Diffraction of acoustic waves and embedding theory

Abstract

The diffraction and scattering of sound waves by sharp edges and corners is a ubiquitous feature of acoustic interactions with structures. This talk is on a technique called embedding which is a relatively new, and under used, idea in diffraction theory. The fundamental idea of embedding is that one only ever solves a single master, canonical, scattering problem (or set of problems). Thereafter, to extract the far-field behavior for any plane wave incidence on the same geometry, one only manipulates results from this master problem. The result is that quantities (directivities) previously dependent upon two parameters (incident and observed angle) become factorized into products of a function of a single variable, together with a simple trigonometric term; this facilitates rapid numerical evaluation. In principle, this should revolutionize many scattering calculations in every area where diffraction occurs as one need only evaluate the directivities from the set of canonical problems once. Given these directivities one manipulates them to generate solutions for more general problems, rather than continually recalculating and re-evaluating. At present, the theory has some limitations and the talk will cover these and describe how they can be overcome.