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Consistency of the numerical dispersion relation expressed in different forms for the ADI-FDTD method

✍ Scribed by An Ping Zhao

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 58 KB
Volume: 40
Category: Article
ISSN: 0895-2477
DOI: 10.1002/mop.11272

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✦ Synopsis

Abstract

The relationship of the numerical dispersion relation presented in different mathematical expressions (that are independently derived in 1, 2) for the three‐dimensional alternating direction implicit finite‐difference time‐domain (3D ADI‐FDTD) method is investigated. It is found that, unlike the statement made in 2, the formulae of the numerical dispersion relation proposed in 1, 2 are unconditionally equivalent to each other, as they can be transformed from one to another, which in turn demonstrates the consistency of these formulae. The consistency of the formulae expressed in different forms derived for the one‐dimensional and two‐dimensional cases is also demonstrated, as a by‐product of this paper. Furthermore, it is found that the formulae expressed in the form of tan(ωΔ__t__/2) have the simplest and most convenient forms for the ADI‐FDTD method. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 40: 12–13, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11272

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