On the Attenuation of the Perfectly Matched Layer in Electromagnetic Scattering Problems with the Spectral Element Method

Abstract

Although Spectral Element Method (SEM) has been applied in the modeling of boundary value problems of electromagnetics, its usage is not as common as the Finite Element or Finite Difference approaches in this area. It is well-known that the Perfectly Matched Layer (PML) approach is a mesh/grid truncation method in scattering or radiation applications where the spatial domain is unbounded. In this paper, the PML approach in the SEM context is investigated in two-dimensional, frequency-domain scattering problems. The main aim of this paper is to provide the PML parameters for obtaining an optimum amount of attenuation in the scattered field per wavelength in the PML region for Legendre-Gauss-Lobatto grids. This approach is extended to the analysis of SEM accuracy in scattering by electrically large objects by taking the free space Green's function as the building block of the scattered field. Numerical results presented in this work demonstrate the ability of achieving a high degree of accuracy of SEM as compared to other finite methods, as well as the successful applicability of the PML in electromagnetic scattering problems in terms of the optimum attenuation factors provided in this work.