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

An absorbing boundary formulation for the stratified, linearized, ideal MHD equations based on an unsplit, convolutional perfectly matched layer