2000 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

IEEE Transactions on Antennas and Propagation
Volume 48 Number 2, February 2000

Table of Contents for this issue

Complete paper in PDF format

Maxwellian Material-Based Absorbing Boundary Conditions for Lossy Media in 3-D

David C. Wittwer, Member, IEEE and Richard W. Ziolkowski Fellow, IEEE

Page 200.

Abstract:

A two time-derivative Lorentz material (2TDLM), which has been shown previously to be the correct Maxwellian medium choice to match an absorbing layer to a lossy region, is extended here to a complete absorbing boundary condition (ABC) for three-dimensional (3-D) finite-difference time-domain (FDTD) simulators. The implementation of the lossy 2TDLM (L2TDLM) ABC is presented. It is shown that in contrast to the one-dimensional (1-D) and two-dimensional (2-D) versions, the full 3-D ABC requires a three time-derivative Lorentz material in the edge and corner regions to achieve a rigorous matching of the resulting Maxwellian absorbing layer to the lossy medium. The 3-D ABC implementation thus requires the introduction of an auxiliary field to handle the edge and corner regions to achieve a state-space form of the update equations in the ABC layers. Fully 3-D examples including pulsed dipole radiation and pulsed Gaussian beam propagation in lossless and lossy materials as well as pulse propagation along a microstrip over lossless and lossy materials are included to illustrate the effectiveness of the L2TDLM ABC.

References

  1. D. C. Wittwer and R. W. Ziolkowski, "Two time-derivative Lorentz material (2TDLM) formulation of a Maxwellian absorbing layer matched to a lossy medium", IEEE Trans. Antennas Propagat., vol. 48, pp.  192-199, Feb.  2000.
  2. S. Gedney, "An anisotropic perfectly matched layer-Absorbing medium for the truncation of FDTD lattices", IEEE Trans. Antennas Propagat., vol. 44, pp.  1630-1639, Dec.  1996.
  3. C. M. Rappaport and S. C. Winton, "Modeling dispersive soil for FDTD computation by fitting conductivity parameters", in Proc. Appl. Computat. Electromagn. Soc., Monterey, CA, Mar. 1997, pp.  112-117. 
  4. S. D. Gedney, "An anisotropic PML absorbing media for FDTD simulation of fields in lossy dispersive media", Electromagn., vol. 16, pp.  399-415, July/Aug.  1996.
  5. Y. C. Lau, M. S. Leong and P. S. Kooi, "Extension of Berenger's PML boundary condition in matching lossy medium and evanescent waves", Electron. Lett., vol. 32, no. 11, pp.  974-976, 1996.
  6. J. Fang and Z. Wu, "Generalized perfect matched layer for the absorption of propagating and evanescent waves in lossless and lossy media", IEEE Trans. Microwave Theory Tech., vol. 14, pp.  2216-2222, Dec.  1996.
  7. Q. H. Liu, "An FDTD algorithm with perfectly matched layers for conductive media", Microwave Opt. Technol. Lett., vol. 14, pp.  134-137, Feb.  1997 .
  8. A. Taflove, Advances in Computational Electrodynamics:The Finite-Difference Time-Domain Method, Boston, MA: Artech House, 1998.
  9. J.-P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves", J. Comp. Phys., vol. 114, pp.  185-200,  Oct.  1994.
  10. D. S. Katz, E. T. Thiele and A. Taflove, "Validation and extension to three dimensions of the Berenger PML absorbing boundary condition for FD-TD meshes", IEEE Microwave Guided Wave Lett., vol. 4, pp.  268-270, Aug.  1994.
  11. W. C. Chew and W. H. Weedon, "A 3-D perfectly matched medium from modified Maxwell's equations with stretched coordinates", Microwave Opt. Technol. Lett., vol. 7, no. 9, pp.  599-604, Sept.  1994.
  12. C. E. Reuter, R. M. Joseph, E. T. Thiele, D. S. Katz and A. Taflove, "Ultrawideband absorbing boundary condition for termination of waveguiding structures in FDTD simulations", IEEE Microwave Guided Wave Lett., vol. 4, pp.  246-344,  Oct.  1994.
  13. C. M. Rappaport, "Perfectly matched absorbing boundary conditions based on anisotropic lossy mapping of space", IEEE Microwave Guided Wave Lett., vol. 5, pp.  90-92, Mar.  1995.
  14. R. Mittra and Ü. Pekel, "A new look at the perfectly matched layer (PML) concept for the reflectionless absorption of electromagnetic waves", IEEE Microwave Guided Wave Lett., vol. 5, pp.  84-86, Mar.  1995.
  15. Z. S. Sacks, D. M. Kingsland, R. Lee and J.-F. Lee, "A perfectly matched anisotropic absorber for use as an absorbing boundary condition", IEEE Trans. Antennas Propagat., vol. 43, pp.  1460-1463, Dec.  1995.
  16. D. C. Wittwer and R. W. Ziolkowski, "How to design the imperfect Berenger PML", Electromagn., vol. 16, pp.  465-485, July/Aug.  1996.
  17. L. Zhao and A. C. Cangellaris, "GT-PML: Generalized theory of perfectly matched layers and its application to the reflectionless truncation of finite-difference time-domain grids", IEEE Trans. Microwave Theory Tech., vol. 44, pp.  2555-2563, Dec.  1996 .
  18. R. W. Ziolkowski, "The design of Maxwellian absorbers for numerical boundary conditions and for practical applications using engineered artificial materials", IEEE Trans. Antennas Propagat., vol. 45, pp.  656-671, Apr.  1997.
  19. R. W. Ziolkowski, "Time-derivative Lorentz materials and their utilization as electromagnetic absorbers", Phys. Rev. E, vol. 55, no. 6, pp.  7696-7703, June   1997.
  20. R. W. Ziolkowski, "Time-derivative Lorentz material model-based absorbing boundary condition", IEEE Trans. Antennas Propagat., vol. 45, pp.  1530-1535, Oct.  1997.
  21. P. G. Petropoulos, A. C. Cangellaris and L. Zhao, "A reflectionless sponge layer absorbing boundary condition for the solution of Maxwell's equations with high-order staggered finite difference schemes", J. Computat. Phys., vol. 139, no. 1, pp.  184-208, Jan.  1998.
  22. R. W. Ziolkowski, "Maxwellian material based absorbing boundary conditions", Comput. Methods. Appl. Mech. Engrg., vol. 169, pp.  237 -262, 1999.
  23. E. Turkel and A. Yefet, "Absorbing PML boundary layers for wave-like equations", preprint, July 1997.
  24. S. Abarbanel and D. Gottlieb, "On the construction and analysis of absorbing layers in CEM", in Proc. Appl. Computat. Electromagn. Soc., Monterey, CA, Mar. 1997, pp.  876-883. 
  25. F. Auzanneau and R. W. Ziolkowski, "Theoretical study of synthetic bianisotropic materials", J. Electromagn. Waves Applicat., vol. 12, no.  3, pp.  353-370, Dec.  1997.
  26. F. Auzanneau and R. W. Ziolkowski, "Microwave signal rectification using artificial composite materials composed of diode loaded, electrically small dipole antennas", IEEE Trans. Microwave Theory Tech., vol. 46, pp.  1628-1637, Nov.  1998.
  27. D. C. Wittwer and R. W. Ziolkowski, "The effect of dielectric loss in FDTD simulations of microstrip structures", IEEE Trans. Microwave Theory Tech., Oct.  1998, submitted for publication.