Numerical interaction of boundary waves with perfectly matched layers in two space dimensional elastic waveguides

•We analyze the stability and accuracy of the PML in transient elastic waveguides bounded by free-surface boundary conditions.•Using the SBP-SAT methodology we develop a stable numerical approximation of the PML in waveguides.•We demonstrate that back-propagating modes are not harmful to a finite width discrete PML.•Numerical experiments verify the theoretical results.

Perfectly matched layers (PMLs) are now a standard approach to simulate the absorption of waves in open domains. Wave propagation in elastic waveguides has the possibility to support back-propagating modes (propagating modes with oppositely directed group and phase velocities) with long wavelengths. Back-propagating modes can lead to temporally growing solutions in the PML. In this paper, we demonstrate that back-propagating modes in a two space dimensional isotropic elastic waveguide are not harmful to a discrete and finite width PML. Analysis and numerical experiments confirm the accuracy and stability of the PML.