A general method for introducing nonuniform grids into high-order FDTD methods: Formulation and microwave applications

This paper introduces a nonuniform gridding scheme that can be applied to any finite-difference time-domain method with an arbitrarily high order of accuracy. The most attractive feature of the proposed scheme is that it preserves the simplicity of the p-th order accurate update equations on a uniform grid. It is shown that all the details of a nonuniform grid can be absorbed into effective constitutive parameters through a coordinate system transformation. By using the proposed step summing transformation, a nonuniformly spaced grid can be mapped onto a uniformly spaced grid where a standard set of p-th order accurate update equations can be applied.