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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:342

Article

Van Londersele, Arne¹  De Zutter, Daniel¹  Vande Ginste, Dries¹ 

[1] Univ Ghent, Electromagnet Grp, Dept Informat Technol, Imec,IDLab, Technol Pk Zwijnaarde 15, Ghent, Belgium

关键词: Finite-difference time-domain (FDTD);    Stability;    Nonuniform;    Newmark;    Crank-Nicolson (CN);    Alternating-direction-implicit (ADI);    Hybrid implicit-explicit (HIE);    Alternating-direction-hybrid-implicit-explicit (ADHIE);   

DOI  :  10.1016/j.jcp.2017.04.036

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free