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All issues Volume 55 / No 2 (March-April 2021) ESAIM: M2AN, 55 2 (2021) 479-506 References
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Issue
ESAIM: M2AN
Volume 55, Number 2, March-April 2021
Page(s) 479 - 506
DOI https://doi.org/10.1051/m2an/2021004
Published online 15 March 2021
  1. A. Alegria, L. Goitiandia, I. Telleria and J. Colmenero, α-relaxation in the glass-transition range of amorphous polymers. 2. Influence of physical aging on the dielectric relaxation. Macromolecules 30 (1997) 3881–3888. [Google Scholar]
  2. C.S. Antonopoulos, N.V. Kantartzis and I.T. Rekanos, FDTD method for wave propagation in Havriliak-Negami media based on fractional derivative approximation. IEEE T. Magn. 53 (2017) 1–4. [Google Scholar]
  3. P. Bia, D. Caratelli, L. Mescia, R. Cicchetti, G. Maione and F. Prudenzano, FDTD method for wave propagation in Havriliak-Negami media based on fractional derivative approximation. Sign. Process. 107 (2015) 312–318. [Google Scholar]
  4. K. Biswas, G. Bohannan, R. Caponetto, A.M. Lopes and J.A.T. Machado, Fractional-order models of vegetable tissues. In: Fractional-Order Devices. Springer (2017) 73–92. [Google Scholar]
  5. M.F. Causley, P.G. Petropoulos and S. Jiang, Incorporating the Havriliak-Negami dielectric model in the FDTD method. J. Comput. Phys. 230 (2011) 3884–3899. [Google Scholar]
  6. J. Chakarothai, Novel FDTD scheme for analysis of frequency-dependent medium using fast inverse Laplace transform and Prony’s method. IEEE Trans. Antennas Propag. 67 (2019) 6076–6089. [Google Scholar]
  7. G. Cohen and S. Pernet, Finite Elements and Discontinuous Galerkin Methods for Transient Wave Equations. Springer Series in Scientific Computation. Springer (2017). [Google Scholar]
  8. K.S. Cole and R.H. Cole, Dispersion and absorption in dielectrics I. Alternating current characteristics. J. Chem. Phys. 9 (1941) 341–351. [Google Scholar]
  9. D.W. Davidson and R.H. Cole, Dielectric relaxation in glycerol, propylene glycol, and n-propanol. J. Chem. Phys. 19 (1951) 1484–1490. [Google Scholar]
  10. P.J.W. Debye, Polar Molecules. Dover (1929). [Google Scholar]
  11. L. Demkowicz, Computing with hp-Adaptive Finite Elements: Vol. 1. One- and Two-Dimensional Elliptic and Maxwell Problems. Chapman and Hall/CRC (2006). [Google Scholar]
  12. A.Z. Elsherbeni and V. Demir, The Finite-Difference Time-Domain Method for Electromagnetics with MATLAB Simulations. SciTech, Edison, NJ, USA (2015). [Google Scholar]
  13. A. Garca-Bernabé, R.D. Calleja, M. Sanchis, A. Del Campo, A. Bello and E. Pérez, Amorphous-smectic glassy main chain LCPs. II. Dielectric study of the glass transition. Polymer 45 (2004) 1533–1543. [Google Scholar]
  14. R. Garrappa, Numerical evaluation of two and three parameter Mittag-Leffler functions. SIAM J. Numer. Anal. 53 (2015) 1350–1369. [Google Scholar]
  15. R. Garrappa and G. Maione, Fractional Prabhakar derivative and applications in anomalous dielectrics: a numerical approach. Lecture Notes Electr. Eng. 407 (2017) 429–439. [Google Scholar]
  16. R. Garrappa, F. Mainardi and M. Guido, Models of dielectric relaxation based on completely monotone functions. Fract. Calc. Appl. Anal. 19 (2016) 1105–1160. [Google Scholar]
  17. A. Giusti, I. Colombaro, R. Garra, R. Garrappa, F. Polito, M. Popolizio and F. Mainardi, A practical guide to Prabhakar fractional calculus. Fract. Calc. Appl. Anal. 23 (2020) 9–54. [Google Scholar]
  18. R. Gorenflo, A.A. Kilbas, F. Mainardi and S.V. Rogosin, Mittag-Leffler Functions, Related Topics and Applications. Springer, Berlin (2014). [Google Scholar]
  19. S. Havriliak and S. Negami, A complex plane analysis of α-dispersions in some polymer systems. J. Polym. Sci. C 14 (1966) 99–117. [Google Scholar]
  20. S. Havriliak and S. Negami, A complex plane representation of dielectric and mechanical relaxation processes in some polymers. Polymer 8 (1967) 161–210. [Google Scholar]
  21. C. Huang and L.-L. Wang, An accurate spectral method for the transverse magnetic mode of Maxwell equations in Cole-Cole dispersive media. Adv. Comput. Math. 45 (2019) 707–734. [Google Scholar]
  22. D.F. Kelley, Piecewise linear recursive convolution for the FDTD analysis of propagation through linear isotropic dispersive dielectrics. Ph.D. thesis, Pennsylvania State University (1999). [Google Scholar]
