Questioning Degree of Accuracy Offered by the Spectral Element Method in Computational Electromagnetics

In this paper, a comparison amongst the spectral element method (SEM), the finite difference method (FDM), and the first-order finite element method (FEM) is presented. For the sake of consistency, the comparison is carried out on one-dimensional and two-dimensional boundary value problems based on the same measure of error in order to emphasize on the high accuracy gained by the SEM. Then, the deterioration in the accuracy of the SEM due to the elemental deformation is demonstrated. Following this, we try to answer the question: Do we need the high accuracy offered by the SEM in computational electromagnetics? The answer is supported by solving a typical, unbounded electromagnetic scattering problem in the frequency domain by the SEM. Domain truncation is performed by the well-known perfectly matched layer (PML).