The method of fundamental solutions for the identification of a scatterer with impedance boundary condition in interior inverse acoustic scattering

We employ the method of fundamental solutions (MFS) for detecting a scatterer surrounding a host acoustic homogeneous medium D due to a given point source inside it. On the boundary of the unknown scatterer (assumed to be star-shaped), allowing for the normal velocity to be proportional to the excess pressure, a Robin impedance boundary condition is considered. The coupling Robin function A may or may not be known. The additional information which is supplied in order to compensate for the lack of knowledge of the boundary partial derivative D of the interior scatterer D and/or the function lambda is given by the measurement of the scattered field (generated by the interior point source) on a curve inside D. These measurements may be contaminated with noise so their inversion requires regularization. This is enforced by minimizing a penalised least-squares functional containing various regularization parameters to be prescribed. In the MFS, the unknown scattered field u(s) is approximated with a linear combination of fundamental solutions of the Helmholtz operator with their singularities excluded from the solution domain D and this yields the discrete version of the objective functional. Physical constraints are added and the resulting constrained minimization problem is solved using the MATLAB(C) toolbox routine lsqnonlin. Numerical results are presented and discussed. (C) 2017 Elsevier Ltd. All rights reserved.