A DG-FEM-GSTC Method for Fast Simulation of Metasurfaces With Strong Normal Polarization

An improved discontinue Galerkin (DG) finite-element method (FEM) incorporated with generalized sheet transition conditions (GSTC) for rapid simulation of metasurfaces is proposed. Replacing the actual electrically small structure of meta-atoms with a zero-thickness sheet with surface polarizations realizes the rapid simulation of the macroscopic field response. Compared with the previous work on the FEM-GSTC method, the improved method takes the normal components of surface polarizations into account, thus it can accurately simulate the metasurfaces with strong response in the normal direction or deal with the oblique incidence problem. We introduce the flux in the DG method to handle the gradient of normal polarizations in FEM, and propose the special treatments at the boundary of the finite GSTC interface. Both two-dimensional and three-dimensional versions of the DG-FEM-GSTC method are presented for different simulation scenarios. Numerical examples including an ideal model and some practical metasurfaces are provided. Comparisons with the results of actual structures obtained from commercial software demonstrate that the improved method can accurately reproduce the macroscopic response of the metasurface, while consuming less computational time and memory resources.