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Zbl 1105.35143
Lee, Kuo-Ming
Inverse scattering via nonlinear integral equations for a Neumann crack. (English)
[J] Inverse Probl. 22, No. 6, 1989-2000 (2006). ISSN 0266-5611

Summary: We present a new method for solving the time-harmonic acoustic inverse scattering problem for a sound-hard crack in $\mathbb R^2$. Using the integral equation method to solve the inverse scattering problem, one obtains a Fredholm integral equation of the first kind. Instead of applying regularized Newton's method directly to this integral equation, we derive an equivalent system of two nonlinear integral equations for the inverse problem. In this setting, not only can the regularized Newton's method still be used to solve the inverse problem numerically, but also has the advantage of removing the need to solve a related direct problem at every iteration.

MSC 2000:: *35R30 Inverse problems for PDE
35J25 Second order elliptic equations, boundary value problems
76Q05 Density waves (fluid mechanics)
35P25 Scattering theory (PDE)
45B05 Fredholm integral equations
74J25 Inverse problems

Keywords: Helmholtz equation; Neumann problem; crack detection; non-destructive testing; integral equation numerical method; acoustic inverse scattering; sound-hard crack; Fredholm integral equation of the first kind

Cited in: Zbl 1153.65367

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