Anisotropic Perfectly Matched Layers for Elastic Waves in Cartesian and Curvilinear Coordinates

Abstract

We develop new numerical anisotropic perfectly matched layer (PML) boundaries for elastic waves in Cartesian, cylindrical and spherical coordinate systems. The elasticity tensor of this absorbing boundary is chosen to be anisotropic and complex so that waves from the computational domain are attenuated in the boundary layer without reflection. The new PMLs are easy to formulate for both isotropic and anisotropic solid media. They utilize fewer unknowns in a general three-dimensional problem than the existing elastic wave PMLs using the field splitting scheme. Moreover, it can be implemented directly to the finite element method (FEM), as well as the finite difference time domain (FDTD) method. The high efficiency of these PMLs is illustrated by some numerical samples in FEM.