TY - JOUR
T1 - Incorporating the Havriliak-Negami dielectric model in the FD-TD method
AU - Causley, Matthew F.
AU - Petropoulos, Peter G.
AU - Jiang, Shidong
PY - 2011/5/10
Y1 - 2011/5/10
N2 - 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,Tcomp] 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.
AB - 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,Tcomp] 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.
UR - https://doi.org/10.1016/j.jcp.2011.02.012
U2 - 10.1016/j.jcp.2011.02.012
DO - 10.1016/j.jcp.2011.02.012
M3 - Article
VL - 230
JO - Journal of Computational Physics
JF - Journal of Computational Physics
ER -