A hybrid method combining the surface integral equation method and ray tracing for the numerical simulation of high frequency diffraction involved in ultrasonic NDT

Bonnet, Marc; Collino, Francis; Demaldent, Édouard; Impériale, Alexandre; Pesudo, L.

doi:10.1088/1742-6596/1017/1/012007

Cited by 1 publication

(1 citation statement)

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“…Problems of high frequency scattering by one large relatively simple obstacle and one (or many) small obstacle(s) are potentially of practical interest. An approach used in Lenoir et al (2017) and Bonnet et al (2018) for such problems is to appeal to high frequency asymptotics on the large obstacle, via Geometrical/Physical Optics approximation, and approximate the solution on (or in some neighbourhood of) the small components using a standard BEM/FEM. This approximation works well at sufficiently high frequencies, but ignores diffracted waves emanating from the large obstacle, and so is not controllably accurate across all frequencies.…”

Section: Introductionmentioning

confidence: 99%

A high-frequency boundary element method for scattering by a class of multiple obstacles

Gibbs

Chandler-Wilde

Langdon

et al. 2020

IMA Journal of Numerical Analysis

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We propose a boundary element method for problems of time-harmonic acoustic scattering by multiple obstacles in two dimensions, at least one of which is a convex polygon. By combining a hybrid numerical-asymptotic (HNA) approximation space on the convex polygon with standard polynomial-based approximation spaces on each of the other obstacles, we show that the number of degrees of freedom required in the HNA space to maintain a given accuracy needs to grow only logarithmically with respect to the frequency, as opposed to the (at least) linear growth required by standard polynomial-based schemes. This method is thus most effective when the convex polygon is many wavelengths in diameter and the small obstacles have a combined perimeter comparable to the problem wavelength.

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Section: Introductionmentioning

confidence: 99%