Edge Diffraction Coefficients around Critical Rays

The classical GTD (Geometrical Theory of Diffraction) gives a recipe, based on high-frequency asymptotics, for calculating edge diffraction coefficients in the geometrical regions where only diffracted waves propagate. The Uniform GTD extends this recipe to transition zones between irradiated and si...

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Bibliographic Details
Published inJournal of physics. Conference series Vol. 498; no. 1; pp. 12010 - 10
Main Authors Fradkin, L, Harmer, M, Darmon, M
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 01.01.2014
IOP Science
Subjects
Asymptotic properties
Boundaries
Coalescing
Coefficients
Critical point
Diffraction
Geometrical theory of diffraction
Mathematical analysis
Mathematical models
Physics
Reflected waves
Shadows
Transducers
Wave diffraction
Industrial materials
Numerical methods
Diffracted waves
High-frequency asymptotics
Stationary points
Transition regions
Elastic waves
Shadow boundaries
Transition zones
Geometry
Ultrasonic transducers
Diffraction
Geometrical theory of diffraction
Seismic waves
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Summary:The classical GTD (Geometrical Theory of Diffraction) gives a recipe, based on high-frequency asymptotics, for calculating edge diffraction coefficients in the geometrical regions where only diffracted waves propagate. The Uniform GTD extends this recipe to transition zones between irradiated and silent regions, known as penumbra. For many industrial materials, e.g. steels, and frequencies utlized in industrial ultrasonic transducers, that is, around 5 MHz, asymptotics suggested for description of geometrical regions supporting the head waves or transition regions surrounding their boundaries, known as critical rays, prove unsatisfactory. We present a numerical extension of GTD, which is based on a regularized, variable step Simpson's method for evaluating the edge diffraction coefficients in the regions of interference between head waves, diffracted waves and/or reflected waves. In mathematical terms, these are the regions of coalescence of three critical points - a branch point, stationary point and/or pole, respectively. We show that away from the shadow boundaries, near the critical rays the GTD still produces correct values of the edge diffraction coefficients.
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ISSN:1742-6596
1742-6588
1742-6596
1742-6588
DOI:10.1088/1742-6596/498/1/012010