Edge finite element method for periodic structures using random meshes

Abstract

ABSTRACT This paper introduces a new method to impose the periodic boundary conditions on the arbitrary mesh when we use the edge finite element method. By using the Floquet theorem, we reduce the analysis of an infinite bi-periodic structure to an elementary cell with pseudo-periodic conditions on the lateral sides. In this method, we establish a relationship between the electric field circulation along an edge on a face and the circulation of the associated edges on the opposite face. After that, we introduce periodic relations in the finite element system. To show the possibilities of the proposed method, we present two numerical studies and the obtained numerical results are compared to those produced by the existing methods.