An Analysis of Periodic Structure with Arbitrary Dispersive Media by DG-FETD method

In this paper, a valid discontinuous Galerkin finite element time domain (DG-FETD) method is presented for calculating periodic structure of arbitrary dispersive media. By incorporating the transformed field variable approach and Floquet boundary condition, the permittivity and permeability of a given dispersive medium are further modeled as the sum of complex-conjugate pole-residue pairs. With the use of Galerkin discretized method and Runge-Kutta time-marching scheme, a high order precision time domain framework is established. Numerical example demonstrates the effective computational performance of the proposed technique.

I. Introduction

Periodic structure of dispersive media has become the focus of attention in the electromagnetic field due to the special properties of materials [1]. Numerous time domain algorithms have been developed for this topic [2]–[4]. However, the finite-difference time-domain (FDTD) method may not fit the fine and complex structure. On the other hand, even though the finite-element time-domain method (FETD) shows advantage in tetrahedral meshing flexibility, it needs to solve large linear algebraic equations in each time step. In contrast, the FETD method with discontinuous Galerkin technology (DG-FETD) can not only inherit the superiority of reducing modeling errors, but also avoids the shortcoming by forming block diagonal coefficient matrix.