Stability Considerations for Perfectly Matched Layers in Piezoelectric Crystals

We show that a Perfectly Matched Layer (PML) can experience numerical instabilities when used for Finite Difference Time Domain (FDTD) calculations in piezoelectric crystals. For example, simulations of acoustic wave propagation in bismuth germanate (Bi4Ge3O12) lead to numerical instabilities in the PML, while similar simulations in barium sodium niobate (Ba2NaNb5O15) do not. We present examples of FDTD simulations and use the results to deduce the conditions necessary for stability.