An improved Perfectly Matched Layer (PML) boundary condition is introduced that addresses the previously reported instabilities. A PML for acoustic waves is derived by closely following Bérenger's derivation of a PML for electromagnetic waves. A new matching condition is developed to relate the velocity and stress loss-coefficients similar to the matching condition defined for electromagnetic waves.
Whereas, the spatial and temporal derivatives are related by simple scalars in Maxwell's equations, elastodynamic equations describing waves in piezoelectric materials require the use of tensor quantities whose general forms are material dependent.
In practice, SAW generation is often also accompanied by some small creation of SAWs, which act as parasitic waves. It is thus desired to remove the reflection of these waves from the bottom, in both physical SAW devices and in modeling.