Implementation of uniaxial perfectly matched layer based on hexahedron element in discontinuous Galerkin time domain

Abstract

Abstract The uniaxial perfectly matched layer (UPML), an important link in the numerical calculation of the discontinuous Galerkin time domain (DGTD), truncates the size of the computational domain and absorbs the outward‐travelling waves. In traditional DGTD, tetrahedral meshes are used to divide the computational domain. These meshes are also used in UPML. As the scope of the computational domain is wide, many meshes will be generated after the UPML division wraps the external part of the domain, thereby resulting in inefficient computation. The use of a UPML in DGTD form based on hexahedral meshes is proposed. The internal propagation and UPML regions are divided by a tetrahedral element and a hexahedral element, respectively. Among the relevant numerical examples given, a few cases are analysed to demonstrate the feasibility of the proposed method: the high efficiency of the UPML with hexahedral mesh, attenuation of electromagnetic waves inside the UPML, and relative error of the electric field values at the observation points.

Keywords

• electromagnetic wave attenuation
• finite difference time-domain analysis
• Galerkin method
• Maxwell equations
• mesh generation
• time‐domain analysis