Unified Formulation of Leapfrog Complying Divergence Implicit FDTD Method for Lossy Media

The leapfrog alternating direction implicit finite-difference time-domain (ADI-FDTD) method for lossy media has been found to suffer from the nonphysical field leakage problem in the non-penetrable structures, which gives rise to inaccuracies in modeling lossy media during scattering analyses. To address such problem, in this article, we propose a unified formulation of leapfrog complying divergence implicit (CDI)-finite-difference time-domain (FDTD) method for lossy media without field leakage problem. Several different lossy schemes to incorporate the conductivity terms of lossy media, including exponential time differencing (ETD), averaging, and forward–forward schemes, are integrated into a unified formulation. The proposed leapfrog CDI-FDTD method not only resolves the problem of field leakage but also has complying divergence. Moreover, since the implicit update procedures in the proposed formulation are in the fundamental form with matrix-operator-free right-hand sides (RHS), the floating-point operations (flops) are fewer than that of the conventional leapfrog ADI-FDTD formulation for lossy media. Numerical results are given to demonstrate the advantages of the proposed method over the leapfrog ADI-FDTD method in accuracy, efficiency, complying divergence, and resolving the field leakage problem for lossy media.