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An introduction to absorbing layers and non-reflecting boundary conditions.

I will give an overview of different techniques to truncate unbounded domains by absorbing layers and non-reflecting or artificial boundary conditions. Among other topics I will describe the perfectly matched layer (PML) introduced in 1994 by Berenger (cited >10,000 times on Google Scholar!). Ie will discuss the following questions: Is PML well-posed in general? For what problems is PML stable? What is the most general model for a PML? I will also mention some more recent results by Hagstrom and Warburton on complete radiation boundary conditions (CRBC) which, in some sense, is an optimal solution to domain truncation problem for linear Friedrich systems. Finally, I will discuss absorbing layer techniques for more complex problems where PML and CRBC may not be stable.

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