A multidimensional inverse Z-transform evaluation of the discrete time domain Green´s function

The FDTD algorithm can also be converted into an integral formulation with an appropriate Green´s function within the context of the same grid. In this work, we present a derivation from spectral domain representations obtained from the difference equations via a multidimensional Z-transform. The details of the two-step inverse transform are shown, leading to a closed form representation of the discrete Green´s function in the time domain. This procedure is shown to retrieve the results obtained in Rospsha and Kastner, as well as the direct, numerical evaluation in Holtzman and Kastner (2001) both for the one-dimensional case with z = z´.