Conformal FDTD-methods to avoid time step reduction with and without cell enlargement

During the last decades there have been considerable efforts to develop accurate and yet simple conformal methods for modelling curved boundaries within the finite difference time domain (FDTD) algorithm. In an earlier publication we proposed the uniformly stable conformal (USC) approach as a general three-dimensional extension of FDTD without the need to reduce the maximum stable time step. The main idea of USC is the usage of virtually enlarged cells near to the boundary, leading to an increased implementation effort. In this paper we review the USC method and introduce a new simple and accurate conformal scheme which does not use such enlarged cells. This simplified conformal (SC) scheme has the same number of operations and algorithmic logic as the standard “staircase” method, and thus is easily realizable in existing FDTD codes. Like USC, it leads to accurate results without time step reduction, showing a nearly second order convergence in practice. The method is verified and compared to other approaches by means of several numerical 2D and 3D examples.