The Lobatto Cell: Robust, Explicit, Higher Order FDTD That Handles Inhomogeneous Media

Abstract

To improve numerical dispersion and second-order convergence behavior of the traditional Yee finite-difference time-domain (FDTD) algorithm, various higher order finite difference implementations have been proposed. Many have difficulty handling interfaces between distinct dielectric media or metallic sheets, because the high-order Taylor expansions on which these codes are based are invalidated by field or derivative discontinuities. One-sided extensions/extrapolations are a common approach to remedy interface discontinuities. Here, another approach based upon Whitney form, mass lumped finite elements is pursued to develop the ldquoLobatto Cell,rdquo a high-order replacement for the Yee cell with appropriate continuity behavior at contrasting media interfaces. The Lobatto Cell retains many robust features of the Yee method (discrete conservation laws, a guarantee of conditional stability and straightforward explicit updating), but provides higher order interpolation and dispersion error convergence. A notable drawback of the method is larger modeling granularity (staircasing), which is managed here by combining the Lobatto Cell method with preexisting, robust subgridding techniques.