A Dispersive Formulation of Time-Domain Meshless Method With PML Absorbing Boundary Condition for Analysis of Left-Handed Materials

We have proposed a dispersive formulation of scalar-based meshless method for time-domain analysis of electromagnetic wave propagation through left-handed materials (LHMs). Moreover, we have incorporated Berenger’s perfectly matched layer (PML) absorbing boundary condition (ABC) into the dispersive formulation to truncate open-domain structures. In general, the dispersive formulations of conventional numerical methods are proper tools for analysis of left-handed (LH) media, whenever the LH media can be characterized by considering spatial or frequency dispersion effect for the constitutive parameters. In comparison to the grid-based numerical methods, it is proven that meshless methods not only are strong tools for accurate approximation of derivatives in Maxwell’s equations but also can provide more flexibility in modeling the spatial domain of problems. However, we have not seen any reports on using dispersive forms of meshless methods for simulation of wave propagation in metamaterials and applying any PML ABCs to dispersive formulation of meshless method. The proposed formulation enables us to take advantage of meshless methods in analysis of LH media with frequency-dependent parameters. For modeling the frequency behavior of the medium, we have used auxiliary differential equation (ADE) method based on the relations between electromagnetic fields intensities and current densities. Effectiveness of the proposed formulation is verified by analysis of 2-D and 3-D numerical examples; also, some basic factors which affect the accuracy, stability, and computational cost of the simulations are studied.