Lyapunov and Matrix Norm Stability Analysis of ADI-FDTD Schemes for Doubly Lossy Media

Lyapunov and matrix norm stability analysis is applied on various alternating-direction-implicit finite-difference time-domain (ADI-FDTD) schemes for doubly lossy media. The stability analysis is performed rigorously in both time and Fourier domains. Among the schemes considered are averaging, forward-backward, backward-forward, forward-forward, exponential time differencing and backward-backward. From the analysis, it is found that all schemes except backward-backward scheme are unconditionally stable. For backward-backward scheme, the condition for stability is determined.