On the Accuracy and Stability of Several Widely Used FDTD Approaches for Modeling Lorentz Dielectrics

A rigorous and comparative study on the approximation accuracy and stability limits of several widely used finite-difference time-domain (FDTD) approaches, namely the auxiliary differential equation (ADE) approach, the bilinear transform (BT) approach, the Z-transform approach (ZT) and the piecewise...

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Bibliographic Details
Published in:IEEE transactions on antennas and propagation 2009-10, Vol.57 (10), p.3378-3381
Main Authors: Lin, Zhili, Thylen, Lars
Format: Article
Language:English
Subjects:
Accuracy
Applied classical electromagnetism
Convolution
Density
Dielectrics
Differential equations
Dispersion
dispersive media
Electromagnetic wave propagation, radiowave propagation
Electromagnetism
electron and ion optics
Exact sciences and technology
Finite difference methods
Finite difference time domain method
finite-difference
Finite-difference time domain (FDTD) methods
Fundamental areas of phenomenology (including applications)
Mathematical analysis
Mathematical models
metamaterials
numerical
numerical stability
permittivity
Physics
Piecewise linear approximation
Piecewise linear techniques
Preserves
propagation
Stability
Time domain analysis
Transforms
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Summary:A rigorous and comparative study on the approximation accuracy and stability limits of several widely used finite-difference time-domain (FDTD) approaches, namely the auxiliary differential equation (ADE) approach, the bilinear transform (BT) approach, the Z-transform approach (ZT) and the piecewise linear recursive convolution (PLRC) approach, for modeling dispersive Lorentz dielectrics is presented following the given updating equations between the electric flux density and the electric field intensity. We find the ZT approach with modified material parameters is much more accurate than the original ZT approach and the other three approaches for modeling Lorentz dielectrics. The stability limits of the ADE, ZT and PLRC approaches in simulating Lorentz dielectrics are also shown to be a bit more stringent than that of BT approach which preserves the Courant stability limit as previously reported.
ISSN:0018-926X
1558-2221
1558-2221
DOI:10.1109/TAP.2009.2029383