  In this paper, we have proposed a dispersive formulation of scalar-based
meshless method for time-domain analysis of electromagnetic wave propagation
through left-handed (LH) materials. 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 LH
medium as a kind of dispersive media can be described by frequency-dependent
constitutive parameters. The most appropriate numerical techniques for analysis
of LH media are dispersive formulations of conventional numerical methods. In
comparison to the conventional grid-based numerical methods, it is proved 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 in this paper enables
us to take advantage of meshless methods in analysis of LH media. For modeling
the frequency behavior of the medium in the proposed dispersive formulation, 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 a numerical example; also, some
basic factors which affect the accuracy and computational cost of the
simulations are studied.
