A leapfrog formulation of the 3-D ADI-FDTD algorithm

We introduce a new, alternative form of the 3-D 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 tri-diagonal equations at each step, similar to the original ADI-FDTD scheme, so that the scheme is not constrained by the Courant-Friedrichs-Lewy 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.