SingularIntegralEquations.jl
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Different material properties
We should be able to look at Helmholtz and Laplace's equation with homogeneous regions with different material properties: permeability & permittivity, and different wave numbers. I believe this would only change the Dirichlet/Neumann traces and how the solutions are evaluated, but the problem structure is the same.
There's also a dual problem to scattering of screens. The set complement of the original obstacles can also be considered the scatterer.
Negative permittivity and permeability give rise to meta materials that can cloak embedded objects in a certain frequency band.
http://m.sciencemag.org/content/314/5801/977