An Exact Modal Impedance Boundary Condition for Finite Element Simulation of Local Seismic Response

This work presents a novel impedance-based non-reflecting boundary condition for finite element simulations of elastodynamic wave propagation, referred to as the Adaptive Boundary Mode–Impedance Boundary Condition (ABM-IBC). The method is derived from the exact Dirichlet-to-Neumann (DtN) map of an elastic half-space and is implemented through a local modal decomposition of the wavefield along the computational boundary. The formulation is developed for two-dimensional isotropic elastodynamics and explicitly accounts for both propagating and evanescent modes associated with compressional (P) and vertically polarized shear (SV) waves. For each horizontal wavenumber, the exact dynamic impedance of the elastic half-space is evaluated in modal space and applied to boundary velocities, while the corresponding physical tractions are reconstructed efficiently via an inverse spectral transform. The ABM-IBC is integrated into a time-domain finite element framework using a local spectral decomposition of boundary velocities and a fast Fourier transform (FFT)-based reconstruction of boundary tractions. Unlike conventional absorbing-layer techniques, such as Perfectly Matched Layers (PML) and Convolutional PML (C-PML), the proposed boundary condition operates directly on the physical boundary, requires no additional computational domains or auxiliary variables, and introduces no empirical parameters for calibration. Numerical simulations representative of local seismic response analyses demonstrate that the ABM-IBC effectively suppresses spurious boundary reflections, including for oblique and near-grazing incidence, while ensuring numerical stability and achieving lower computational costs compared with classical PML-based approaches. The results highlight the potential of the ABM-IBC as a robust and efficient tool for high-fidelity elastodynamic simulations in geotechnical and seismic engineering applications.