A Discontinuous Galerkin Finite Element Time-Domain Method Modeling of Dispersive Media

Abstract

A method is proposed for solving the time-dependent Maxwell's equations via the discontinuous Galerkin finite-element time-domain (DGFETD) method with dispersive media. An auxiliary differential equation (ADE) method is used to represent the constitutive relations. The method is applied to Drude materials, as well as to multiple pole Debye and Lorentz materials. An efficient implementation for high-order Runge-Kutta time integration schemes is presented. The method is validated and is shown to exhibit high-order convergence.Index Terms-Discontinuous Galerkin methods, electromagnetic propagation in dispersive media, finite element time-domain, high-order methods.

Analysis of a Generalized Dispersive Model Coupled to a DGTD Method with Application to Nanophotonics

“…More recently, more papers are concerned with Finite Element or even Discontinuous Galerkin Time-Domain approaches (DGTD) (see e.g. [GYKR12] and [BKN11] and references therein), aiming at overcoming the limitations of FDTD. In this context, some works are more precisely focused on the numerical analysis.…”

A Resistive Boundary Condition Enhanced DGTD Scheme for the Transient Analysis of Graphene

“…The set Ω RBC consists of mesh elements interfacing with the graphene sheet (or RBC), while the set Ω NRBC contains those meshes not touching the graphene sheet (or RBC). For elements in Ω NRBC , the fourth-order RK method is employed to solve the two first-order time derivative Maxwell's equations [17]; while for elements in Ω RBC , FIT is applied to discrete the integral operators. Since RK marching scheme based DGTD formulation is already well developed [16], [17], [24], we only detail the FIT based DGTD formulation in this work.…”

“…For elements in Ω NRBC , the fourth-order RK method is employed to solve the two first-order time derivative Maxwell's equations [17]; while for elements in Ω RBC , FIT is applied to discrete the integral operators. Since RK marching scheme based DGTD formulation is already well developed [16], [17], [24], we only detail the FIT based DGTD formulation in this work. To obtain the time-domain matrix equations, we start with the two first-order Maxwell's equations in the Laplace-domain.…”

A Discontinuous Galerkin Surface Integral Equation Method for Electromagnetic Wave Scattering From Nonpenetrable Targets

“…As a consequence, it results in a Galerkin type of formulation. We then write the surface penalty term for any test current as (20) with the surface integral term defined by (21) Using the definition of EFIO (9), we further expand (20) as (22) The direct evaluation of (22) is less favorable since the last term in (22) contains hyper-singular integrals. A common remedy is to apply the Green's identity to reduce the order of the singularity, and we have (23) where denotes all the line contours of element , and is the corresponding unit normal on pointing away from .…”

“…DG methods [18]- [20] were first applied for the solution of the time-dependent Maxwell's equations. Recently, it has been extended to the frequency-domain finite-element method (FEM) [21], [22].…”