scholarly journals Well-conditioned boundary integral formulations for high-frequency elastic scattering problems in three dimensions

2014 ◽  
Vol 38 (9) ◽  
pp. 1705-1733 ◽  
Author(s):  
M. Darbas ◽  
F. Le Louër
Keyword(s):  
Elastic Scattering ◽  
High Frequency ◽  
Boundary Integral ◽  
Three Dimensions ◽  
Scattering Problems

scholarly journals Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering

Acta Numerica ◽  
2012 ◽  
Vol 21 ◽  
pp. 89-305 ◽  
Author(s):  
Simon N. Chandler-Wilde ◽  
Ivan G. Graham ◽  
Stephen Langdon ◽  
Euan A. Spence
Keyword(s):  
High Frequency ◽  
Recent Progress ◽  
Design Analysis ◽  
Boundary Integral ◽  
Original Research ◽  
Scattering Problems ◽  
Asymptotic Boundary ◽  
Boundary Integral Methods ◽  
Integral Methods ◽  
Highly Oscillatory

In this article we describe recent progress on the design, analysis and implementation of hybrid numerical-asymptotic boundary integral methods for boundary value problems for the Helmholtz equation that model time harmonic acoustic wave scattering in domains exterior to impenetrable obstacles. These hybrid methods combine conventional piecewise polynomial approximations with high-frequency asymptotics to build basis functions suitable for representing the oscillatory solutions. They have the potential to solve scattering problems accurately in a computation time that is (almost) independent of frequency and this has been realized for many model problems. The design and analysis of this class of methods requires new results on the analysis and numerical analysis of highly oscillatory boundary integral operators and on the high-frequency asymptotics of scattering problems. The implementation requires the development of appropriate quadrature rules for highly oscillatory integrals. This article contains a historical account of the development of this currently very active field, a detailed account of recent progress and, in addition, a number of original research results on the design, analysis and implementation of these methods.

BROADBAND MULTILEVEL FAST MULTIPOLE ALGORITHM FOR ACOUSTIC SCATTERING PROBLEMS

2006 ◽  
Vol 14 (04) ◽  
pp. 507-526 ◽  
Author(s):  
HENRIK WALLÉN ◽  
SEPPO JÄRVENPÄÄ ◽  
PASI YLÄ-OIJALA
Keyword(s):  
High Frequency ◽  
Acoustic Scattering ◽  
Boundary Integral ◽  
Resonance Problem ◽  
Fast Multipole ◽  
Scattering Problems ◽  
Half Wavelength ◽  
Multilevel Fast Multipole Algorithm ◽  
Fast Multipole Algorithm ◽  
Sub Wavelength

A broadband multilevel fast multipole algorithm (MLFMA) for the acoustic scattering from a sound-hard obstacle is presented. The formulation is based on the Burton–Miller boundary integral equation and Galerkin's method, avoiding any hypersingular integral operators. The resulting matrix equation has good iterative properties for all frequencies and avoids the interior resonance problem. The main novel feature is the use of a broadband MLFMA to accelerate the iterative generalized minimal residual (GMRES) solver. The algorithm is based on a combination of Rokhlin's translation formula for large division cubes and the spectral representation of the Green's function for cubes smaller than one half wavelength, thereby avoiding the sub-wavelength breakdown of the high-frequency MLFMA.

Scattering of a Plane Elastic Wave From Objects Near an Interface

1972 ◽  
Vol 39 (4) ◽  
pp. 1019-1026 ◽  
Author(s):  
Stephen B. Bennett
Keyword(s):  
Elastic Wave ◽  
Electromagnetic Waves ◽  
Three Dimensions ◽  
Circular Cylinders ◽  
Scattering Problems ◽  
Reflection And Refraction ◽  
Time Harmonic ◽  
Incident Plane ◽  
Boundary Curves ◽  
Consistent Formulation

The displacement field generated by the reflection and refraction of plane (time harmonic) elastic waves by finite obstacles of arbitrary shape, in the neighborhood of a plane interface between two elastic media, is investigated. The technique employed allows a consistent formulation of the problem for both two and three dimensions, and is not limited either to boundary shapes which are level surfaces in appropriate coordinate systems, i.e., circular cylinders, spheres, etc., or to closed boundary curves or surfaces. The approach is due to Twersky, and has been applied to many problems of the scattering of electromagnetic waves. The method consists of expressing the net field due to all multiple scattering in terms of the field reflected from each boundary in isolation when subjected to an incident plane elastic wave. Thus the technique makes use of more elemental scattering problems whose solutions are extant. By way of illustration, a numerical solution to the scattering of a plane elastic wave by a rigid circular cylindrical obstacle adjacent to a plane free surface is considered.

scholarly journals Solitary flexural–gravity waves in three dimensions

2018 ◽  
Vol 376 (2129) ◽  
pp. 20170345 ◽  
Author(s):  
Olga Trichtchenko ◽  
Emilian I. Părău ◽  
Jean-Marc Vanden-Broeck ◽  
Paul Milewski
Keyword(s):  
Gravity Waves ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Boundary Integral ◽  
Three Dimensions ◽  
Cosserat Theory ◽  
Theme Issue ◽  
Flexural Gravity Waves ◽  
Forced Waves ◽  
Ice Phenomena

The focus of this work is on three-dimensional nonlinear flexural–gravity waves, propagating at the interface between a fluid and an ice sheet. The ice sheet is modelled using the special Cosserat theory of hyperelastic shells satisfying Kirchhoff's hypothesis, presented in (Plotnikov & Toland. 2011 Phil. Trans. R. Soc. A 369 , 2942–2956 ( doi:10.1098/rsta.2011.0104 )). The fluid is assumed inviscid and incompressible, and the flow irrotational. A numerical method based on boundary integral equation techniques is used to compute solitary waves and forced waves to Euler's equations. This article is part of the theme issue ‘Modelling of sea-ice phenomena’.

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