Nonlinear integral equation methods for the reconstruction of an acoustically sound-soft obstacle

Olha Ivanyshyn, Tomas Johansson

Research output: Contribution to journalArticle

Abstract

The problem considered is that of determining the shape of a planar acoustically sound-soft obstacle from knowledge of the far-field pattern for one time-harmonic incident field. Two methods, which are based on the solution of a pair of integral equations representing the incoming wave and the far-field pattern, respectively, are proposed and investigated for finding the unknown boundary. Numerical resultsare included which show that the methods give accurate numerical approximations in relatively few iterations.
Original languageEnglish
Pages (from-to)289-308
Number of pages20
JournalJournal of Integral Equations and Applications
Volume19
Issue number3
DOIs
Publication statusPublished - Jan 2007

Fingerprint

Far-field Pattern
Integral Equation Method
Nonlinear Integral Equation
Integral equations
Acoustic waves
Numerical Approximation
Integral Equations
Harmonic
Iteration
Unknown
Sound
Knowledge

Bibliographical note

Copyright © 2007 Rocky Mountain Mathematics Consortium

Keywords

  • far field pattern
  • ill-posed
  • inverse scattering
  • Newton method
  • sound-soft
  • Tikhonov regularization.

Cite this

@article{83c5d7bc0901431282d3dccc21961fe8,
title = "Nonlinear integral equation methods for the reconstruction of an acoustically sound-soft obstacle",
abstract = "The problem considered is that of determining the shape of a planar acoustically sound-soft obstacle from knowledge of the far-field pattern for one time-harmonic incident field. Two methods, which are based on the solution of a pair of integral equations representing the incoming wave and the far-field pattern, respectively, are proposed and investigated for finding the unknown boundary. Numerical resultsare included which show that the methods give accurate numerical approximations in relatively few iterations.",
keywords = "far field pattern , ill-posed , inverse scattering , Newton method , sound-soft , Tikhonov regularization.",
author = "Olha Ivanyshyn and Tomas Johansson",
note = "Copyright {\circledC} 2007 Rocky Mountain Mathematics Consortium",
year = "2007",
month = "1",
doi = "10.1216/jiea/1190905488",
language = "English",
volume = "19",
pages = "289--308",
journal = "Journal of Integral Equations and Applications",
issn = "0897-3962",
publisher = "Rocky Mountain Mathematics Consortium",
number = "3",

}

Nonlinear integral equation methods for the reconstruction of an acoustically sound-soft obstacle. / Ivanyshyn, Olha; Johansson, Tomas.

In: Journal of Integral Equations and Applications, Vol. 19, No. 3, 01.2007, p. 289-308.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Nonlinear integral equation methods for the reconstruction of an acoustically sound-soft obstacle

AU - Ivanyshyn, Olha

AU - Johansson, Tomas

N1 - Copyright © 2007 Rocky Mountain Mathematics Consortium

PY - 2007/1

Y1 - 2007/1

N2 - The problem considered is that of determining the shape of a planar acoustically sound-soft obstacle from knowledge of the far-field pattern for one time-harmonic incident field. Two methods, which are based on the solution of a pair of integral equations representing the incoming wave and the far-field pattern, respectively, are proposed and investigated for finding the unknown boundary. Numerical resultsare included which show that the methods give accurate numerical approximations in relatively few iterations.

AB - The problem considered is that of determining the shape of a planar acoustically sound-soft obstacle from knowledge of the far-field pattern for one time-harmonic incident field. Two methods, which are based on the solution of a pair of integral equations representing the incoming wave and the far-field pattern, respectively, are proposed and investigated for finding the unknown boundary. Numerical resultsare included which show that the methods give accurate numerical approximations in relatively few iterations.

KW - far field pattern

KW - ill-posed

KW - inverse scattering

KW - Newton method

KW - sound-soft

KW - Tikhonov regularization.

UR - http://projecteuclid.org/euclid.jiea/1190905488

U2 - 10.1216/jiea/1190905488

DO - 10.1216/jiea/1190905488

M3 - Article

VL - 19

SP - 289

EP - 308

JO - Journal of Integral Equations and Applications

JF - Journal of Integral Equations and Applications

SN - 0897-3962

IS - 3

ER -