By James H. Bramble, Joseph E. Pasciak, and Dimitar Trenev.
Abstract: We consider a perfectly matched layer technique for the elastic wave scattering problem in this talk. Elastic wave scattering problems are posed on the complement of a bounded domain $\Omega\subset \RR^3$ (the scatterer). The boundary condition at infinity is given by the Kupradze-Sommerfeld radiation condition and involves different Sommerfeld conditions on different components of the field (the shear and compression waves). We shall see that the PML approach can be used to provide an artificial boundary condition which leads to an effective domain truncation strategy. This approach transparently deals with the different wave speeds and avoids the computational separation of shear and compression waves. The stability of the finite element and negative norm least-squares methods will also be discussed and the results of numerical experiments will be reported.