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.
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.
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References
Yee KS (1966) Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Trans Antennas Propag AP-16:302–307
Taflove A, Hagness SC (2005) Computational electrodynamics—the finite-difference time domain method, 3rd edn. Artech House, Boston, ISBN 1-58053-832-0
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, Jan
Namiki T (1999) A New FDTD algorithm based on the alternating-direction implicit method. IEEE Trans Microwave Tech 47(10):2003–2007, Oct
Namiki T (2000) Investigation of numerical errors of the two-dimensional ADI-FDTD method. IEEE Trans Microwave Tech 48(11):1950–1956, Nov
Zhao P (2002) Analysis of the numerical dispersion of the 2D alternating-direction implicit FDTD method. IEEE Trans Microwave Tech 50(4):1156–1164, April
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, Oct
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, Sept
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, Aug
Xiao F (2006) High-order accurate unconditionally-stable implicit multi-stage FDTD method. Electron Lett 42(10):564–566, May
Kole JS, Figge MT, De Raedt H (2001) Unconditionally stable algorithms to solve the time-dependent Maxwell equations. Phys Rev E 64(066705):1–14
Kole JS, Figge MT, De Raedt H (2002) Higher-order unconditionally stable algorithms to solve the time-dependent Maxwell equations. Phys Rev E 65:066705
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 156:43–61
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):1–12
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):3155–3160
Bérenger J-P (1996) Perfectly matched layer for the FDTD solution of wave-structure interaction problems. IEEE Trans Antennas Propag AP-44(1):110–117
Bérenger J-P (1996) Three-dimensional perfectly matched layer for the absorption of electromagnetic waves. J Comput Phys 127(0181):363–379
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Silly-Carette, J., Lautru, D., Wong, MF. et al. Analysis of the numerical One-Step method for the study applied on bio electromagnetics. Ann. Telecommun. 63, 29–41 (2008). https://doi.org/10.1007/s12243-007-0002-5
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DOI: https://doi.org/10.1007/s12243-007-0002-5