A discontinuous galerkin finite element time domain method with PML

Discontinuous Galerkin methods are a class of finite element methods that employ piecewise continuous basis and testing functions. The methods are characterized as being high-order accurate, able to model complex geometries, efficient, stable, and are highly parallel [1]. Discontinuous Galerkin Time-Domain (DGTD) methods have more recently been employed for the solution of Maxwell’s equations [2–4]. In this paper, a discontinuous finite-element time-domain method (DGFETD) is introduced that utilizes hierarchical Nedelec curl-conforming mixed-order basis functions. Such basis naturally satisfy the divergence free-nature of the fields, and hence the formulation avoids the need for penalty methods [3]. It also allows for local hp-refinement of the discretization. The method is shown to be stable and high-order convergent.