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Introducing Nonuniform Grids into the FDTD Solution of the Transmission-Line Equations by Renormalizing the Per-Unit-Length Parameters

A challenging aspect of using the finite-difference time-domain (FDTD) method to solve nonuniform transmission-line equations is to choose a discretization grid with an adequate spatial resolution. When the per-unit-length parameters have strong variations, an efficient problem-solving strategy requires the use of a nonuniform discretization grid. This paper presents a nonuniform gridding method that makes use of an analytically defined coordinate transformation to map a nonuniformly spaced grid onto a uniformly spaced grid where the standard FDTD time stepping equations can be applied. This approach absorbs all the details of the nonuniform grid into effective or renormalized per-unit-length parameters.