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Higher order boundary conditions involve derivatives of the fields beyond the first and were recently shown to be more effective than traditional first-order conditions in modeling dielectric coatings and layers. In this paper an application is presented of a third-order generalized boundary condition to scattering by a filled rectangular groove. Deficiencies of such higher order boundary conditions are addressed, and a correction is proposed for the present case. As part of the process of examining and correcting the accuracy of the proposed generalized boundary conditions, an exact solution is developed and a comparison is provided with a solution based on the standard impedance boundary condition.

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