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- Title
EMBEDDING FORMULAE FOR SCATTERING IN A WAVEGUIDE CONTAINING POLYGONAL OBSTACLES.
- Authors
BIGGS, N. R. T.
- Abstract
For certain wave scattering problems embedding formulae can be derived, which express the solution, or far-field 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 ℝ2, and to a lesser extent ℝ3; in this article we derive embedding formulae for wave scattering in a class of two-dimensional waveguide. The waveguide is straight and of uniform width outside a finite length region within which the boundaries are piecewise-linear 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 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 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.
- Subjects
SCATTERING (Physics); ELASTIC wave scattering; BORN approximation; MODULES (Algebra); WAVEGUIDES; POLYGONAL numbers
- Publication
Quarterly Journal of Mechanics & Applied Mathematics, 2016, Vol 69, Issue 4, p409
- ISSN
0033-5614
- Publication type
Article
- DOI
10.1093/qjmam/hbw012