A Mixed E-B Finite Element Formulation for the analysis of Periodic Structures

The analysis of periodic structures with the Finite Element Method (FEM) has received a lot of attention in recent years. FEM formulates Maxwell's curl equations as either a second-order wave equation or two dual first-order (mixed) equations. Up until now the analysis of the periodic structures was primarily restricted to using the second-order wave equation. In this work, a new mixed vector finite element method for solving the coupled Maxwell's equations for the periodic boundary condition is presented. The mixed-order formulation gives a higher accuracy compared to the second-order for the same number of mesh elements. Numerical experiments are performed to validate the new formulation with analytical and commercial methods.