Cheng, J.; Liu, J. J.; Nakamura, G. The numerical realization of the probe method for the inverse scattering problems from the near-field data. (English) Zbl 1071.35121 Inverse Probl. 21, No. 3, 839-855 (2005). Summary: We present some results on the numerical realization of the probe method for the inverse scattering problem of determining an obstacle with impedance boundary condition from the near-field data. The keys are how to construct the Runge approximate function for the fundamental solutions and compute the indicator function for the boundary of an obstacle. We test the performance of the probe method for a 2D obstacle by taking the simulated Dirichlet-to-Neumann map as inversion input data. Cited in 9 Documents MSC: 35R30 Inverse problems for PDEs 35J25 Boundary value problems for second-order elliptic equations 76Q05 Hydro- and aero-acoustics Keywords:Helmholtz equation; optimization procedure; impedance boundary condition; Runge approximate function; Dirichlet-to-Neumann map PDFBibTeX XMLCite \textit{J. Cheng} et al., Inverse Probl. 21, No. 3, 839--855 (2005; Zbl 1071.35121) Full Text: DOI