Study on the Stability of Perfectly Matched Layer Implementations Using a Hybrid Implicit–Explicit Update Scheme

Abstract

The perfectly matched layer (PML) technique is a general-purpose absorbing boundary condition for finite methods which is usually applied within explicit time-domain schemes. There are a number of slightly different implementations of the extended update equations, and many of them have been reported in the literature to show some long-term instabilities, typically only weakly depending on the time step size. In this contribution, we present a hybrid implicit–explicit algorithm that introduces two additional parameters to control the stability. The implicit part of the algorithm is used only locally within the PML region, and for a simple setup, stability is reached for a certain range of the additional parameters.