Publisher: Oxford University Press
Languages: English
Types: Article
Identifiers:doi:10.1093/qjmam/hbw012
For certain wave scattering problems embedding formulae can be derived, which express the solution, or farfield behaviour of the solution, for arbitrary plane wave incident angle in terms of the corresponding quantities for a finite number of other related problems. Their scope has so far been limited to scattering in R^2, and to a lesser extent R^3; in this paper we derive embedding formulae for wave scattering in a class of twodimensional waveguide. The waveguide is straight and of uniform width outside a finite length region within which the boundaries are piecewiselinear and the waveguide can contain polygonal obstacles, a restriction being that all boundaries of the waveguide and obstacles must be inclined at a rational angle to the axis of the waveguide. Once solutions are determined for a finite set of incident propagating modes, the embedding formulae provide expressions for reflection and transmission\ud coefficients for all remaining incident propagating modes. The precise number of solutions required is a function of the number and nature of the corners of the\ud boundaries and obstacles. The formulae are illustrated for a particular waveguide geometry for which the problem can be formulated as an integral equation and approximate numerical solutions determined using the Galerkin method.

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