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Embedding formulae for scattering in a waveguide containing polygonal obstacles

Biggs, N. R. T. (2016) Embedding formulae for scattering in a waveguide containing polygonal obstacles. The Quarterly Journal of Mechanics and Applied Mathematics, 69 (4). pp. 409-429. ISSN 0033-5614

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To link to this item DOI: 10.1093/qjmam/hbw012

Abstract/Summary

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 R^2, and to a lesser extent R^3; in this paper 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.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:66108
Publisher:Oxford University Press

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