Inverse scattering via nonlinear integral equations method for a sound-soft crack with phaseless data

Peng Gao; Heping Dong; Fuming Ma

Applications of Mathematics (2018)

  • Volume: 63, Issue: 2, page 149-165
  • ISSN: 0862-7940

Abstract

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We consider the inverse scattering of time-harmonic plane waves to reconstruct the shape of a sound-soft crack from a knowledge of the given incident field and the phaseless data, and we check the invariance of far field data with respect to translation of the crack. We present a numerical method that is based on a system of nonlinear and ill-posed integral equations, and our scheme is easy and simple to implement. The numerical implementation is described and numerical examples are presented to illustrate the feasibility of the proposed method.

How to cite

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Gao, Peng, Dong, Heping, and Ma, Fuming. "Inverse scattering via nonlinear integral equations method for a sound-soft crack with phaseless data." Applications of Mathematics 63.2 (2018): 149-165. <http://eudml.org/doc/294238>.

@article{Gao2018,
abstract = {We consider the inverse scattering of time-harmonic plane waves to reconstruct the shape of a sound-soft crack from a knowledge of the given incident field and the phaseless data, and we check the invariance of far field data with respect to translation of the crack. We present a numerical method that is based on a system of nonlinear and ill-posed integral equations, and our scheme is easy and simple to implement. The numerical implementation is described and numerical examples are presented to illustrate the feasibility of the proposed method.},
author = {Gao, Peng, Dong, Heping, Ma, Fuming},
journal = {Applications of Mathematics},
keywords = {inverse scattering problem; Helmholtz equation; crack; phaseless; translation invariance},
language = {eng},
number = {2},
pages = {149-165},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Inverse scattering via nonlinear integral equations method for a sound-soft crack with phaseless data},
url = {http://eudml.org/doc/294238},
volume = {63},
year = {2018},
}

TY - JOUR
AU - Gao, Peng
AU - Dong, Heping
AU - Ma, Fuming
TI - Inverse scattering via nonlinear integral equations method for a sound-soft crack with phaseless data
JO - Applications of Mathematics
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 2
SP - 149
EP - 165
AB - We consider the inverse scattering of time-harmonic plane waves to reconstruct the shape of a sound-soft crack from a knowledge of the given incident field and the phaseless data, and we check the invariance of far field data with respect to translation of the crack. We present a numerical method that is based on a system of nonlinear and ill-posed integral equations, and our scheme is easy and simple to implement. The numerical implementation is described and numerical examples are presented to illustrate the feasibility of the proposed method.
LA - eng
KW - inverse scattering problem; Helmholtz equation; crack; phaseless; translation invariance
UR - http://eudml.org/doc/294238
ER -

References

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