Perfectly matched layer for FDTD computations in piezoelectric crystals

In (P. M. Smith et al, IEEE Ultrasonics Symp. Proc., p.313-316, 2002) the finite difference time domain technique was first applied to acoustic wave propagation in piezoelectric materials. A problem of spurious reflections from the edge of the computational region was observed. In this paper, a perfectly matched layer (PML) is developed that solves the issue of spurious reflections and provides the capability of simulating acoustic wave propagation in a sub-region of an infinite medium. Several snapshots of an acoustic wave are presented to illustrate the functionality of the PML. The maximum error due to edge reflections is found to be less than 0.5%.