Stable perfectly-matched-layer boundary conditions for finite-difference time-domain simulation of acoustic waves in piezoelectric crystals

Perfectly matched layer (PML) boundary conditions are derived for finite-difference timedomain analysis of acoustic waves within piezoelectric crystals. The robustness and effectiveness of the derived boundary conditions are demonstrated by simulating acoustic wave propagation in the bismuth germanate material system—a system in which simple absorbing boundary conditions cause instabilities. An investigation into the stability and effectiveness of the PML is then presented in terms of the PML thickness and absorption profile. A range of optimised absorption profiles were determined by finding the maximum permissible absorption within the stability limit of the system. In the optimised case, the form of the absorption profile had little influence on the effectiveness of the PML. However, in the unoptimised case the linearly increasing absorption profile was found to be the most effective.