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Implementation of Collocated Surface Impedance Boundary Conditions in FDTD

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.