  23. D.F. Kelley, T.J. Destan and R.J. Luebbers, Debye function expansions of complex permittivity using a hybrid particle swarm-least squares optimization approach. IEEE T. Antenn. Propag. 55 (2007) 1999–2005. [Google Scholar]
  24. A.A. Kilbas, M. Saigo and R.K. Saxena, Generalized Mittag-Leffler function and generalized fractional calculus operators. Integr. Transf. Spec. F. 15 (2004) 31–49. [Google Scholar]
  25. J. Li and Y. Huang, Time-Domain Finite Element Methods for Maxwell’s Equations in Metamaterials. Springer Series in Computational Mathematics. Springer (2013). [Google Scholar]
  26. J. Li, Y. Huang and Y. Lin, Developing finite element methods for Maxwell’s equations in a Cole-Cole dispersive medium. SIAM J. Sci. Comput. 33 (2011) 3153–3174. [Google Scholar]
  27. A.M. Lopes, J.T. Machado and E. Ramalho, Fractional-order model of wine. In: Chaotic, Fractional, and Complex Dynamics: New Insights and Perspectives. Springer (2018) 191–203. [Google Scholar]
  28. C. Lubich and A. Schädle, Fast convolution for nonreflecting boundary conditions. SIAM J. Sci. Comput. 24 (2002) 161–182. [Google Scholar]
  29. W. McLean, V. Thomée and L.B. Wahlbin, Discretization with variable time steps of an evolution equation with a positive-type memory term. J. Comput. Appl. Math. 69 (1996) 49–69. [Google Scholar]
  30. L. Mescia, P. Bia and D. Caratelli, Fractional derivative based FDTD modeling of transient wave propagation in Havriliak-Negami media. IEEE Trans. Microwave Theory Tech. 62 (2014) 1920–1929. [Google Scholar]
  31. P. Monk, Finite Element Methods for Maxwell’s Equations. Oxford University Press (2003). [CrossRef] [Google Scholar]
  32. P. Monk, A comparison of three mixed methods for the time-dependent Maxwell’s equations. SIAM J. Sci. Stat. Comput. 13 (1992) 1097–1122. [Google Scholar]
  33. I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations to Methods of their Solution and some of their Applications. Academic, San Diego, CA (1999). [Google Scholar]
  34. C. Polk and E. Postow, Handbook of Biological Effects of Electromagnetic Fields. CRC Press (1995). [Google Scholar]
  35. T.R. Prabhakar, A singular integral equation with a generalized Mittag-Leffler function in the kernel. J. Yokohama Math. 19 (1971) 7–15. [Google Scholar]
  36. A. Quarteroni and A. Valli, Numerical Approximation of Partial Differential Equations. Springer, Berlin (1994). [Google Scholar]
  37. G.G. Raju, Dielectrics in Electric Fields. CRC Press, New York (2016). [Google Scholar]
  38. I.T. Rekanos, An auxiliary differential equation method for FDTD modeling of wave propagation in Cole-Cole dispersive media. IEEE Trans. Antennas Propag. 58 (2012) 3666–3674. [Google Scholar]
  39. I.T. Rekanos, FDTD modeling of Havriliak-Negami media. IEEE Microw. Wirel. Co. 22 (2012) 49–51. [Google Scholar]
  40. I.T. Rekanos, FDTD schemes for wave propagation in Davidson-Cole dispersive media using auxiliary differential equations. IEEE Trans. Antennas Propag. 60 (2012) 1467–1478. [Google Scholar]
  41. T. Repo and S. Pulli, Application of impedance spectroscopy for selecting frost hardy varieties of English ryegrass. Ann. Botany 78 (1996) 605–609. [Google Scholar]
  42. A. Schonhals, Fast calculation of the time dependent dielectric permittivity for the Havriliak-Negami function. Acta Polym. 42 (1991) 149–151. [Google Scholar]
  43. J.W. Schuster and R.J. Luebbers, An FDTD algorithm for transient propagation in biological tissue with a Cole-Cole dispersion relation. Proc. IEEE Antennas Propag. Soc. Int. Symp. 4 (1998) 1988–1991. [Google Scholar]
  44. J. Shen, T. Tang and L.-L. Wang, Spectral Methods: Algorithms, Analysis and Applications. Springer (2011). [Google Scholar]
  45. A. Taflove and S.C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method. Artech House, London (2005). [Google Scholar]
  46. F. Torres, P. Vaudon and B. Jecko, Application of new fractional derivatives to the FDTD modeling of pulse propagation in a Cole-Cole medium. Microwave Opt. Technol. 13 (1996) 300–304. [Google Scholar]
  47. K. Xu and S. Jiang, A bootstrap method for sum-of-poles approximations. J. Sci. Comput. 55 (2013) 16–39. [Google Scholar]
  48. F. Zeng, I. Turner and K. Burrage, A stable fast time-stepping method for fractional integral and derivative operators. J. Sci. Comput. 77 (2018) 283–307. [Google Scholar]

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