When solving innite domain wave problems numerically, there is no easy way to eliminate reflections from the edge of the computational domain. One way to have no reflections is to surround your computational domain with a layer. In this layer, we solve a modied equation induced by a transformation of the coordinate space.
We have a lot of choice over this transformation and, indirectly, the modied equation and solution in the layer. Given some information about the solution in the computational domain, can we make the solution in the layer as trivial as a straight line?
Yes we can! Can we turn it into an effective numerical method? Maybe not. Is it a good idea to ask so many rhetorical questions? Probably not.
I will present the inspiration and motivation for this problem, along with some tentative results and (hopefully) thought provoking questions.