Stability and convergence analysis of time-domain perfectly matched layers for the wave equation in waveguides

This work is dedicated to the proof of stability and convergence of the Bérenger's perfectly matched layers (PMLs) in the waveguides for an arbitrary nonnegative L∞damping function. The proof relies on the Laplace-domain techniques and an explicit representation of the solution to the PML problem in the waveguide. A bound for the PML error that depends on the absorption parameter and the length of the PML is presented. Numerical experiments confirm the theoretical findings.