Perfectly Matched Layer for meshless analysis of wave propagation in layered elastic-poroelastic half-space

Dynamic response of a transversely isotropic layered half-space composed of alternatively arbitrary poroelastic and elastic materials is numerically investigated through the Meshless Local Petrov–Galerkin (MLPG) method. The governing equations of the porous layers are the $u-p$ formulation of the Biot’s theory, and the equations of motion for single-phase elastic media are considered for pure elastic layers. Furthermore, the Perfectly Matched Layer (PML) concepts are utilized to prepare the geometry of unbounded domain for the numerical analysis. In this regard, the stretched coordinates in PML are introduced in such a way that the truncating procedure does not affect the responses in an arbitrary part of the truncated domain. The continuity condition at the interface of adjacent layers, which may be either elastic-elastic, elastic-poroelastic, or poroelastic-poroelastic, and the jump condition on the excitation area are directly and precisely imposed to the inhomogeneous media. As the error estimation is an indispensable part of the numerical analysis, the $L_2$-norm of error is used to assess the truncated model and control the numerical results. To show the validity of the solution, the numerical evaluation for homogeneous case is compared with the analytical solution. For the inhomogeneous media, the layers can be defined based on some fictitious interfaces to have several homogeneous bodies.