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

• 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
• ISSN: 0018-926X; 1558-2221; 1558-2221
• DOI: 10.1109/TAP.2009.2029383

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.