The 1D ADI-FDTD Method in Lossy Media

A stability and numerical dispersion analysis for the one-dimensional alternating-direction implicit finite-difference time-domain method in lossy media is presented. To conduct a general study, the conduction term is approximated by a weighted average in time. The stability analysis is based on the von Neumann method and the numerical dispersion relation is derived in a closed-form. The analytical results are validated by numerical simulations, showing that errors for both the attenuation and phase constants can be very high if the weighted-average coefficients are not properly selected.