This work focuses on efficient full-wave solutions of multiscale electromagnetic problems in the time domain. Three local implicitization techniques are proposed and carefully analyzed in order to relax the traditional time step limit of the Finite-Difference Time-Domain (FDTD) method on a nonuniform, staggered, tensor product grid: Newmark, Crank-Nicolson (CN) and Alternating-Direction-Implicit (ADI) implicitization. All of them are applied in preferable directions, alike Hybrid Implicit-Explicit (HIE) methods, as to limit the rank of the sparse linear systems. Both exponential and linear stability are rigorously investigated for arbitrary grid spacings and arbitrary inhomogeneous, possibly lossy, isotropic media. Numerical examples confirm the conservation of energy inside a cavity for a million iterations if the time step is chosen below the proposed, relaxed limit. Apart from the theoretical contributions, new accomplishments such as the development of the leapfrog Alternating-Direction-Hybrid-Implicit-Explicit (ADHIE) FDTD method and a less stringent Courant-like time step limit for the conventional, fully explicit FDTD method on a nonuniform grid, have immediate practical applications. (C) 2017 Elsevier Inc. All rights reserved

Abstract-The conventional Finite-Difference Time-Domain (FDTD) method with staggered Yee scheme does not easily allow including thin material layers, especially so if these layers are highly conductive. This paper proposes a novel subgridding technique for 2D problems, based on a Hybrid Implicit-Explicit (HIE) scheme, that efficiently copes with this problem. In the subgrid, the new method collocates field components such that the thin layer boundaries are defined unambiguously. Moreover, aspect ratios of more than a million do not impair the stability of the method and allow for very accurate predictions of the skin effect. The new method retains the Courant limit of the coarse Yee grid and is easily incorporated into existing FDTD codes. A number of illustrative examples, including scattering by a metal grating, demonstrate the accuracy and stability of the new method.

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This letter proposes a novel hybrid implicit-explicit finite-difference time-domain method with collocation in the direction of implicitization. In this direction, the method features increased accuracy, the reason being twofold: 1) the applied combination of interpolations and differentiations preserves second-order accuracy upon nonuniform discretization and 2) material boundaries are more accurately approximated by the grid. The method's stability and accuracy are verified by a microstrip line example. An appropriate PML is included