  Perfectly matched layers are a very efficient and accurate way to absorb
waves in media. We present a stable convolutional unsplit perfectly matched
formulation designed for the linearized stratified Euler equations. However,
the technique as applied to the Magneto-hydrodynamic (MHD) equations requires
the use of a sponge, which, despite placing the perfectly matched status in
question, is still highly efficient at absorbing outgoing waves. We study
solutions of the equations in the backdrop of models of linearized wave
propagation in the Sun. We test the numerical stability of the schemes by
integrating the equations over a large number of wave periods.
