Perfectly Matched Layers for Acoustic and Elastic Waves

The modelling of linear wave propagation on unbounded domains is of interest in various fields of both science and engineering. It is especially of interest in the earthquake analysis of dams because the foundation rock and impounded water may be modelled as unbounded domains undergoing wave motion generated by the motion of the dam. One approach to the numerical solution of a wave equation on an unbounded domain uses a bounded domain surrounded by an absorbing boundary or layer that absorbs waves propagating outward from the bounded domain. A perfectly matched layer (PML) is an absorbing layer model that absorbs, almost perfectly, all waves incident upon it. This report develops the concept of a PML for elastic and acoustic waves using some of the insights obtained in the context of electromagnetics and presents PMLs for (1) a rod on elastic foundation, (2) acoustic waves in two and three dimensions, and (3) elastic waves in two and three dimensions. Furthermore, this report develops displacement-based finite-element implementations for the PMLs, both in the frequency-domain and the time-domain. In particular, an efficient finite-element implementation suitable for explicit integration is presented for the three-dimensional elastic PML, thus allowing the solution of realistic three-dimensional problems without the overhead of solving a large system of equations at each time step.