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

Ivan Graham, Euan Spence, Simon Chandler-Wilde, Stephen Langdon

Research output: Contribution to journalArticle

96 Citations (Scopus)
103 Downloads (Pure)

Abstract

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.
Original languageEnglish
Pages (from-to)89-305
Number of pages216
JournalActa Numerica
Volume21
DOIs
Publication statusPublished - May 2012

Fingerprint

Boundary Integral Method
Acoustic Scattering
Acoustics
Scattering
Oscillatory Integrals
Acoustic wave scattering
Scattering Problems
Polynomial approximation
Helmholtz equation
Oscillatory Solution
Boundary value problems
Wave Scattering
Mathematical operators
Numerical analysis
Exterior Domain
Boundary Integral
Piecewise Polynomials
Quadrature Rules
Polynomial Approximation
Acoustic Waves

Cite this

Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering. / Graham, Ivan; Spence, Euan; Chandler-Wilde, Simon ; Langdon , Stephen .

In: Acta Numerica, Vol. 21, 05.2012, p. 89-305.

Research output: Contribution to journalArticle

Graham, Ivan ; Spence, Euan ; Chandler-Wilde, Simon ; Langdon , Stephen . / Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering. In: Acta Numerica. 2012 ; Vol. 21. pp. 89-305.
@article{db3815840d4f47088af8bc4d72d1a459,
title = "Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering",
abstract = "In this article we describe recent progress on the design, analysis and implementationof hybrid numerical-asymptotic boundary integral methods forboundary value problems for the Helmholtz equation that model time harmonicacoustic wave scattering in domains exterior to impenetrable obstacles.These hybrid methods combine conventional piecewise polynomial approximationswith high-frequency asymptotics to build basis functions suitablefor representing the oscillatory solutions. They have the potential to solvescattering problems accurately in a computation time that is (almost) independentof frequency and this has been realized for many model problems.The design and analysis of this class of methods requires new results on theanalysis and numerical analysis of highly oscillatory boundary integral operatorsand on the high-frequency asymptotics of scattering problems. Theimplementation requires the development of appropriate quadrature rules forhighly oscillatory integrals. This article contains a historical account of thedevelopment of this currently very active field, a detailed account of recentprogress and, in addition, a number of original research results on the design,analysis and implementation of these methods.",
author = "Ivan Graham and Euan Spence and Simon Chandler-Wilde and Stephen Langdon",
year = "2012",
month = "5",
doi = "10.1017/S0962492912000037",
language = "English",
volume = "21",
pages = "89--305",
journal = "Acta Numerica",
issn = "0962-4929",
publisher = "Cambridge University Press",

}

TY - JOUR

T1 - Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering

AU - Graham, Ivan

AU - Spence, Euan

AU - Chandler-Wilde, Simon

AU - Langdon , Stephen

PY - 2012/5

Y1 - 2012/5

N2 - In this article we describe recent progress on the design, analysis and implementationof hybrid numerical-asymptotic boundary integral methods forboundary value problems for the Helmholtz equation that model time harmonicacoustic wave scattering in domains exterior to impenetrable obstacles.These hybrid methods combine conventional piecewise polynomial approximationswith high-frequency asymptotics to build basis functions suitablefor representing the oscillatory solutions. They have the potential to solvescattering problems accurately in a computation time that is (almost) independentof frequency and this has been realized for many model problems.The design and analysis of this class of methods requires new results on theanalysis and numerical analysis of highly oscillatory boundary integral operatorsand on the high-frequency asymptotics of scattering problems. Theimplementation requires the development of appropriate quadrature rules forhighly oscillatory integrals. This article contains a historical account of thedevelopment of this currently very active field, a detailed account of recentprogress and, in addition, a number of original research results on the design,analysis and implementation of these methods.

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

UR - http://www.scopus.com/inward/record.url?scp=84861481644&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1017/S0962492912000037

U2 - 10.1017/S0962492912000037

DO - 10.1017/S0962492912000037

M3 - Article

VL - 21

SP - 89

EP - 305

JO - Acta Numerica

JF - Acta Numerica

SN - 0962-4929

ER -