An efficient implementation of surface impedance boundary conditions for the finite-difference time-domain method

Abstract

An efficient way to implement the surface impedance boundary conditions (SIBC) for the finite-difference time-domain (FDTD) method is presented in this paper. Surface impedance boundary conditions are first formulated for a lossy dielectric half-space in the frequency domain. The impedance function of a lossy medium is approximated with a series of first-order rational functions. Then, the resulting time-domain convolution integrals are computed using recursive formulas which are obtained by assuming that the fields are piecewise linear in time. Thus, the recursive formulas derived here are second-order accurate. Unlike a previously published method [7] which requires preprocessing to compute the exponential approximation prior to the FDTD simulation, the preprocessing time is eliminated by performing a rational approximation on the normalized frequency-domain impedance. This approximation is independent of material properties, and the results are tabulated for reference. The implementation of the SIBC for a PEC-backed lossy dielectric shell is also introduced.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>