Geodesic
Inverse scattering via nonlinear integral equations method for a sound-soft crack with phaseless data
Applications of Mathematics, Tome 63 (2018) no. 2, pp. 149-165.

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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.
DOI : 10.21136/AM.2018.0154-17
Classification : 35J05, 35P25, 35R30, 45E05, 65R32, 78A46
Keywords: inverse scattering problem; Helmholtz equation; crack; phaseless; translation invariance 
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     title = {Inverse scattering via nonlinear integral equations method for a sound-soft crack with phaseless data},
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Gao, Peng; Dong, Heping; Ma, Fuming. Inverse scattering via nonlinear integral equations method for a sound-soft crack with phaseless data. Applications of Mathematics, Tome 63 (2018) no. 2, pp. 149-165. doi : 10.21136/AM.2018.0154-17. http://geodesic.mathdoc.fr/articles/10.21136/AM.2018.0154-17/

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