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

摘要

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 Pade 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.