This paper presents a time-domain formulation of a meshless method based on the generalized sheet transition conditions (GSTCs). This formulation is applicable for modeling a kind of dispersive metasurface and a time-varying metasurface. This is the first time a meshless method is developed for analysis of the metasurfaces using GSTCs. The significance of time-domain meshless methods originates from their capabilities for multi-scale and conformal modeling in addition to analysis of problems in a broad frequency-range. Here, for simplicity, the meshless method formulation is presented for analysis of 1-D problems consisting of metasurfaces which are monoisotropic. The extension of this method to 2-D and 3-D problems and bianisotropic metasurfaces is straightforward. The efficiency of the proposed formulations is verified by numerical examples.

We have proposed a dispersive formulation of the meshless radial point interpolation method (RPIM) to precisely analyze the unusual wave propagation characteristics of left-handed material (LHM) slabs. To absorb both propagating and evanescent waves, we have implemented the generalized perfectly matched layer (GPML) absorbing boundary condition (ABC) to the meshless method. As the evanescent waves play a significant role in the phenomenon of subwavelength imaging by LHM slabs, the material interfaces have to be correctly treated to accurately simulate the amplification of evanescent waves through the slab. By applying new considerations to the systematic approach of the nondispersive meshless method for accurate modeling of material interfaces, we have obtained a new set of equations for the GPML formulations to update the fields at the interfaces of the LHM slab. Numerical experiments show that the proposed formulations have a considerable impact on improving the accuracy of the meshless method for analysis of the LHM slabs.