Optimization of the Periodic PML for SEM

A periodic perfectly matched layer (PML) is proposed for the spectral element method (SEM) for the first time, which not only simplifies the recognition process of a PML domain, but also saves degrees of freedom (DoFs) when squeezing its layer number to 1. An objective function to evaluate and optimize its performance has been theoretically derived. In the use of this objective function, the PML parameters are optimized under different conditions; the relationships between the PML's performance and the scaling factor profile, the source position, the basis functions' order, and the PML layer number are studied, which can help guide the practical applications of PML in the SEM modeling. An estimation method is also introduced to facilitate the selection of the scaling factor.