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 (displacement-based) 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 (time-domain) 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 time-domain 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 displacement-based finite element codes. For computational efficiency, the proposed time-domain 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.

这篇评论文章回顾并概述了过去25年开发的完全匹配层（PML）方法及其各种公式，用于数值模拟和模拟无边界介质中的波传播。基于复杂坐标拉伸的概念，提出了一种有效的混合位移-应变非分裂场PML公式，用于二阶（基于位移）线性弹性力学方程，用于模拟弹性波在无界（无限或半）中的传播和吸收-无限）域。对于二维和三维线性弹性动力学问题，导出了时谐（频域）和时相关（时域）PML公式。通过仅引入一些由低阶辅助微分方程控制的变量，所得的混合时域PML公式在时间上是二阶的，从而允许使用计算结构动力学中常用的标准时间积分方案，从而便于将其合并到现有的基于位移的有限元代码中。为了提高计算效率，建议的时域PML公式是使用混合方法实现的，该方法使用标准将PML区域的混合（位移-应变）公式与感兴趣的物理域的经典（基于位移）公式耦合在一起用于空间离散化的Galerkin有限元方法（FEM）和Newmark时间方案，以及用于时间采样的有限差分（Crank-Nicolson）时间方案。数值实验显示了PML方法在精度方面的性能，