New Results on Absorbing Layers and Radiation Boundary Conditions

Perhaps the defining feature of waves is the fact that they propagate long distances relative to their characteristic dimension, the wavelength. This allows us to use them to probe the world around us — optically, acoustically, and now at a wide range of wavelengths in a variety of media. For numerical simulations, it is precisely this essential characteristic — the radiation of waves to the far field — that leads to the greatest difficulties. One may view this fundamental difficulty as rooted in the existence of (at least) two widely separated spatial scales. The first are the small scales associated with the wavelengths and the scatterer, and the second is the long distance between the scatterer and the observers.