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Four unequal substep FDTD (4 USS‐FDTD) method with extremely low numerical dispersion error
Author(s) -
Kusaf Mehmet,
Oztoprak Abdullah Y.
Publication year - 2018
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.2515
Subject(s) - finite difference time domain method , mathematics , anisotropy , mathematical analysis , dispersion (optics) , bandwidth (computing) , computer simulation , phase (matter) , physics , optics , computer science , quantum mechanics , telecommunications , statistics
A new unconditionally stable split‐step FDTD method is introduced which has unequal substeps. The ratio of the unequal substeps, τ , is utilized to obtain extremely low anisotropic errors. It is shown that for any set of space step and time step values, there is a τ value which gives zero anisotropic error. Polynomials are obtained in terms of time and space step sizes for τ and the average normalized numerical phase velocity which can be used to correct for anisotropic error and the average numerical phase velocity. The 2 polynomials can be integrated into the simulation programs, so that the user gets an almost unity normalized phase velocity in all directions, for any chosen time step size and space step size. In this way, large time steps up to Nyquist rate can be used. The method is also suitable for multidomain applications, which makes the method very efficient. A further study shows that the method is very wideband, and for 1% dispersion, error bandwidth is larger than 10:1.