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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
Author(s) -
Kantartzis Nikolaos V.,
Tsiboukis Theodoros D.
Publication year - 2000
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/1099-1204(200009/10)13:5<417::aid-jnm375>3.0.co;2-7
Subject(s) - finite difference time domain method , perfectly matched layer , tensor (intrinsic definition) , mathematics , perfect conductor , anisotropy , mathematical analysis , diagonal , boundary value problem , dispersion (optics) , optics , physics , geometry , scattering
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. Copyright © 2000 John Wiley & Sons, Ltd.