Multiscale analysis of metamaterial

The investigation of multiscale homogenization of metamaterial has important theoretical and application value.Among the existing theories of homogenization of metamaterial,the electromagnetic(EM)characteristics of vector fields are not fully considered.Considering the micro-scale characteristic of the periodic structure and the divergence and curl characteristics of EM field,a new vector correction is proposed to describe the micro-scale EM characteristics,which both the irrotational field and the non-divergence field are considered,so the new micro-scale functions are obtained.By using the multiscale functions and multiscale finite element method(FEM)based on the edge-based vector basis functions,the effective EM parameters and the E-field distributions of periodic composite materials are calculated. Compared with FEM,it is shown that the multiscale FEM can calculate the EM parameters and E-field effectively.