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

Matthew F. Causley, Peter G. Petropoulos, Shidong Jiang

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)3884-3899
Number of pages16
JournalJournal of Computational Physics
Issue number10
StatePublished - May 10 2011

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


  • Computational electromagnetics
  • Dispersive dielectrics
  • Finite-difference time-domain
  • Time-domain


Dive into the research topics of 'Incorporating the Havriliak-Negami dielectric model in the FD-TD method'. Together they form a unique fingerprint.

Cite this