Efficient Low Order Approximation for Surface Impedance Boundary Conditions in Finite-Difference Time-Domain Method

An efficient implementation of low order surface impedance boundary conditions (SIBCs) for the finite-difference time-domain (FDTD) method is presented. The surface impedance function of a lossy medium is approximated with a series of first-order rational functions by using the vector fitting (VF) technique. Thus, the resulting time-domain convolution integrals are efficiently computed using recursive formulas. The numerical error of the surface impedance modeled by the FDTD method is carried out analytically. A sensitivity analysis is performed to determine the minimum number of poles required by the VF technique to achieve good accuracy in modeling regions bounded by several lossy media with near- or far-field source excitations.