An Effective Unconditionally Stable Algorithm for Dispersive Finite Difference Time Domain Simulations

Unconditionally stable formulations of the stretched coordinates perfectly matched layer (SCPML) are presented for truncating linear dispersive finite difference time domain (FDTD) grids. In the proposed formulations, the Crank Nicolson and the Bilinear frequency approximation techniques are incorporated with the SCPML to obtain the update equations for the field components in linear dispersive media. Numerical example carried out in one dimensional Lorentz dispersive FDTD domain is included and it has been observed that the proposed formulations not only give accurate results but also remove completely the stability limit of the conventional FDTD algorithm.

[1]  John G. Proakis,et al.  Digital signal processing (3rd ed.): principles, algorithms, and applications , 1996 .

[2]  Jean-Pierre Berenger,et al.  A perfectly matched layer for the absorption of electromagnetic waves , 1994 .

[3]  Angel Vegas,et al.  Analyzing the stability of the FDTD technique by combining the von Neumann method with the Routh-Hurwitz criterion , 2001 .

[4]  Allen Taflove,et al.  Computational Electrodynamics the Finite-Difference Time-Domain Method , 1995 .

[5]  A Taflove,et al.  Direct time integration of Maxwell's equations in linear dispersive media with absorption for scattering and propagation of femtosecond electromagnetic pulses. , 1991, Optics letters.

[6]  Gang Liu,et al.  Perfectly matched layer media with CFS for an unconditionally stable ADI-FDTD method , 2001 .

[7]  O. Ramadan.  Unconditionally stable ADI-FDTD implementation of PML for frequency dispersive Debye media , 2004 .

[8]  John G. Proakis,et al.  Digital Signal Processing: Principles, Algorithms, and Applications , 1992 .

[9]  Tae-Woo Lee,et al.  On the accuracy of the ADI-FDTD method , 2002, IEEE Antennas and Wireless Propagation Letters.

[10]  Weng Cho Chew,et al.  A 3D perfectly matched medium from modified maxwell's equations with stretched coordinates , 1994 .

[11]  T. Namiki,et al.  A new FDTD algorithm based on alternating-direction implicit method , 1999 .

[12]  O. Ramadan.  Generalized unconditionally stable Crank-Nicolson PML formulations for truncating FDTD domains , 2005, 2005 European Microwave Conference.

[13]  S. Cummer,et al.  A simple, nearly perfectly matched layer for general electromagnetic media , 2003, IEEE Microwave and Wireless Components Letters.

[14]  S. Gedney.  An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices , 1996 .