  This review article revisits and outlines the perfectly matched layer (PML)
method and its various formulations developed over the past 25 years for the
numerical modeling and simulation of wave propagation in unbounded media. Based
on the concept of complex coordinate stretching, an efficient mixed
displacement-strain unsplit-field PML formulation for second-order
(displacementbased) linear elastodynamic equations is then proposed for
simulating the propagation and absorption of elastic waves in unbounded
(infinite or semi-infinite) domains. Both time-harmonic (frequency-domain) and
time-dependent (timedomain) PML formulations are derived for two-and
three-dimensional linear elastodynamic problems. Through the introduction of
only a few additional variables governed by low-order auxiliary differential
equations, the resulting mixed timedomain PML formulation is second-order in
time, thereby allowing the use of standard time integration schemes commonly
employed in computational structural dynamics and thus facilitating the
incorporation into existing displacementbased finite element codes. For
computational efficiency, the proposed timedomain PML formulation is
implemented using a hybrid approach that couples a mixed (displacement-strain)
formulation for the PML region with a classical (displacement-based)
formulation for the physical domain of interest, using a standard Galerkin
finite element method (FEM) for spatial discretization and a Newmark time
scheme coupled with a finite difference (Crank-Nicolson) time scheme for time
sampling. Numerical experiments show the performances of the PML method in
terms of accuracy, efficiency and stability for two-dimensional linear
elastodynamic problems in single-and multi-layer isotropic homogeneous elastic
media.
