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On the identification of the flatness of a sound-hard acoustic crack. (English) Zbl 1113.35147
Summary: We present results concerning the far field pattern generated by flat and almost flat cracks in 3D and the possibility of identifying these geometrical features from direct inspection of the far field pattern. We address the direct problem using a variational formulation of the boundary integral equation to avoid the hypersingularity in the double layer potential representation. Concerning the inverse problem, some estimates presenting a direct dependence on the far field behavior and the flatness of the crack are derived. From the knowledge of the plane that defines the main directions of the crack, it is possible to get a first approximation that may be used as an initial guess for the Newton method. Numerical simulations validate the direct relation between a far field plane having almost null amplitude and the main directions of a plane that defines an almost flat crack.

MSC:
35R30 Inverse problems for PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
74J25 Inverse problems for waves in solid mechanics
74R10 Brittle fracture
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