Embedding techniques for directivities in acoustics and elasticity

Lead Research Organisation: Imperial College London
Department Name: Dept of Mathematics

Abstract

It is often required, during say the evaluation of the safety of a structure or evaluating the radar profile of an aircraft, that one needs a diffraction coefficient. This coefficient characterizes the signal seen far from the object; these can be awkward to evaluate and re-evaluate as a parameter changes.Embedding offers the possibility of revolutionizing how these are calculated, basically one instead solves a master problem and one evaluates its directivity. The directivity one actually wants to have is found from this by manipulations, the key point is that less variables are involved in the master problem so you evaluate this directivity only a few times. Hence one could potentially model, say, scattering by a crack in a rail track by doing just a few calculations and model the effect of altering the incoming wavefield without ever having solve the problem again.

Publications

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Shanin A (2010) Pseudo-differential operators for embedding formulae in Journal of Computational and Applied Mathematics

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Skelton E (2007) Embedding formulae for diffraction by non-parallel slits in The Quarterly Journal of Mechanics and Applied Mathematics