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In this paper, we have proposed a dispersive formulation of scalar-basedmeshless method for time-domain analysis of electromagnetic wave propagationthrough left-handed (LH) materials. Moreover, we have incorporated Berenger'sperfectly matched layer (PML) absorbing boundary condition (ABC) into thedispersive formulation to truncate open-domain structures. In general, the LHmedium as a kind of dispersive media can be described by frequency-dependentconstitutive parameters. The most appropriate numerical techniques for analysisof LH media are dispersive formulations of conventional numerical methods. Incomparison to the conventional grid-based numerical methods, it is proved thatmeshless methods not only are strong tools for accurate approximation ofderivatives in Maxwell's equations but also can provide more flexibility inmodeling the spatial domain of problems. However, we have not seen any reportson using dispersive forms of meshless methods for simulation of wavepropagation in metamaterials and applying any PML ABCs to dispersiveformulation of meshless method. The proposed formulation in this paper enablesus to take advantage of meshless methods in analysis of LH media. For modelingthe frequency behavior of the medium in the proposed dispersive formulation, wehave used auxiliary differential equation (ADE) method based on the relationsbetween electromagnetic fields intensities and current densities. Effectivenessof the proposed formulation is verified by a numerical example; also, somebasic factors which affect the accuracy and computational cost of thesimulations are studied.

Time-Domain Analysis of Left-Handed Materials Based on a Dispersive Meshless Method with PML Absorbing Boundary Condition