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We analyze the accuracy and well-posedness of generalized impedance
boundary value problems in the framework of scattering problems
from unbounded highly absorbing media. We restrict ourselves in this first work
to the scalar problem (E-mode for electromagnetic scattering problems). Compared to earlier works, the unboundedness of the rough absorbing layer introduces severe difficulties
in the analysis for the generalized impedance boundary conditions, since
classical compactness arguments are no...
Consider time-harmonic electromagnetic wave scattering from a biperiodic dielectric structure mounted on a perfectly conducting plate in three dimensions. Given that uniqueness of solution holds, existence of solution follows from a well-known Fredholm framework for the variational formulation of the problem in a suitable Sobolev space. In this paper, we derive a Rellich identity for a solution to this variational problem under suitable smoothness conditions on the material parameter. Under additional...
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