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Fourth‐order finite‐difference time‐domain method based on error‐controlling concepts
Author(s) -
Zygiridis Theodoros T.
Publication year - 2012
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/jnm.845
Subject(s) - finite difference time domain method , truncation error , operator (biology) , narrowband , algorithm , computer science , truncation (statistics) , harmonic , mathematics , wideband , finite difference , mathematical analysis , telecommunications , optics , physics , biochemistry , chemistry , repressor , quantum mechanics , machine learning , transcription factor , gene
SUMMARY Conventional finite‐difference time‐domain (FDTD) methodologies incorporate discrete operators with the smallest truncation errors, as those are determined from the application of Taylor expansions. It is generally accepted that such choices, although quite efficient, do not necessarily provide optimum solutions when simulating electromagnetic wave phenomena. With the aim at improving accuracy without increasing the involved computational burden, the present paper is concerned with the development of a higher‐order FDTD algorithm, which, in contrast to classic trends, is primarily based on the application of error‐controlling ideas to its difference approximations. In essence, a fourth‐order scheme is presented, whose spatial expressions are designed to remedy the leading terms of suitable error formulae. The latter can be easily extracted for each operator, given that the general nature of the expected solutions is known in advance. A correction factor is next added to the temporal operators to compensate for remaining errors at a selected wavelength. Unlike other approaches with single‐frequency optimization, our technique is not strictly narrowband but capable of outperforming the conventional fourth‐order FDTD algorithm in wideband simulations as well, without further modifications. The properties of the proposed scheme are verified through theoretical studies, as well as harmonic and multifrequency numerical tests, where comparisons with other standard techniques are performed. Copyright © 2012 John Wiley & Sons, Ltd.