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Inverse scattering via nonlinear integral equations for a Neumann crack. (English) Zbl 1105.35143
Summary: We present a new method for solving the time-harmonic acoustic inverse scattering problem for a sound-hard crack in 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:
35R30Inverse problems for PDE
35J25Second order elliptic equations, boundary value problems
76Q05Hydro- and aero-acoustics
35P25Scattering theory (PDE)
45B05Fredholm integral equations
74J25Inverse problems (waves in solid mechanics)