The First-Order Dispersion Mur Absorbing Boundary Condition Based on the SO-FDTD Method

This letter has derived the first-order Mur absorbing boundary condition (ABC) formula for Debye and Lorentz dispersion models, by introducing the shift operator from the shift operator finite-difference time-domain (SO-FDTD) method framework, and using a second-order Taylor expansion. Through simulations of electromagnetic wave propagation in dispersive media within 1-D space, a comparison was conducted between the Mur formula developed in this letter and the sampled electric field in a large computation domain. The observed maximum relative errors for both the models, approximately −50 dB, serve to validate the effectiveness of the derived formula. In addition, 3-D example was designed to compare the derived Mur formula with the traditional Mur, and the results show that the Mur ABC derived in this letter outperforms the traditional Mur ABC in terms of performance. This research introduces a novel approach to enhance the efficiency and accuracy of the Mur ABC, representing a significant advancement in simulating electromagnetic wave propagation in dispersive media.