Efficient Implementation of the UPML in the Generalized Finite-Difference Time-Domain Method

In this paper, we show how to use hexahedral and prismatic elements for the efficient development of uniaxial anisotropic dispersive media (UPML) around an initial unstructured tetrahedral primal mesh using the generalized finite-difference (GFD) method. The initial mesh is assumed to have plane external boundaries. Taking into account the properties of the UPML medium, we build a special discrete Hodge in order to have a simple scheme for the time-domain solution of Maxwell's equations. The method is presented for the general 3-D case and numerical results show its efficiency.