Multi-directional approach of perfectly matched layers

One of the popular non-reflection boundary methods is perfectly matched layers (PML), in which the damping is introduced depending on only a single variable. There is no effective absorption for the waves with low-grazing incidence angles (high incidence angles) to the interface, which is one of the limitations of the classical PML method. In this paper, we introduce additional damping terms, which are positive functions of multi-variables and show the effectiveness of the absorption for the incident wave in the parallel to the interface when the wave propagates in a PML.