and ADI-FDTD methods, and confirm our results numerically.