Implementation of the Second-Order Dispersion Mur Absorbing Boundary Condition Based on the Shift Operator

This letter derives formulas for the second-order dispersion Mur absorbing boundary condition (ABC) in Debye and Lorentz media by introducing the shift operator into finite difference time-domain (FDTD) and using the first-order Taylor expansion. In addition, according to the characteristics of dispersive media, a new expansion form is used. The results of the 1-D example show that the new form is better than using the first-order Taylor expansion directly. Therefore, this expansion form is used to derive the second-order ABC. Furthermore, a 2 D example is designed to compare the results obtained using the second-order Mur ABC with those simulated in a large computation domain. The results show that the maximum error is less than-35dB in Debye media and Lorentz media, and the maximum error is reduced by 15dB to 25dB compared with the first-order Mur ABC, which proves the effectiveness of the proposed method.