Analysis of the Discretization Error at Material Interfaces in Staggered Grids

We address the problem of modeling discontinuities at material interfaces and we propose an intuitive model to discuss the origin of spurious discrete reflections. We restrict ourselves to the 1-D analysis and we consider perfectly matched layers as a case study. The approach, based on an approximation, leads to a closed form expression to quantitatively evaluate the performance of perfectly matched layers. Furthermore, the algorithms are presented in details for reproducibility.