Incorporating the Havriliak-Negami dielectric model in the FD-TD method

Authors:
Matthew F. Causley;Peter G. Petropoulos;Shidong Jiang
Affiliations:
Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, United States;Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, United States;Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, United States
Venue:
Journal of Computational Physics
Year:
2011

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Abstract

We derive and analyze an efficient algorithm to incorporate the anomalously dispersive Havriliak-Negami dielectric model of induced polarization in the Finite-difference time-domain (FD-TD) method. Our algorithm implements this dielectric model, which in the time-domain involves fractional derivatives and fractional differential operators, with a preset error over the desired computational time interval [0,T"c"o"m"p] and correctly takes into account the singularity at t=0^+ of the corresponding time-domain dielectric susceptibility. The overall algorithm is shown to be second-order accurate in space and time, and to obey the standard FD-TD stability condition. Numerical experiments confirm our analysis.