Absorbing Boundary Conditions in Wave Propagation Simulations

Accurate numerical modelling of wave phenomena in unbounded or large domains requires special treatments at the artificial boundaries of the computational grid to prevent non-physical reflections. Absorbing boundary conditions (ABCs) serve to emulate an infinite medium, allowing outgoing waves to leave the domain without spurious back-scattering that could contaminate the solution. Among the most widely used techniques is the perfectly matched layer (PML), which surrounds the region of interest with a fictitious medium engineered—via complex coordinate stretching—to absorb incident energy over a broad frequency range. Variants have been developed in both time-domain and frequency-domain solvers, in conjunction with finite-difference, finite-element and spectral methods. More recent efforts address limitations of classical PMLs, such as breakdown in heterogeneous or non-analytic media interfaces, by introducing gradual absorption profiles (adiabatic absorbers) or by combining local high-order ABCs with thin non-reflecting layers. The choice of boundary treatment depends on the governing wave equation (acoustic, elastic, electromagnetic or poroelastic), discretisation strategy, computational cost and desired accuracy. Innovations in automatic parameter selection, stability analysis and extension to complex geometries have broadened applicability to industrial acoustics, seismic exploration, marine engineering and photonic device design, while preserving a balance between fidelity and efficiency.

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Absorbing Boundary Conditions in Wave Propagation Simulations publication trend

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Technical terms

Absorbing boundary condition (ABC): A numerical treatment applied at the edge of a computational domain to minimise artificial reflections of outgoing waves.

Perfectly matched layer (PML): A fictitious anisotropic or complex-stretched medium surrounding the domain that absorbs incident waves with theoretically zero reflection.

Adiabatic absorber: A graded absorbing layer in which the absorption coefficient varies smoothly to suppress reflections arising from abrupt impedance changes.

Finite-difference time-domain (FDTD): A time-stepping numerical scheme that discretises both space and time to solve wave equations directly in the time domain.

References

1. The failure of perfectly matched layers, and towards their redemption by adiabatic absorbers.. Optics Express (2008).
2. An automatic perfectly matched layer for acoustic finite element simulations in convex domains of general shape. International Journal for Numerical Methods in Engineering (2020).
3. Perfectly matched absorbing layer for modelling transient wave propagation in heterogeneous poroelastic media. Journal of Geophysics and Engineering (2019).