Locally-Conformal FDTD for Anisotropic Conductive Interfaces

Locally-conformal discretizations have been developed for the finite-difference time-domain (FDTD) method to mitigate staircasing errors that arise in the modeling of arbitrary (e.g., curved, slanted) interfaces by regular orthogonal grids. In particular, locally-conformal algorithms based on the computation of effective material parameters in partially-filled FDTD cells are attractive because they are simple to implement and maintain the basic conditional stability of FDTD, with only minor changes on the Courant limit. In this paper, we propose a new locally-conformal implementation for FDTD tailored for anisotropic conductive interfaces. Instead of employing arithmetic or geometrical averages, we invoke the quasi-static relationship between the current density and the electric field to derive the effective conductivities of partially-filled FDTD cells.