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Analytical solution to the FDTD scalar-wave equation

✍ Scribed by Paul Aoyagi; Jin-Fa Lee; Makoto Katsurai

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
139 KB
Volume
20
Category
Article
ISSN
0895-2477

No coin nor oath required. For personal study only.

✦ Synopsis

A general analytical solution to the finite-difference time-(

) domain FDTD scalar-wa¨e equation is deri¨ed in terms of its initial conditions using Fourier analysis. The fundamental sources of FDTD modeling error, namely, phase and sampling errors, are demonstrated by comparing this expression with a corresponding analytical solution to the continuous scalar-wa¨e equation. A detailed analysis of the phase error is gi¨en which pro¨es mathematically why increasing the time step will decrease error rather than increase it. This explanation, in turn, is used to conclude that the FDTD approximation will, in general, suffer from less numerical dispersion than a frequency-domain finite-difference approximation of the same order. In addition, it is shown that sources can exist implicitly in the FDTD scalar-wa¨e formulation, e¨en though no such sources are explicitly defined. By accounting for these implicit sources, the equi¨alence between the FDTD scalar-wa¨e equation and the Yee algorithm is demonstrated.

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