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Analysis of the numerical One-Step method for the study applied on bio electromagnetics

  • Jessica Silly-Carette
  • David Lautru
  • Man-Faï Wong
  • Joe Wiart
  • Victor Fouad Hanna
Original Paper
  • 57 Downloads

Abstract

The development of wireless technologies arises important questions about the effects of the wave propagation in the human body. To study accurately these effects, we have to use rigorous numerical methods. In this paper, we present and analyze the One-Step time domain method. This method, which was proposed by De Raedt [Phys Rev E 67(056706):1–12, 2003] for lossless media, is known to be unconditionally stable and so it can be used for applications for which the Courant–Friedrich–Levy (CFL) stability condition can be a limiting factor, e.g., for bioelectromagnetic applications. The numerical dispersion and the insertion of lossy media in the One-Step method are evaluated. The perfectly matched layer (PML) absorbing conditions are also introduced in our study.

Keywords

One-Step method Dispersion Lossy media PML absorbing conditions FDTD method 

Résumé

Le développement des technologies sans fils soulèvent des questions sur l’effet de la propagation des ondes sur le corps humain. Aussi nous utilisons des méthodes numériques afin de pouvoir simuler ces effets. Dans ce papier, nous présentons et nous analysons les spécificités de la méthode One-Step. Cette méthode, qui fut proposée par l’équipe de De Raedt [Phys Rev E 67(056706):1–12, 2003] pour les milieux sans pertes, est connue pour être inconditionnellement stable, et aussi, il peut être intéressant de l’utiliser dans des applications pour lesquelles la condition de stabilité de Courant–Friedrich–Levy (CFL) peut être un facteur limitant, par exemple, dans les applications bio électromagnétiques. La dispersion numérique et l’insertion des pertes sont évaluées. Les conditions absorbantes de type Perfectly Matched Layer (PML) sont aussi introduites dans notre étude.

Mots clés

Méthode One-Step Dispersion Milieux à pertes Conditions absorbantes PML Méthode FDTD 

References

  1. 1.
    Yee KS (1966) Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Trans Antennas Propag AP-16:302–307Google Scholar
  2. 2.
    Taflove A, Hagness SC (2005) Computational electrodynamics—the finite-difference time domain method, 3rd edn. Artech House, Boston, ISBN 1-58053-832-0Google Scholar
  3. 3.
    Sun G, Trueman CW (2004) Some fundamental characteristics of the one-dimensional alternate-direction-implicit finite-difference time-domain method. IEEE Trans Microwave Tech 52(1):46–52, JanCrossRefMathSciNetGoogle Scholar
  4. 4.
    Namiki T (1999) A New FDTD algorithm based on the alternating-direction implicit method. IEEE Trans Microwave Tech 47(10):2003–2007, OctCrossRefGoogle Scholar
  5. 5.
    Namiki T (2000) Investigation of numerical errors of the two-dimensional ADI-FDTD method. IEEE Trans Microwave Tech 48(11):1950–1956, NovCrossRefGoogle Scholar
  6. 6.
    Zhao P (2002) Analysis of the numerical dispersion of the 2D alternating-direction implicit FDTD method. IEEE Trans Microwave Tech 50(4):1156–1164, AprilCrossRefGoogle Scholar
  7. 7.
    Namiki T (2002) 3D ADI-FDTD method-unconditionally stable time-domain algorithm for solving full vector Maxwell’s equations. IEEE Trans Microwave Tech 48(10):1743–1748, OctCrossRefGoogle Scholar
  8. 8.
    Zheng F, Chen Z, Zhang J (2000) Toward the development of a three-dimensional unconditionally stable finite-difference time-domain method. IEEE Trans Microwave Tech 48(9):1550–1558, SeptCrossRefGoogle Scholar
  9. 9.
    Yang Y, Chen RS, Yung EKN (2006) The unconditionally stable Crank-Nicholson FDTD method for three-dimensional Maxwell’s equations. Microw Opt Technol Lett 48(8):1619–1622, AugCrossRefGoogle Scholar
  10. 10.
    Xiao F (2006) High-order accurate unconditionally-stable implicit multi-stage FDTD method. Electron Lett 42(10):564–566, MayCrossRefGoogle Scholar
  11. 11.
    Kole JS, Figge MT, De Raedt H (2001) Unconditionally stable algorithms to solve the time-dependent Maxwell equations. Phys Rev E 64(066705):1–14Google Scholar
  12. 12.
    Kole JS, Figge MT, De Raedt H (2002) Higher-order unconditionally stable algorithms to solve the time-dependent Maxwell equations. Phys Rev E 65:066705Google Scholar
  13. 13.
    De Raedt H, Kole JS, Michielsen KFL, Figge MT (2003) Unified framework for numerical methods to solve the time-dependent Maxwell equations. Comp Phys Commun 156:43–61CrossRefGoogle Scholar
  14. 14.
    De Raedt H, Michielsen K, Kole JS, Figge MT (2003) One-step finite-difference time-domain algorithm to solve the Maxwell equations. Phys Rev E 67(056706):1–12Google Scholar
  15. 15.
    De Raedt H, Michielsen K, Kole JS, Figge MT (2003) Solving the Maxwell equations by the Chebyshev method: a one-step finite difference time-domain algorithm. IEEE Trans Antennas Propag AP-51(11):3155–3160CrossRefGoogle Scholar
  16. 16.
    Bérenger J-P (1996) Perfectly matched layer for the FDTD solution of wave-structure interaction problems. IEEE Trans Antennas Propag AP-44(1):110–117CrossRefGoogle Scholar
  17. 17.
    Bérenger J-P (1996) Three-dimensional perfectly matched layer for the absorption of electromagnetic waves. J Comput Phys 127(0181):363–379zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© GET and Springer Verlag France 2008

Authors and Affiliations

  • Jessica Silly-Carette
    • 1
  • David Lautru
    • 2
  • Man-Faï Wong
    • 1
  • Joe Wiart
    • 1
  • Victor Fouad Hanna
    • 2
  1. 1.France Telecom RESA/FACE/IOPIssy les Moulineaux Cedex 09France
  2. 2.UPMC Univ Paris 06, EA 2385, LISIFParisFrance

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