https://cea.hal.science/cea-01820753Fradkin, L.L.FradkinSound Mathematics Ltd.Harmer, M.M.HarmerSound Mathematics Ltd.Darmon, M.M.DarmonDISC - Département Imagerie et Simulation pour le Contrôle - LIST (CEA) - Laboratoire d'Intégration des Systèmes et des Technologies - DRT (CEA) - Direction de Recherche Technologique (CEA) - CEA - Commissariat à l'énergie atomique et aux énergies alternatives - Université Paris-SaclayEdge diffraction coefficients around critical raysHAL CCSD2014Elastic waves Geometry Numerical methods Seismic waves Ultrasonic transducers Diffracted waves Geometrical theory of diffraction High-frequency asymptotics Industrial materials Shadow boundaries Stationary points Transition regions Transition zones Diffraction[PHYS] Physics [physics]Le Roy, Léna2018-06-22 09:50:022023-08-01 13:01:312018-06-22 09:50:02enJournal articles10.1088/1742-6596/498/1/0120101The 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.