Abstract: (Joint with D.P. Nicholls). A popular technique for truncating
infinite computational regions is the exact Dirichlet-to-Neumann map of
Givoli and Keller, prescribed on an artificial boundary surrounding a
scatterer. This map relies on the exterior of the artificial boundary
being a seperable geometry. In particular, the map has been executed for
spherical and elliptical geometries. These geometries may not be optimal
for many classes of scatterers.
In this talk we describe a perturbative technique which allows us to
prescribe DtN maps on analytic perturbations of simple geometries. We
prove analyticity of the method, and show numerical experiments validating
our approach. Careful summation techniques allow the perturbations to be
large relative to the size of the scatterer.