Use of Non-uniform Grids for Reduced Spatial Sampling in FDTD Simulation

An algorithm for the generation of non-uniform finite-difference grids for the analysis of electrically long wave propagating structures is presented. The methodology is based on the use of a Pade-Chebyshev approximation of the input impedance of the discrete model of the electrically-long dimension of the structure, generated using an equidistant grid, and the subsequent use of the Lanczos algorithm to cast the approximation in terms of a reduced-order model that is interpreted in terms of a non-uniform grid of reduced spatial sampling. A numerical study is used to demonstrate that structures with non-uniform material properties can be modeled using a non-uniform grid constructed for the simpler case of a uniform structure.