Leakage-Free Leapfrog ADI-FDTD Method for Lossy Media

The leapfrog alternating direction implicit finite-difference time-domain (ADI-FDTD) method, as an effective implementation of ADI-FDTD, has garnered widespread attention and extension. However, it has been found that the commonly used leapfrog ADI-FDTD method for lossy media exhibits field leakage whereby nonzero electromagnetic fields could leak through structures that should be nonpenetrable, such as perfect electrical conductor structures. This numerical flaw limits the broader application of the leapfrog ADI-FDTD method. To address this issue, this article introduces a leapfrog ADI-FDTD method for lossy media free from field leakage. The method is derived from the unified ADI-FDTD formulation employing the fundamental scheme with matrix-operator-free right-hand sides. Numerical results demonstrate that the method is not only immune to field leakage issue but also yielding higher accuracy when modeling lossy media. Furthermore, due to the utilization of the fundamental scheme, it requires less computational operations compared with the conventional leapfrog ADI-FDTD method for lossy media.