Studies of FE/PML for exterior problems of time-harmonic elastic waves

The equation of an absorbing layer for time-harmonic elastic waves, based on the Perfectly Matched Layer (PML) concept, is formulated in a manner that is easily implemented in finite element software. The proposed approach modifies a recent, symmetric, displacement based formulation, which employs complex-valued coordinate stretching. This formulation requires rotation matrices and an unconventional structure of the finite element stiffness integrand, obscuring its symmetry. Instead, the layer may be viewed as an anisotropic material with continuously varying complex material properties, following a similar approach for acoustics. The major symmetry of the conventional linear elasticity tensor is retained, as in the case of the linearized theory of small displacements superposed upon large. Simple, explicit expressions for the modified material coefficients are provided for configurations of plane strain and stress, and three dimensions. Guidelines for proper selection of the PML parameters are presented. These guidelines are based on recent work on the affect of discretization on the performance of the PML. The formulation, with the parameters selected according to the guidelines proposed, performs well in computation.