Testing the integrity of some cavity – the Cauchy problem and the range test

The MFS for the identification of a sound-soft interior acoustic scatterer

“…The analysis was repeated by employing the PWM, but the obtained results were less accurate than the MFS ones. Moreover, comparison with the methods presented in [12,22,23] is also satisfactory.…”

“…where the vectors d n are N distinct unitary direction vectors taken to be 12) and C n ∈ C are unknown complex coefficients to be determined by imposing boundary condition (2.5) and condition (2.7). This results in the minimization of the regularized nonlinear leastsquares functional 13) subject to the simple bounds on the variables…”

“…In particular, in [23] the determination of the boundary of a sound-soft scatterer was achieved using the linear sampling method while the same method was used for the recovery of an impedance boundary in [24]. In [12], the structural integrity of a cavity was tested using the Kirsch-Kress approach applied to the analytical extension of the scattered field to the interior of the tested domain via the solution of the corresponding Cauchy problem. The boundary of the scatterer in [22] was obtained using a regularized Newton iterative approach.…”

The interior inverse scattering problem for cavities with an artificial obstacle

“…These problems occur in many industrial applications of non-destructive testing where both the sources (incident waves) and measurements (scattered waves) are inside the cavity [11,19]. As noted in [19], in some ways the interior inverse scattering problem is physically more complicated since the scattered waves are "trapped" inside the cavity.…”

“…The interior inverse scattering problems are fairly new research topics for reconstructing the shape of a cavity from the measurements taken on a curve or surface inside the cavity [10,11,[17][18][19][20][21][22][23]. These problems occur in many industrial applications of non-destructive testing where both the sources (incident waves) and measurements (scattered waves) are inside the cavity [11,19].…”