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An in-depth stability analysis of nonuniform FDTD combined with novel local implicitization techniques

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 nonunifor...

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Bibliographic Details
Published in:Journal of computational physics 2017-08, Vol.342, p.177-193
Main Authors: Van Londersele, Arne, De Zutter, Daniël, Vande Ginste, Dries
Format: Article
Language:English
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Summary: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. •A novel Newmark-beta FDTD method is proposed in 3D.•The leapfrog ADHIE-FDTD method is for the first time proposed.•A Courant-like time step limit, less stringent than the currently known limits, is found for conventional nonuniform FDTD.•The stability of three local implicitization techniques is rigorously analyzed (in the algebraic sense).•The stability of the proposed implicitization techniques is numerically validated by a cavity example.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2017.04.036