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Embedding formulae for wave diffraction by a circular arc
Institution:Department of Mathematics and Statistics, School of Mathematical and Physical Sciences, University of Reading, P.O. Box 220, Whiteknights, Reading RG6 6AX, United Kingdom
Abstract:For certain wave diffraction problems, embedding formulae can be derived, which represent the solution (or far-field behaviour of the solution) for all plane wave incident angles in terms of solutions of a (typically small) set of other auxiliary problems. Thus a complete characterisation of the scattering properties of an obstacle can be determined by only determining the solutions of the auxiliary problems, and then implementing the embedding formula. The class of scatterers for which embedding formulae can be derived has previously been limited to obstacles with piecewise linear boundaries; here this class is extended to include a simple curved obstacle, consisting of a thin circular arc. Approximate numerical calculations demonstrate the accuracy of the new embedding formulae.
Keywords:Waves  Diffraction  Embedding  Circular arc
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