A minimally intrusive unsplit, non-convolutional perfectly matched layer preserving standard finite element mass and stiffness matrices for transient elastodynamics

The numerical analysis of wave propagation in unbounded domains is crucial in engineering but computationally demanding. Domain truncation with absorbing layers, particularly the perfectly matched layer (PML), is standard for mitigating spurious reflections. However, in the finite element method (FEM), existing PML formulations in the time domain often modify the system matrices and may introduce additional global degrees of freedom, thereby complicating spatial discretization and numerical implementation. To address these challenges, this study presents a minimally intrusive, unsplit and non-convolutional PML formulation for FEM simulations of transient elastic wave propagation. Two sets of auxiliary variables, associated respectively with strain and stress, are introduced to recast the PML contributions as two additional nodal force vectors within the standard FEM framework. A major advantage of the proposed formulation is that it does not alter the standard mass or stiffness matrices. It therefore remains fully compatible with the classical FEM framework and has a concise structure that is straightforward to implement. Moreover, the proposed FEM-PML method is applicable to both explicit and implicit time integration schemes. The proposed method is validated through numerical examples covering different source frequencies and wave-propagation scenarios. It provides effective absorption over the tested frequency range at a lower computational cost. Robust performance is also demonstrated for oblique incidence, surface waves, heterogeneous media, and dynamic fault rupture. These results confirm that the method is an efficient and practical PML formulation for transient FEM analysis.