DSP-based stability framework for the analysis of the explicit and the implicit frequency dependent finite difference time domain methods

In this paper, digital signal processing (DSP) stability framework is presented for the analysis of the explicit and the implicit frequency dependent finite difference time domain (FDTD) methods. The stability of the formulations is studied in the Z-domain by using the the root-locus method. In addition, the material's conductivity is modeled in the frequency domain by a [2/2] Padé-approximation function and implemented in the discrete time domain by means of the bilinear frequency approximation technique. Numerical simulation is included to verify the obtained theoretical stability results.