Implementation of Collocated Surface Impedance Boundary Conditions in FDTD

Abstract

Surface impedance boundary conditions (SIBCs) for finite-difference time-domain (FDTD) are implemented with collocated H and E components in which first-order spatial finite difference have been used for the spatial derivatives. Transient error analysis is done for the reflected field for the whole possible range of modeled material conductivity. Magnitude and phase error analysis of the calculated reflection coefficients for wideband pulses is presented as well. The resulting numerical errors are compared with the errors of traditional SIBCs implementation when the tangential magnetic fields on the boundary are approximated with the neighboring FDTD magnetic field component located at half-cell size distance in space and half time step behind in time. It is shown that the collocated fields approach is considerably more accurate for both constant real resistive and dispersive complex lossy dielectric SIBCs, in both magnitude and especially phase. Unlike the traditional approach, it is stable for all values of modeled material conductivity. The collocated fields approach is also applied to SIBCs with coating, and the transient and reflection coefficient errors are studied. It is shown that in contrast to the traditional implementation, it is stable for arbitrarily thin coating and for any substrate conductivity, and requires storage only half of the auxiliary coefficients when computing the convolution integrals.Index Terms-Error analysis, finite-difference time-domain (FDTD) method, surface impedance boundary conditions (SIBCs).

From Microscopic to Macroscopic Description of Composite Thin Panels: A Road Map for Their Simulation in Time Domain

“…Different bulk constitutive parameters will be found for slabs with different t h values, all with the same S-parameters. From (12) and (13b), the procedure is as follows.…”

“…For this, a partial fraction expansion, in terms of complex-conjugate pole-residue pairs, is performed by fitting the frequency-dependent S-parameters, e.g., by using a vector-fitting (VF) technique [11]. However, the poles need to be carefully chosen to avoid instabilities, and, even in this case, late-time instabilities are reported to appear because of the noncollocated nature of FDTD [12], [13].…”

SIVA UAV: A Case Study for the EMC Analysis of Composite Air Vehicles

“…A main drawback of NIBC resides in the appearance of latetime instabilities with an origin that is still not well known. Let us mention just that these have often been attributed [30], [31] to the H-node space-time upwind extrapolation required in classical FDTD to co-locate the electric and magnetic field tangential components on the slab surface for the application of IBCs. In our experience, even if canonical problems do not suffer from late-time instabilities, large and complex ones may exhibit them.…”

Collocated Sibc-FDTD Method for Coated Conductors at Oblique Incidence

“…In this paper, Equation (14) is dealt with collocated magnetic and electric components on the boundary according to the Reference [14]. At time step t = n∆t, the finite difference expression of the SIBC fields and their derivatives are as follows:…”

“…In many cases the approximate method may result in errors and instabilities. A more accurate SIBC method for coated conductors, utilizing collocated electric and magnetic field components on the interface in FDTD method [14] has been presented but without taking into account the incidence angle and polarization of plane wave. Based on collocated SIBC, the FDTD models of lossy dielectric coatings on perfect conductors for parallel polarization and vertical polarization plane wave at oblique incidence are developed in this article.…”