Kantartzis, Nikolaos V.; Tsiboukis, Theodoros D. A generalized methodology based on higher-order conventional and non-standard FDTD concepts for the systematic development of enhanced dispersionless wide-angle absorbing perfectly matched layers. (English) Zbl 1090.78527 Int. J. Numer. Model. 13, No. 5, 417-440 (2000). Summary: A generalized theory of higher-order finite-difference time-domain (FDTD) schemes for the construction of new dispersionless Berenger and Maxwellian unsplit-field perfectly matched layers (PMLs), is presented in this paper. The technique incorporates both conventional and non-standard approximating concepts. Superior accuracy and modelling attributes are further attained by biasing the FDTD increments on generalizations of Padé formulae and derivative definitions. For the inevitably widened spatial stencils, we adopt the compact operators procedure, whereas temporal integration is alternatively performed via the four-stage Runge-Kutta integrator. In order to terminate the PML outer boundaries and decrease the absorber’s necessary thickness, various higher-order lossy absorbing boundary conditions (ABCs) are implemented. Based on the previous theory, we finally introduce an enhanced reflection-annihilating PML for wide-angle absorption. The novel unsplit-field PML has a non-diagonal symmetric complex tensor anisotropy and by an appropriate choice of its parameters together with new conductivity profiles, it can successfully absorb waves of grazing incidence, thus allowing its imposition much closer to electrically large structures. Numerical results reveal that the proposed 2- and 3-D PMLs suppress dispersion and anisotropy errors, alleviate the near-grazing incidence effect and achieve significant savings in the overall computational resources. Cited in 5 Documents MSC: 78M20 Finite difference methods applied to problems in optics and electromagnetic theory 78M25 Numerical methods in optics (MSC2010) PDFBibTeX XMLCite \textit{N. V. Kantartzis} and \textit{T. D. Tsiboukis}, Int. J. Numer. Model. 13, No. 5, 417--440 (2000; Zbl 1090.78527) Full Text: DOI References: [1] Computational Electrodynamics. The Finite-Difference Time-Domain Method, Artech House: Boston, MA, 1995. · Zbl 0840.65126 [2] The Finite Difference Time Domain Method for Electromagnetics. CRC Press: Boca Raton, FL, 1993. [3] Tsynkov, Applied Numerical Mathematics 27 pp 465– (1998) · Zbl 0939.76077 [4] Berenger, Journal of Computational Physics 114 pp 185– (1994) · Zbl 0814.65129 [5] Andrew, IEEE Microwave Guided Wave Letters 5 pp 192– (1995) [6] Kantartzis, IEEE Transactions Magnetism 33 pp 1460– (1997) [7] Turkel, Applied Numerical Mathematics 27 pp 533– (1998) · Zbl 0933.35188 [8] De Moerloose, IEEE Microwave Guided Wave Letters 5 pp 344– (1995) [9] Ramahi, IEEE Microwave Guided Wave Letters 8 pp 55– (1998) [10] Chew, Microwave Optics and Technology Letters 7 pp 599– (1994) [11] Rappaport, IEEE Microwave Guided Wave Letters 5 pp 90– (1995) [12] Sacks, IEEE Transactions on Antennas and Propagation 43 pp 1460– (1995) [13] Zhao, IEEE Microwave Guided Wave Letters 6 pp 209– (1996) [14] Zhao, IEEE Transactions on Microwave Theory Technology 44 pp 2555– (1996) [15] Gedney, IEEE Transactions on Antennas and Propagation 44 pp 1630– (1996) [16] Gedney, Electromagnetism 16 pp 399– (1996) [17] Fang, IEEE Transactions on Microwave Theory Technology 44 pp 2216– (1996) [18] Veihl, IEEE Microwave Guided Wave Letters 6 pp 94– (1996) [19] Abarbanel, Journal of Computational Physics 134 pp 357– (1997) · Zbl 0887.65122 [20] Ziolowski, IEEE Transactions on Antennas Propagation 45 pp 1530– (1997) [21] Petropoulos, Journal of Computational Mathematics (1999) [22] Petropoulos, SIAM Journal of Applied Mathematics 60 pp 1037– (2000) · Zbl 1025.78016 [23] Ramahi, IEEE Transactions on Antennas and Propagation 43 pp 697– (1995) [24] Petropoulos, Journal of Computational Physics 143 pp 665– (1998) · Zbl 0920.65077 [25] Yioultsis, IEEE Transactions on Magnetism 34 pp 2733– (1998) [26] Cole, IEEE Transactions on Microwave Theory Technology 43 pp 2053– (1995) [27] Petropoulos, IEEE Transactions on Antennas and Propagation 42 pp 859– (1994) [28] Time domain finite difference computation for Maxwells equations. PhD thesis, University of California at Berkeley, 1989. [29] Advances in Computational Electrodynamics: The Finite-Difference Time-Domain Method. In: High order methods. (ed.). Artech House: Boston, MA, 1998. [30] Young, IEEE Transactions on Antennas and Propagation 45 pp 1573– (1997) · Zbl 0947.78612 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.