A High-Resolution Z-Transform Tensor Formulation of the FDTD Method

Abstract

A high-resolution FDTD formulation is presented by using a tensor formulation and Z transforms. This method is particularly effective in media with different types of material that vary rapidly. The method is implemented while maintaining the cubic structure of the FDTD paradigm and is applicable for lossless and lossy media. This is accomplished by a 3 x 3 matrix equation to relate the E field to the flux density, a formulation we refer to as the tensor FDTD (TFDTD) method. Z transforms are used for the transformation from the frequency domain to the sample time-domain.