A Z-transform matrix formulation for a tensor FDTD method

The finite-difference time-domain (FDTD) method remains one of the most widely used and versatile methods used in electromagnetic simulation. The simple structure of this method avoids complex mathematic formulations but is vulnerable to errors from the regular homogeneous cubes that make up the problem space. Recently, there has been activity to improve the accuracy without leaving the regular cubic structure of FDTD. However, a bottle-neck in the use of this approach with lossy media was the fact that a complex matrix had to be inverted. In this paper a Z-transform formulation is added to the tensor formulation to avoid the inversion of complex matrices, thereby facilitating its use in lossy media, an approach we call the tensor FDTD (TFDTD) formulation.