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

  • Omar Ramadan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4707)


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.


Perfectly Match Layer Finite Difference Time Domain Simulation Perfectly Match Layer Region Perfectly Match Layer Formulation Perfectly Match Layer Layer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Berenger, J.-P.: A perfectly matched layer for the absorption of electromagnetic waves. Journal of Computational Physics 114, 185–200 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Taflove, A., Hangess, S.C.: Computational electrodynamics: The Finite-Difference Time-Domain Method, 2nd edn. Artech-House, Boston (2000)zbMATHGoogle Scholar
  3. 3.
    Chew, W.C., Weedon, W.H.: A 3-D perfectly matched medium from modified Maxwell’s equation with stretched coordinates. Microwave and Optical Technology Letters 7(13), 599–604 (1994)CrossRefGoogle Scholar
  4. 4.
    Gedney, S.D.: An anisotropic perfectly-matched layer-absorbing medium for the truncation of FD-TD lattices. IEEE Transactions on Antennas and Propagation 44(12), 1630–1639 (1996)CrossRefGoogle Scholar
  5. 5.
    Cummer, S.A.: A simple, nearly perfectly matched layer for general electromagentic media. IEEE Microwave and Wireless Components Letters 13(3), 128–130 (2003)CrossRefGoogle Scholar
  6. 6.
    Namiki, T.: A new FDTD algorithm based on alternating-direction implicit method. IEEE Transactions on Microwave Theory and Techniques 47(10), 2003–2007 (1999)CrossRefGoogle Scholar
  7. 7.
    Gedney, S.D., Liu, G., Roden, J.A., Zhu, A.: Perfectly matched layer media with CFS for an unconditionally stable ADI-FDTD method. IEEE Transactions on Antennas and Propagation 49(11), 1554–1559 (2001)zbMATHCrossRefGoogle Scholar
  8. 8.
    Ramadan, O.: Unconditionally stable ADI-FDTD implementation of PML for frequency dispersive debye media. Electron. Lett. 40(4), 230–232 (2004)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Carcia, S.G., Lee, T.W., Hagness, S.C.: On the accuracy of the ADI-FDTD method. IEEE Antennas and Wireless Propagation Letters 1, 31–34 (2002)CrossRefGoogle Scholar
  10. 10.
    Ramadan, O.: Generalized unconditionally stable Crank-Nicolson PML formulations for truncating FDTD domains. In: The 35th European Microwave Conference (EuMC), Paris, France (October 4-6, 2005)Google Scholar
  11. 11.
    Proakis, J.G., Manolakis, D.G.: Digital signal processing: principles, algorithms and applications, 3rd edn. Prentice-Hall, Englewood Cliffs (1995)Google Scholar
  12. 12.
    Pereda, J.A., Vielva, L.A., Vegas, A., Prieto, A.: Analyzing the stability of the FDTD technique by combining the Von Neumann method with Routh-Hurwitz criterion. IEEE Transactions on Microwave Theory and Techniques 49(2), 377–381 (2001)CrossRefGoogle Scholar
  13. 13.
    Joseph, R.M., Hagness, S.C., Taflove, A.: Direct time integration of Maxwell’s equations in linear dispersive media with absorption for scattering and propagation of femtosecond electromagnetic pulses. Optics Letters 16(18), 1412–1414 (1991)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Omar Ramadan
    • 1
  1. 1.Department of Computer Engineering, Eastern Mediterranean University, Gazimagusa, Mersin 10Turkey

Personalised recommendations