We have an adaptive mesh refinement (AMR) code for solving the elastic wave equation with frictional fault interfaces (based on Chombo for those that are interested). One of the things that we have realized is that our results are being strongly affected by the presence of the outer absorbing boundary (which we implement as a simple characteristic boundary condition). For reference we currently use the multidimensional Godunov (Finite Volume) scheme of Colella and collaborators. Though we are not wed to these methods (just easy to use since they are already in Chombo) we do need adaptivity in time.
What I am wondering is if anyone one has any experience with more efficient absorbing boundary conditions with AMR using adaptive time stepping, such as perfectly matched layers or high-order boundary conditions. Any reason not to go down this road? My limited searching hasn't really turned up any useful references or mentions of this in the literature.
Edit: clarified that this is a finite volume method.