Optimum Loss Factor for a Perfectly Matched Layer in Finite-Difference Time-Domain Acoustic Simulation

A perfectly matched layer (PML) is commonly used in finite-difference time-domain (FDTD) simulation to absorb outgoing waves and thereby reduce artifactual reflections from the computational domain boundaries. However, previous two-dimensional studies have noted that increasing the PML loss factor does not monotonically improve the PML's performance. This paper evaluates the PML in three-dimensional FDTD acoustic simulations. It confirms the existence of an optimum loss factor, with higher values degrading PML performance. An empirical formula is offered for estimating the optimum loss factor for a linear or a quadratic profile, that depends on the PML depth, sound speed, and grid resolution.